View Full Version : Re: How important is GR in order to calc the precession of Mercury
tessel@tum.bot
Nov17-04, 10:46 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)\n\n> In the newsgroup sci.physics.relativity I started a posting with the\n> subject title. The purpose\n\nquestion?\n\n> was how do you simulate the movement of the planets, specific the\n> movement of Mercury.\n>\n> Not many people responded to my messages and as such I try in this\n> newsgroup, maybe with a better result.\n>\n> The approach I take is slightly different as maybe expected and that\n> maybe explains the low responds.\n\nYou have asked very similar questions before in various forums including\ns.a.r. and s.p.r., and on several previous occasions, I have gone to great\nlengths to help you understand what gtr says about the extraNewtonian\nprecession of Mercury (and why gtr is such a satisfactory theory for\npurposes of explaining this and a multitude of other\nobservational/experimental evidence). Unfortunately, results have been\nunsatisfactory. But for the benefit of lurkers who may have similar\nquestions, I\'ll just restate a few general and oft-repeated observations.\n\n1. Prerequisites for discussion of this topic include some elements of\nperturbation theory itself. This is an important body of\nconcepts/techniques in applied mathematics which applies to equations in\ngeneral. Once you acquire this background, you can see that similar\ntechniques are used in several places in standard textbooks on gtr:\n\n(a) locating horizons (in some parameterized family of solutions, such as\nthe Schwarzschild family, which is parameterized by a parameter m which\ncan be interpreted as the mass of the gravitating object) sometimes\ninvolves studying the location of positive real roots of univariate\npolynomials, and then it is helpful to know what happens to the roots as\nwe let a parameter (e.g. m) get small,\n\n(b) in studying geodesics in (semi)-Riemannian manifolds (as in the\nproblem at hand!), perturbation analysis of approximate solutions of a\nsuitable ODE (in this case, the Einstein-Binet equation) can be very\nhelpful,\n\n(c) metric perturbations of Lorentzian spacetimes are useful in studying\nsay a Schwarzschild hole perturbed by incoming radiation.\n\n2. In addition, of course, perturbation theory is needed to follow\nclassical work (predating gtr!) within Newtonian gravitation. Here too,\nexact solutions for multibody systems such as our Solar System are hard to\ncome by, so one attempts to find approximate solutions modeling a\nsituation "close" to a situation for which we have an exact solution (e.g.\nKeplerian motion). This is how one tries to study analytically the effect\nof the motion of Jupiter on the motions of the other planets, etc., within\nthe context of Newtonian gravity. This is needed in the problem at hand\nbecause the theoretical problem confronting Einstein in 1916 was not to\nexplain the precession of Mercury in its orbit around the Sun, but rather\nto explain a small residual remaining after a perturbation theory analysis\nof a model in Newtonian gravity had explained all but a small part of the\nobserved motion.\n\n3. A solid background in "mathematical methods", and other prerequisites\nfor manifold theory and elementary modern differential geometry are needed\nfor both gtr and Newtonian gravitation. Knowledge of Maxwell\'s theory of\nEM is also very helpful in many places, e.g. for supplying analogous\nconcepts to compare and contrast with gtr. A typical case in point: I am\nabout to mention "multipole moments", a concept which is best studied in\nNewtonian gravitation, then Maxwell\'s theory of EM, then weak-field gtr.\n\n4. Notice that in Newtonian gravitation, the field equation (Laplace\'s\nequation) is linear; nonetheless, as I said, exact solutions suitable for\nmodeling our Solar System are unavailable. This is why the nineteenth\ncentury mathematical physicists turned to perturbation analysis. In gtr,\nwe have the additional complication that the full field equation (the EFE)\nis nonlinear, but this plays no role here because we can get away with\nstudying solutions to a linearized version of the EFE.\n\n5. AE\'s analysis of the extraNewtonian precession of Mercury uses\nlinearized gtr. (Indeed, his original paper slightly precedes\nSchwarzschild\'s discovery of the first exact solution of the full field\nequations.) This is a key point because you can superimpose solutions in\na linear theory. This explains why Einstein was justified in -isolating-\nthe extra-Newtonian precession, the part which was observed but could not\nbe explained by Newtonian theory. This extra-Newtonian precession is\nquite small compared to the actual precession, which is mostly\nattributable to the perturbing influence of Jupiter\'s motion. Note that\nAE studied a single test particle (modeling Mercury) in an almost\nelliptical orbit about a weak-field Schwarzschild object (modeling the\nSun), which is what I mean by saying he "isolated the extraNewtonian\nprecession". This procedure only makes sense because of what I have just\nsaid!\n\n6. If you lack the assumed background in differential geometry, you will\nprobably find it very difficult to separate out physical/geometric\nphenomena from mere coordinate artifacts. E.g. if you follow my advice\nand compare AE\'s method in exact Schwarzschild with its weak field limit\n(of course you should get the same result!), presumably working with polar\nspherical type local coordinate charts, you might get confused by the\nvarious "radii". See the "coordinate tutorial" on Baez\'s "Relativity on\nthe World Wide Web" for some help on this kind of issue. This falls under\nthe heading of textbook authors assuming suitable "mathematical maturity".\nSimilarly, beginners might get confused by the question of justifying\ninterpretation of parameters as "mass" or whatever. This falls under the\nheading of textbook authors assuming sufficient prior experience with\nsimpler theories.\n\n7. "ExtraNewtonian" deserves a small caveat because of an issue which was\nraised in some "early modern" gtr textbooks (but which has since largely\nbeen laid to rest): if the Sun had a slightly different shape from the\nsimplest possibility, it might acquire multipole moments sufficient to\nalter some predictions from a suitable Newtonian model. Unfortunately, it\nis notoriously difficult to make direct observations of the shape of the\nSun! So we study the motion of the planets, etc., and try to deduce what\nwe can from these; basically, it turns out that the results are consistent\nwith the simplest possible shape, even though this is difficult to confirm\nby direct observation. This might seem circular, but here is one quick\nway to see that such indirect reasoning need not be unjustifiable: note\nthat the effects of a nonzero quadrupole moment scale quite differently\nfrom the extraNewtonian precession from linearized gtr which was found by\nAE. This is most easily studied by deriving the precession of a test\nparticle in almost elliptical orbit around a static axisymmetric object\nwith a finite number of nonzero multipole moments (all in weak-field gtr).\nI have carried out this exercise in great detail on previous occasions and\ndiscussed the implications of the results for the question of whether\npossible undiscovered solar oblateness could explain the observed motions\nof various systems such as our solar system.\n\n8. Perturbation analysis in Newtonian gravitation or gtr is usually\npreferable to numerical simulation where possible, precisely because\nperturbation analysis is very good at giving analytical results in a\nsituation which is "close" to a much simpler and well-understood\nsituation. Typically we get information about how various effects "scale"\nwith small values of perturbation parameters. This kind of result is easy\nto interpret and almost always gives valuable physical insight, whereas it\ncan be very difficult to extract similar insight from numerical\nsimulations. However, if you insist on doing numerical simulation, as I\ngather is the case, you need to be aware of a multitude of pitfalls which\ncan lead to -wildly misleading results- if you are not careful, even in\nNewtonian gravitation.\n\n9. If you want to conveniently compare predictions for the extraNewtonian\nprecession from various competing classical relativistic field theories of\ngravitation, there is a highly developed formalism for doing this: PPN and\nits derivatives. One important result from PPN is that in various precise\nsenses, gtr is the simplest such theory, which makes it even more striking\nthat gtr explains -all- current observational/experimental evidence (at\nleast, all the evidence everyone agrees is solid). Some competing\ntheories yield the same weak-field extraNewtonian precession formula as\ngtr, but presumably we are not interested in a theory which explains one\nmore thing than Newton did, but fails to explain say the observed "Shapiro\ntime delay" effect! This is analogous to the point I made above, at a\nlower level of structure, where assuming a suitable amount of solar\noblateness (too small to directly observe) we could perhaps after all\nexplain the motion of Mercury within Newtonian gravitation--- but then\nwe\'d have a problem with the motion of Venus, and so on.\n\n10. To set up something like PPN, you need to begin by defining some class\nof theories. Inevitably, this involves making -some- assumptions,\npossibly including "hidden" assumptions. If later on you with to remove\none of them (e.g. possibly different speeds of gravitational and EM\nradiation), you should probably begin by setting up a more general "theory\nof intertheory comparison", starting with a more general class of\ntheories.\n\nOK, \'nuff said.\n\nSuggested reading:\n\nSee a very recent post in s.p.r. where I suggested some good places to\nbegin studying perturbation theory in the sense of applied mathematics.\nSee also the gtr problem book by Press et al. for a problem on solar\noblateness versus Einstein\'s precession formula; compare their solution in\nthe back to the one I gave in the above mentioned posts to s.p.r. a few\nyears ago. Note that they directly compare a result from Newtonian theory\nto one from weak-field gtr, without comment. Again, this is entirely\njustified, but only because weak-field gtr is a linear field theory! As I\nsaid, in my solution I worked entirely in weak-field gtr to obtain both\nresults, which may help some students understand that there is no "funny\nbusiness" going on here. For numerical simulations, again the textbook by\nRichards is a good place to start on trying to understand "stability" in\ngeneral. Then one can consult specialized textbooks on numerical methods\nfor more about careful numerical integration of differential equations.\nFor PPN, see a survey paper by Clifford Will on the ArXiV.\n\n"T. Essel" (hiding somewhere in cyberspace)\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)
> In the newsgroup sci.physics.relativity I started a posting with the
> subject title. The purpose
question?
> was how do you simulate the movement of the planets, specific the
> movement of Mercury.
>
> Not many people responded to my messages and as such I try in this
> newsgroup, maybe with a better result.
>
> The approach I take is slightly different as maybe expected and that
> maybe explains the low responds.
You have asked very similar questions before in various forums including
s.a.r. and s.p.r., and on several previous occasions, I have gone to great
lengths to help you understand what gtr says about the extraNewtonian
precession of Mercury (and why gtr is such a satisfactory theory for
purposes of explaining this and a multitude of other
observational/experimental evidence). Unfortunately, results have been
unsatisfactory. But for the benefit of lurkers who may have similar
questions, I'll just restate a few general and oft-repeated observations.
1. Prerequisites for discussion of this topic include some elements of
perturbation theory itself. This is an important body of
concepts/techniques in applied mathematics which applies to equations in
general. Once you acquire this background, you can see that similar
techniques are used in several places in standard textbooks on gtr:
(a) locating horizons (in some parameterized family of solutions, such as
the Schwarzschild family, which is parameterized by a parameter m which
can be interpreted as the mass of the gravitating object) sometimes
involves studying the location of positive real roots of univariate
polynomials, and then it is helpful to know what happens to the roots as
we let a parameter (e.g. m) get small,
(b) in studying geodesics in (semi)-Riemannian manifolds (as in the
problem at hand!), perturbation analysis of approximate solutions of a
suitable ODE (in this case, the Einstein-Binet equation) can be very
helpful,
(c) metric perturbations of Lorentzian spacetimes are useful in studying
say a Schwarzschild hole perturbed by incoming radiation.
2. In addition, of course, perturbation theory is needed to follow
classical work (predating gtr!) within Newtonian gravitation. Here too,
exact solutions for multibody systems such as our Solar System are hard to
come by, so one attempts to find approximate solutions modeling a
situation "close" to a situation for which we have an exact solution (e.g.
Keplerian motion). This is how one tries to study analytically the effect
of the motion of Jupiter on the motions of the other planets, etc., within
the context of Newtonian gravity. This is needed in the problem at hand
because the theoretical problem confronting Einstein in 1916 was not to
explain the precession of Mercury in its orbit around the Sun, but rather
to explain a small residual remaining after a perturbation theory analysis
of a model in Newtonian gravity had explained all but a small part of the
observed motion.
3. A solid background in "mathematical methods", and other prerequisites
for manifold theory and elementary modern differential geometry are needed
for both gtr and Newtonian gravitation. Knowledge of Maxwell's theory of
EM is also very helpful in many places, e.g. for supplying analogous
concepts to compare and contrast with gtr. A typical case in point: I am
about to mention "multipole moments", a concept which is best studied in
Newtonian gravitation, then Maxwell's theory of EM, then weak-field gtr.
4. Notice that in Newtonian gravitation, the field equation (Laplace's
equation) is linear; nonetheless, as I said, exact solutions suitable for
modeling our Solar System are unavailable. This is why the nineteenth
century mathematical physicists turned to perturbation analysis. In gtr,
we have the additional complication that the full field equation (the EFE)
is nonlinear, but this plays no role here because we can get away with
studying solutions to a linearized version of the EFE.
5. AE's analysis of the extraNewtonian precession of Mercury uses
linearized gtr. (Indeed, his original paper slightly precedes
Schwarzschild's discovery of the first exact solution of the full field
equations.) This is a key point because you can superimpose solutions in
a linear theory. This explains why Einstein was justified in -isolating-
the extra-Newtonian precession, the part which was observed but could not
be explained by Newtonian theory. This extra-Newtonian precession is
quite small compared to the actual precession, which is mostly
attributable to the perturbing influence of Jupiter's motion. Note that
AE studied a single test particle (modeling Mercury) in an almost
elliptical orbit about a weak-field Schwarzschild object (modeling the
Sun), which is what I mean by saying he "isolated the extraNewtonian
precession". This procedure only makes sense because of what I have just
said!
6. If you lack the assumed background in differential geometry, you will
probably find it very difficult to separate out physical/geometric
phenomena from mere coordinate artifacts. E.g. if you follow my advice
and compare AE's method in exact Schwarzschild with its weak field limit
(of course you should get the same result!), presumably working with polar
spherical type local coordinate charts, you might get confused by the
various "radii". See the "coordinate tutorial" on Baez's "Relativity on
the World Wide Web" for some help on this kind of issue. This falls under
the heading of textbook authors assuming suitable "mathematical maturity".
Similarly, beginners might get confused by the question of justifying
interpretation of parameters as "mass" or whatever. This falls under the
heading of textbook authors assuming sufficient prior experience with
simpler theories.
7. "ExtraNewtonian" deserves a small caveat because of an issue which was
raised in some "early modern" gtr textbooks (but which has since largely
been laid to rest): if the Sun had a slightly different shape from the
simplest possibility, it might acquire multipole moments sufficient to
alter some predictions from a suitable Newtonian model. Unfortunately, it
is notoriously difficult to make direct observations of the shape of the
Sun! So we study the motion of the planets, etc., and try to deduce what
we can from these; basically, it turns out that the results are consistent
with the simplest possible shape, even though this is difficult to confirm
by direct observation. This might seem circular, but here is one quick
way to see that such indirect reasoning need not be unjustifiable: note
that the effects of a nonzero quadrupole moment scale quite differently
from the extraNewtonian precession from linearized gtr which was found by
AE. This is most easily studied by deriving the precession of a test
particle in almost elliptical orbit around a static axisymmetric object
with a finite number of nonzero multipole moments (all in weak-field gtr).
I have carried out this exercise in great detail on previous occasions and
discussed the implications of the results for the question of whether
possible undiscovered solar oblateness could explain the observed motions
of various systems such as our solar system.
8. Perturbation analysis in Newtonian gravitation or gtr is usually
preferable to numerical simulation where possible, precisely because
perturbation analysis is very good at giving analytical results in a
situation which is "close" to a much simpler and well-understood
situation. Typically we get information about how various effects "scale"
with small values of perturbation parameters. This kind of result is easy
to interpret and almost always gives valuable physical insight, whereas it
can be very difficult to extract similar insight from numerical
simulations. However, if you insist on doing numerical simulation, as I
gather is the case, you need to be aware of a multitude of pitfalls which
can lead to -wildly misleading results- if you are not careful, even in
Newtonian gravitation.
9. If you want to conveniently compare predictions for the extraNewtonian
precession from various competing classical relativistic field theories of
gravitation, there is a highly developed formalism for doing this: PPN and
its derivatives. One important result from PPN is that in various precise
senses, gtr is the simplest such theory, which makes it even more striking
that gtr explains -all- current observational/experimental evidence (at
least, all the evidence everyone agrees is solid). Some competing
theories yield the same weak-field extraNewtonian precession formula as
gtr, but presumably we are not interested in a theory which explains one
more thing than Newton did, but fails to explain say the observed "Shapiro
time delay" effect! This is analogous to the point I made above, at a
lower level of structure, where assuming a suitable amount of solar
oblateness (too small to directly observe) we could perhaps after all
explain the motion of Mercury within Newtonian gravitation--- but then
we'd have a problem with the motion of Venus, and so on.
10. To set up something like PPN, you need to begin by defining some class
of theories. Inevitably, this involves making -some- assumptions,
possibly including "hidden" assumptions. If later on you with to remove
one of them (e.g. possibly different speeds of gravitational and EM
radiation), you should probably begin by setting up a more general "theory
of intertheory comparison", starting with a more general class of
theories.
OK, 'nuff said.
Suggested reading:
See a very recent post in s.p.r. where I suggested some good places to
begin studying perturbation theory in the sense of applied mathematics.
See also the gtr problem book by Press et al. for a problem on solar
oblateness versus Einstein's precession formula; compare their solution in
the back to the one I gave in the above mentioned posts to s.p.r. a few
years ago. Note that they directly compare a result from Newtonian theory
to one from weak-field gtr, without comment. Again, this is entirely
justified, but only because weak-field gtr is a linear field theory! As I
said, in my solution I worked entirely in weak-field gtr to obtain both
results, which may help some students understand that there is no "funny
business" going on here. For numerical simulations, again the textbook by
Richards is a good place to start on trying to understand "stability" in
general. Then one can consult specialized textbooks on numerical methods
for more about careful numerical integration of differential equations.
For PPN, see a survey paper by Clifford Will on the ArXiV.
"T. Essel" (hiding somewhere in cyberspace)
tessel@tum.bot
Nov17-04, 11:03 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)\n\n> In the newsgroup sci.physics.relativity I started a posting with the\n> subject title. The purpose\n\nquestion?\n\n> was how do you simulate the movement of the planets, specific the\n> movement of Mercury.\n>\n> Not many people responded to my messages and as such I try in this\n> newsgroup, maybe with a better result.\n>\n> The approach I take is slightly different as maybe expected and that\n> maybe explains the low responds.\n\nYou have asked very similar questions before in various forums including\ns.a.r. and s.p.r., and on several previous occasions, I have gone to great\nlengths to help you understand what gtr says about the extraNewtonian\nprecession of Mercury (and why gtr is such a satisfactory theory for\npurposes of explaining this and a multitude of other\nobservational/experimental evidence). Unfortunately, results have been\nunsatisfactory. But for the benefit of lurkers who may have similar\nquestions, I\'ll just restate a few general and oft-repeated observations.\n\n1. Prerequisites for discussion of this topic include some elements of\nperturbation theory itself. This is an important body of\nconcepts/techniques in applied mathematics which applies to equations in\ngeneral. Once you acquire this background, you can see that similar\ntechniques are used in several places in standard textbooks on gtr:\n\n(a) locating horizons (in some parameterized family of solutions, such as\nthe Schwarzschild family, which is parameterized by a parameter m which\ncan be interpreted as the mass of the gravitating object) sometimes\ninvolves studying the location of positive real roots of univariate\npolynomials, and then it is helpful to know what happens to the roots as\nwe let a parameter (e.g. m) get small,\n\n(b) in studying geodesics in (semi)-Riemannian manifolds (as in the\nproblem at hand!), perturbation analysis of approximate solutions of a\nsuitable ODE (in this case, the Einstein-Binet equation) can be very\nhelpful,\n\n(c) metric perturbations of Lorentzian spacetimes are useful in studying\nsay a Schwarzschild hole perturbed by incoming radiation.\n\n2. In addition, of course, perturbation theory is needed to follow\nclassical work (predating gtr!) within Newtonian gravitation. Here too,\nexact solutions for multibody systems such as our Solar System are hard to\ncome by, so one attempts to find approximate solutions modeling a\nsituation "close" to a situation for which we have an exact solution (e.g.\nKeplerian motion). This is how one tries to study analytically the effect\nof the motion of Jupiter on the motions of the other planets, etc., within\nthe context of Newtonian gravity. This is needed in the problem at hand\nbecause the theoretical problem confronting Einstein in 1916 was not to\nexplain the precession of Mercury in its orbit around the Sun, but rather\nto explain a small residual remaining after a perturbation theory analysis\nof a model in Newtonian gravity had explained all but a small part of the\nobserved motion.\n\n3. A solid background in "mathematical methods", and other prerequisites\nfor manifold theory and elementary modern differential geometry are needed\nfor both gtr and Newtonian gravitation. Knowledge of Maxwell\'s theory of\nEM is also very helpful in many places, e.g. for supplying analogous\nconcepts to compare and contrast with gtr. A typical case in point: I am\nabout to mention "multipole moments", a concept which is best studied in\nNewtonian gravitation, then Maxwell\'s theory of EM, then weak-field gtr.\n\n4. Notice that in Newtonian gravitation, the field equation (Laplace\'s\nequation) is linear; nonetheless, as I said, exact solutions suitable for\nmodeling our Solar System are unavailable. This is why the nineteenth\ncentury mathematical physicists turned to perturbation analysis. In gtr,\nwe have the additional complication that the full field equation (the EFE)\nis nonlinear, but this plays no role here because we can get away with\nstudying solutions to a linearized version of the EFE.\n\n5. AE\'s analysis of the extraNewtonian precession of Mercury uses\nlinearized gtr. (Indeed, his original paper slightly precedes\nSchwarzschild\'s discovery of the first exact solution of the full field\nequations.) This is a key point because you can superimpose solutions in\na linear theory. This explains why Einstein was justified in -isolating-\nthe extra-Newtonian precession, the part which was observed but could not\nbe explained by Newtonian theory. This extra-Newtonian precession is\nquite small compared to the actual precession, which is mostly\nattributable to the perturbing influence of Jupiter\'s motion. Note that\nAE studied a single test particle (modeling Mercury) in an almost\nelliptical orbit about a weak-field Schwarzschild object (modeling the\nSun), which is what I mean by saying he "isolated the extraNewtonian\nprecession". This procedure only makes sense because of what I have just\nsaid!\n\n6. If you lack the assumed background in differential geometry, you will\nprobably find it very difficult to separate out physical/geometric\nphenomena from mere coordinate artifacts. E.g. if you follow my advice\nand compare AE\'s method in exact Schwarzschild with its weak field limit\n(of course you should get the same result!), presumably working with polar\nspherical type local coordinate charts, you might get confused by the\nvarious "radii". See the "coordinate tutorial" on Baez\'s "Relativity on\nthe World Wide Web" for some help on this kind of issue. This falls under\nthe heading of textbook authors assuming suitable "mathematical maturity".\nSimilarly, beginners might get confused by the question of justifying\ninterpretation of parameters as "mass" or whatever. This falls under the\nheading of textbook authors assuming sufficient prior experience with\nsimpler theories.\n\n7. "ExtraNewtonian" deserves a small caveat because of an issue which was\nraised in some "early modern" gtr textbooks (but which has since largely\nbeen laid to rest): if the Sun had a slightly different shape from the\nsimplest possibility, it might acquire multipole moments sufficient to\nalter some predictions from a suitable Newtonian model. Unfortunately, it\nis notoriously difficult to make direct observations of the shape of the\nSun! So we study the motion of the planets, etc., and try to deduce what\nwe can from these; basically, it turns out that the results are consistent\nwith the simplest possible shape, even though this is difficult to confirm\nby direct observation. This might seem circular, but here is one quick\nway to see that such indirect reasoning need not be unjustifiable: note\nthat the effects of a nonzero quadrupole moment scale quite differently\nfrom the extraNewtonian precession from linearized gtr which was found by\nAE. This is most easily studied by deriving the precession of a test\nparticle in almost elliptical orbit around a static axisymmetric object\nwith a finite number of nonzero multipole moments (all in weak-field gtr).\nI have carried out this exercise in great detail on previous occasions and\ndiscussed the implications of the results for the question of whether\npossible undiscovered solar oblateness could explain the observed motions\nof various systems such as our solar system.\n\n8. Perturbation analysis in Newtonian gravitation or gtr is usually\npreferable to numerical simulation where possible, precisely because\nperturbation analysis is very good at giving analytical results in a\nsituation which is "close" to a much simpler and well-understood\nsituation. Typically we get information about how various effects "scale"\nwith small values of perturbation parameters. This kind of result is easy\nto interpret and almost always gives valuable physical insight, whereas it\ncan be very difficult to extract similar insight from numerical\nsimulations. However, if you insist on doing numerical simulation, as I\ngather is the case, you need to be aware of a multitude of pitfalls which\ncan lead to -wildly misleading results- if you are not careful, even in\nNewtonian gravitation.\n\n9. If you want to conveniently compare predictions for the extraNewtonian\nprecession from various competing classical relativistic field theories of\ngravitation, there is a highly developed formalism for doing this: PPN and\nits derivatives. One important result from PPN is that in various precise\nsenses, gtr is the simplest such theory, which makes it even more striking\nthat gtr explains -all- current observational/experimental evidence (at\nleast, all the evidence everyone agrees is solid). Some competing\ntheories yield the same weak-field extraNewtonian precession formula as\ngtr, but presumably we are not interested in a theory which explains one\nmore thing than Newton did, but fails to explain say the observed "Shapiro\ntime delay" effect! This is analogous to the point I made above, at a\nlower level of structure, where assuming a suitable amount of solar\noblateness (too small to directly observe) we could perhaps after all\nexplain the motion of Mercury within Newtonian gravitation--- but then\nwe\'d have a problem with the motion of Venus, and so on.\n\n10. To set up something like PPN, you need to begin by defining some class\nof theories. Inevitably, this involves making -some- assumptions,\npossibly including "hidden" assumptions. If later on you with to remove\none of them (e.g. possibly different speeds of gravitational and EM\nradiation), you should probably begin by setting up a more general "theory\nof intertheory comparison", starting with a more general class of\ntheories.\n\nOK, \'nuff said.\n\nSuggested reading:\n\nSee a very recent post in s.p.r. where I suggested some good places to\nbegin studying perturbation theory in the sense of applied mathematics.\nSee also the gtr problem book by Press et al. for a problem on solar\noblateness versus Einstein\'s precession formula; compare their solution in\nthe back to the one I gave in the above mentioned posts to s.p.r. a few\nyears ago. Note that they directly compare a result from Newtonian theory\nto one from weak-field gtr, without comment. Again, this is entirely\njustified, but only because weak-field gtr is a linear field theory! As I\nsaid, in my solution I worked entirely in weak-field gtr to obtain both\nresults, which may help some students understand that there is no "funny\nbusiness" going on here. For numerical simulations, again the textbook by\nRichards is a good place to start on trying to understand "stability" in\ngeneral. Then one can consult specialized textbooks on numerical methods\nfor more about careful numerical integration of differential equations.\nFor PPN, see a survey paper by Clifford Will on the ArXiV.\n\n"T. Essel" (hiding somewhere in cyberspace)\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)
> In the newsgroup sci.physics.relativity I started a posting with the
> subject title. The purpose
question?
> was how do you simulate the movement of the planets, specific the
> movement of Mercury.
>
> Not many people responded to my messages and as such I try in this
> newsgroup, maybe with a better result.
>
> The approach I take is slightly different as maybe expected and that
> maybe explains the low responds.
You have asked very similar questions before in various forums including
s.a.r. and s.p.r., and on several previous occasions, I have gone to great
lengths to help you understand what gtr says about the extraNewtonian
precession of Mercury (and why gtr is such a satisfactory theory for
purposes of explaining this and a multitude of other
observational/experimental evidence). Unfortunately, results have been
unsatisfactory. But for the benefit of lurkers who may have similar
questions, I'll just restate a few general and oft-repeated observations.
1. Prerequisites for discussion of this topic include some elements of
perturbation theory itself. This is an important body of
concepts/techniques in applied mathematics which applies to equations in
general. Once you acquire this background, you can see that similar
techniques are used in several places in standard textbooks on gtr:
(a) locating horizons (in some parameterized family of solutions, such as
the Schwarzschild family, which is parameterized by a parameter m which
can be interpreted as the mass of the gravitating object) sometimes
involves studying the location of positive real roots of univariate
polynomials, and then it is helpful to know what happens to the roots as
we let a parameter (e.g. m) get small,
(b) in studying geodesics in (semi)-Riemannian manifolds (as in the
problem at hand!), perturbation analysis of approximate solutions of a
suitable ODE (in this case, the Einstein-Binet equation) can be very
helpful,
(c) metric perturbations of Lorentzian spacetimes are useful in studying
say a Schwarzschild hole perturbed by incoming radiation.
2. In addition, of course, perturbation theory is needed to follow
classical work (predating gtr!) within Newtonian gravitation. Here too,
exact solutions for multibody systems such as our Solar System are hard to
come by, so one attempts to find approximate solutions modeling a
situation "close" to a situation for which we have an exact solution (e.g.
Keplerian motion). This is how one tries to study analytically the effect
of the motion of Jupiter on the motions of the other planets, etc., within
the context of Newtonian gravity. This is needed in the problem at hand
because the theoretical problem confronting Einstein in 1916 was not to
explain the precession of Mercury in its orbit around the Sun, but rather
to explain a small residual remaining after a perturbation theory analysis
of a model in Newtonian gravity had explained all but a small part of the
observed motion.
3. A solid background in "mathematical methods", and other prerequisites
for manifold theory and elementary modern differential geometry are needed
for both gtr and Newtonian gravitation. Knowledge of Maxwell's theory of
EM is also very helpful in many places, e.g. for supplying analogous
concepts to compare and contrast with gtr. A typical case in point: I am
about to mention "multipole moments", a concept which is best studied in
Newtonian gravitation, then Maxwell's theory of EM, then weak-field gtr.
4. Notice that in Newtonian gravitation, the field equation (Laplace's
equation) is linear; nonetheless, as I said, exact solutions suitable for
modeling our Solar System are unavailable. This is why the nineteenth
century mathematical physicists turned to perturbation analysis. In gtr,
we have the additional complication that the full field equation (the EFE)
is nonlinear, but this plays no role here because we can get away with
studying solutions to a linearized version of the EFE.
5. AE's analysis of the extraNewtonian precession of Mercury uses
linearized gtr. (Indeed, his original paper slightly precedes
Schwarzschild's discovery of the first exact solution of the full field
equations.) This is a key point because you can superimpose solutions in
a linear theory. This explains why Einstein was justified in -isolating-
the extra-Newtonian precession, the part which was observed but could not
be explained by Newtonian theory. This extra-Newtonian precession is
quite small compared to the actual precession, which is mostly
attributable to the perturbing influence of Jupiter's motion. Note that
AE studied a single test particle (modeling Mercury) in an almost
elliptical orbit about a weak-field Schwarzschild object (modeling the
Sun), which is what I mean by saying he "isolated the extraNewtonian
precession". This procedure only makes sense because of what I have just
said!
6. If you lack the assumed background in differential geometry, you will
probably find it very difficult to separate out physical/geometric
phenomena from mere coordinate artifacts. E.g. if you follow my advice
and compare AE's method in exact Schwarzschild with its weak field limit
(of course you should get the same result!), presumably working with polar
spherical type local coordinate charts, you might get confused by the
various "radii". See the "coordinate tutorial" on Baez's "Relativity on
the World Wide Web" for some help on this kind of issue. This falls under
the heading of textbook authors assuming suitable "mathematical maturity".
Similarly, beginners might get confused by the question of justifying
interpretation of parameters as "mass" or whatever. This falls under the
heading of textbook authors assuming sufficient prior experience with
simpler theories.
7. "ExtraNewtonian" deserves a small caveat because of an issue which was
raised in some "early modern" gtr textbooks (but which has since largely
been laid to rest): if the Sun had a slightly different shape from the
simplest possibility, it might acquire multipole moments sufficient to
alter some predictions from a suitable Newtonian model. Unfortunately, it
is notoriously difficult to make direct observations of the shape of the
Sun! So we study the motion of the planets, etc., and try to deduce what
we can from these; basically, it turns out that the results are consistent
with the simplest possible shape, even though this is difficult to confirm
by direct observation. This might seem circular, but here is one quick
way to see that such indirect reasoning need not be unjustifiable: note
that the effects of a nonzero quadrupole moment scale quite differently
from the extraNewtonian precession from linearized gtr which was found by
AE. This is most easily studied by deriving the precession of a test
particle in almost elliptical orbit around a static axisymmetric object
with a finite number of nonzero multipole moments (all in weak-field gtr).
I have carried out this exercise in great detail on previous occasions and
discussed the implications of the results for the question of whether
possible undiscovered solar oblateness could explain the observed motions
of various systems such as our solar system.
8. Perturbation analysis in Newtonian gravitation or gtr is usually
preferable to numerical simulation where possible, precisely because
perturbation analysis is very good at giving analytical results in a
situation which is "close" to a much simpler and well-understood
situation. Typically we get information about how various effects "scale"
with small values of perturbation parameters. This kind of result is easy
to interpret and almost always gives valuable physical insight, whereas it
can be very difficult to extract similar insight from numerical
simulations. However, if you insist on doing numerical simulation, as I
gather is the case, you need to be aware of a multitude of pitfalls which
can lead to -wildly misleading results- if you are not careful, even in
Newtonian gravitation.
9. If you want to conveniently compare predictions for the extraNewtonian
precession from various competing classical relativistic field theories of
gravitation, there is a highly developed formalism for doing this: PPN and
its derivatives. One important result from PPN is that in various precise
senses, gtr is the simplest such theory, which makes it even more striking
that gtr explains -all- current observational/experimental evidence (at
least, all the evidence everyone agrees is solid). Some competing
theories yield the same weak-field extraNewtonian precession formula as
gtr, but presumably we are not interested in a theory which explains one
more thing than Newton did, but fails to explain say the observed "Shapiro
time delay" effect! This is analogous to the point I made above, at a
lower level of structure, where assuming a suitable amount of solar
oblateness (too small to directly observe) we could perhaps after all
explain the motion of Mercury within Newtonian gravitation--- but then
we'd have a problem with the motion of Venus, and so on.
10. To set up something like PPN, you need to begin by defining some class
of theories. Inevitably, this involves making -some- assumptions,
possibly including "hidden" assumptions. If later on you with to remove
one of them (e.g. possibly different speeds of gravitational and EM
radiation), you should probably begin by setting up a more general "theory
of intertheory comparison", starting with a more general class of
theories.
OK, 'nuff said.
Suggested reading:
See a very recent post in s.p.r. where I suggested some good places to
begin studying perturbation theory in the sense of applied mathematics.
See also the gtr problem book by Press et al. for a problem on solar
oblateness versus Einstein's precession formula; compare their solution in
the back to the one I gave in the above mentioned posts to s.p.r. a few
years ago. Note that they directly compare a result from Newtonian theory
to one from weak-field gtr, without comment. Again, this is entirely
justified, but only because weak-field gtr is a linear field theory! As I
said, in my solution I worked entirely in weak-field gtr to obtain both
results, which may help some students understand that there is no "funny
business" going on here. For numerical simulations, again the textbook by
Richards is a good place to start on trying to understand "stability" in
general. Then one can consult specialized textbooks on numerical methods
for more about careful numerical integration of differential equations.
For PPN, see a survey paper by Clifford Will on the ArXiV.
"T. Essel" (hiding somewhere in cyberspace)
tessel@tum.bot
Nov17-04, 11:14 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)\n\n> In the newsgroup sci.physics.relativity I started a posting with the\n> subject title. The purpose\n\nquestion?\n\n> was how do you simulate the movement of the planets, specific the\n> movement of Mercury.\n>\n> Not many people responded to my messages and as such I try in this\n> newsgroup, maybe with a better result.\n>\n> The approach I take is slightly different as maybe expected and that\n> maybe explains the low responds.\n\nYou have asked very similar questions before in various forums including\ns.a.r. and s.p.r., and on several previous occasions, I have gone to great\nlengths to help you understand what gtr says about the extraNewtonian\nprecession of Mercury (and why gtr is such a satisfactory theory for\npurposes of explaining this and a multitude of other\nobservational/experimental evidence). Unfortunately, results have been\nunsatisfactory. But for the benefit of lurkers who may have similar\nquestions, I\'ll just restate a few general and oft-repeated observations.\n\n1. Prerequisites for discussion of this topic include some elements of\nperturbation theory itself. This is an important body of\nconcepts/techniques in applied mathematics which applies to equations in\ngeneral. Once you acquire this background, you can see that similar\ntechniques are used in several places in standard textbooks on gtr:\n\n(a) locating horizons (in some parameterized family of solutions, such as\nthe Schwarzschild family, which is parameterized by a parameter m which\ncan be interpreted as the mass of the gravitating object) sometimes\ninvolves studying the location of positive real roots of univariate\npolynomials, and then it is helpful to know what happens to the roots as\nwe let a parameter (e.g. m) get small,\n\n(b) in studying geodesics in (semi)-Riemannian manifolds (as in the\nproblem at hand!), perturbation analysis of approximate solutions of a\nsuitable ODE (in this case, the Einstein-Binet equation) can be very\nhelpful,\n\n(c) metric perturbations of Lorentzian spacetimes are useful in studying\nsay a Schwarzschild hole perturbed by incoming radiation.\n\n2. In addition, of course, perturbation theory is needed to follow\nclassical work (predating gtr!) within Newtonian gravitation. Here too,\nexact solutions for multibody systems such as our Solar System are hard to\ncome by, so one attempts to find approximate solutions modeling a\nsituation "close" to a situation for which we have an exact solution (e.g.\nKeplerian motion). This is how one tries to study analytically the effect\nof the motion of Jupiter on the motions of the other planets, etc., within\nthe context of Newtonian gravity. This is needed in the problem at hand\nbecause the theoretical problem confronting Einstein in 1916 was not to\nexplain the precession of Mercury in its orbit around the Sun, but rather\nto explain a small residual remaining after a perturbation theory analysis\nof a model in Newtonian gravity had explained all but a small part of the\nobserved motion.\n\n3. A solid background in "mathematical methods", and other prerequisites\nfor manifold theory and elementary modern differential geometry are needed\nfor both gtr and Newtonian gravitation. Knowledge of Maxwell\'s theory of\nEM is also very helpful in many places, e.g. for supplying analogous\nconcepts to compare and contrast with gtr. A typical case in point: I am\nabout to mention "multipole moments", a concept which is best studied in\nNewtonian gravitation, then Maxwell\'s theory of EM, then weak-field gtr.\n\n4. Notice that in Newtonian gravitation, the field equation (Laplace\'s\nequation) is linear; nonetheless, as I said, exact solutions suitable for\nmodeling our Solar System are unavailable. This is why the nineteenth\ncentury mathematical physicists turned to perturbation analysis. In gtr,\nwe have the additional complication that the full field equation (the EFE)\nis nonlinear, but this plays no role here because we can get away with\nstudying solutions to a linearized version of the EFE.\n\n5. AE\'s analysis of the extraNewtonian precession of Mercury uses\nlinearized gtr. (Indeed, his original paper slightly precedes\nSchwarzschild\'s discovery of the first exact solution of the full field\nequations.) This is a key point because you can superimpose solutions in\na linear theory. This explains why Einstein was justified in -isolating-\nthe extra-Newtonian precession, the part which was observed but could not\nbe explained by Newtonian theory. This extra-Newtonian precession is\nquite small compared to the actual precession, which is mostly\nattributable to the perturbing influence of Jupiter\'s motion. Note that\nAE studied a single test particle (modeling Mercury) in an almost\nelliptical orbit about a weak-field Schwarzschild object (modeling the\nSun), which is what I mean by saying he "isolated the extraNewtonian\nprecession". This procedure only makes sense because of what I have just\nsaid!\n\n6. If you lack the assumed background in differential geometry, you will\nprobably find it very difficult to separate out physical/geometric\nphenomena from mere coordinate artifacts. E.g. if you follow my advice\nand compare AE\'s method in exact Schwarzschild with its weak field limit\n(of course you should get the same result!), presumably working with polar\nspherical type local coordinate charts, you might get confused by the\nvarious "radii". See the "coordinate tutorial" on Baez\'s "Relativity on\nthe World Wide Web" for some help on this kind of issue. This falls under\nthe heading of textbook authors assuming suitable "mathematical maturity".\nSimilarly, beginners might get confused by the question of justifying\ninterpretation of parameters as "mass" or whatever. This falls under the\nheading of textbook authors assuming sufficient prior experience with\nsimpler theories.\n\n7. "ExtraNewtonian" deserves a small caveat because of an issue which was\nraised in some "early modern" gtr textbooks (but which has since largely\nbeen laid to rest): if the Sun had a slightly different shape from the\nsimplest possibility, it might acquire multipole moments sufficient to\nalter some predictions from a suitable Newtonian model. Unfortunately, it\nis notoriously difficult to make direct observations of the shape of the\nSun! So we study the motion of the planets, etc., and try to deduce what\nwe can from these; basically, it turns out that the results are consistent\nwith the simplest possible shape, even though this is difficult to confirm\nby direct observation. This might seem circular, but here is one quick\nway to see that such indirect reasoning need not be unjustifiable: note\nthat the effects of a nonzero quadrupole moment scale quite differently\nfrom the extraNewtonian precession from linearized gtr which was found by\nAE. This is most easily studied by deriving the precession of a test\nparticle in almost elliptical orbit around a static axisymmetric object\nwith a finite number of nonzero multipole moments (all in weak-field gtr).\nI have carried out this exercise in great detail on previous occasions and\ndiscussed the implications of the results for the question of whether\npossible undiscovered solar oblateness could explain the observed motions\nof various systems such as our solar system.\n\n8. Perturbation analysis in Newtonian gravitation or gtr is usually\npreferable to numerical simulation where possible, precisely because\nperturbation analysis is very good at giving analytical results in a\nsituation which is "close" to a much simpler and well-understood\nsituation. Typically we get information about how various effects "scale"\nwith small values of perturbation parameters. This kind of result is easy\nto interpret and almost always gives valuable physical insight, whereas it\ncan be very difficult to extract similar insight from numerical\nsimulations. However, if you insist on doing numerical simulation, as I\ngather is the case, you need to be aware of a multitude of pitfalls which\ncan lead to -wildly misleading results- if you are not careful, even in\nNewtonian gravitation.\n\n9. If you want to conveniently compare predictions for the extraNewtonian\nprecession from various competing classical relativistic field theories of\ngravitation, there is a highly developed formalism for doing this: PPN and\nits derivatives. One important result from PPN is that in various precise\nsenses, gtr is the simplest such theory, which makes it even more striking\nthat gtr explains -all- current observational/experimental evidence (at\nleast, all the evidence everyone agrees is solid). Some competing\ntheories yield the same weak-field extraNewtonian precession formula as\ngtr, but presumably we are not interested in a theory which explains one\nmore thing than Newton did, but fails to explain say the observed "Shapiro\ntime delay" effect! This is analogous to the point I made above, at a\nlower level of structure, where assuming a suitable amount of solar\noblateness (too small to directly observe) we could perhaps after all\nexplain the motion of Mercury within Newtonian gravitation--- but then\nwe\'d have a problem with the motion of Venus, and so on.\n\n10. To set up something like PPN, you need to begin by defining some class\nof theories. Inevitably, this involves making -some- assumptions,\npossibly including "hidden" assumptions. If later on you with to remove\none of them (e.g. possibly different speeds of gravitational and EM\nradiation), you should probably begin by setting up a more general "theory\nof intertheory comparison", starting with a more general class of\ntheories.\n\nOK, \'nuff said.\n\nSuggested reading:\n\nSee a very recent post in s.p.r. where I suggested some good places to\nbegin studying perturbation theory in the sense of applied mathematics.\nSee also the gtr problem book by Press et al. for a problem on solar\noblateness versus Einstein\'s precession formula; compare their solution in\nthe back to the one I gave in the above mentioned posts to s.p.r. a few\nyears ago. Note that they directly compare a result from Newtonian theory\nto one from weak-field gtr, without comment. Again, this is entirely\njustified, but only because weak-field gtr is a linear field theory! As I\nsaid, in my solution I worked entirely in weak-field gtr to obtain both\nresults, which may help some students understand that there is no "funny\nbusiness" going on here. For numerical simulations, again the textbook by\nRichards is a good place to start on trying to understand "stability" in\ngeneral. Then one can consult specialized textbooks on numerical methods\nfor more about careful numerical integration of differential equations.\nFor PPN, see a survey paper by Clifford Will on the ArXiV.\n\n"T. Essel" (hiding somewhere in cyberspace)\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)
> In the newsgroup sci.physics.relativity I started a posting with the
> subject title. The purpose
question?
> was how do you simulate the movement of the planets, specific the
> movement of Mercury.
>
> Not many people responded to my messages and as such I try in this
> newsgroup, maybe with a better result.
>
> The approach I take is slightly different as maybe expected and that
> maybe explains the low responds.
You have asked very similar questions before in various forums including
s.a.r. and s.p.r., and on several previous occasions, I have gone to great
lengths to help you understand what gtr says about the extraNewtonian
precession of Mercury (and why gtr is such a satisfactory theory for
purposes of explaining this and a multitude of other
observational/experimental evidence). Unfortunately, results have been
unsatisfactory. But for the benefit of lurkers who may have similar
questions, I'll just restate a few general and oft-repeated observations.
1. Prerequisites for discussion of this topic include some elements of
perturbation theory itself. This is an important body of
concepts/techniques in applied mathematics which applies to equations in
general. Once you acquire this background, you can see that similar
techniques are used in several places in standard textbooks on gtr:
(a) locating horizons (in some parameterized family of solutions, such as
the Schwarzschild family, which is parameterized by a parameter m which
can be interpreted as the mass of the gravitating object) sometimes
involves studying the location of positive real roots of univariate
polynomials, and then it is helpful to know what happens to the roots as
we let a parameter (e.g. m) get small,
(b) in studying geodesics in (semi)-Riemannian manifolds (as in the
problem at hand!), perturbation analysis of approximate solutions of a
suitable ODE (in this case, the Einstein-Binet equation) can be very
helpful,
(c) metric perturbations of Lorentzian spacetimes are useful in studying
say a Schwarzschild hole perturbed by incoming radiation.
2. In addition, of course, perturbation theory is needed to follow
classical work (predating gtr!) within Newtonian gravitation. Here too,
exact solutions for multibody systems such as our Solar System are hard to
come by, so one attempts to find approximate solutions modeling a
situation "close" to a situation for which we have an exact solution (e.g.
Keplerian motion). This is how one tries to study analytically the effect
of the motion of Jupiter on the motions of the other planets, etc., within
the context of Newtonian gravity. This is needed in the problem at hand
because the theoretical problem confronting Einstein in 1916 was not to
explain the precession of Mercury in its orbit around the Sun, but rather
to explain a small residual remaining after a perturbation theory analysis
of a model in Newtonian gravity had explained all but a small part of the
observed motion.
3. A solid background in "mathematical methods", and other prerequisites
for manifold theory and elementary modern differential geometry are needed
for both gtr and Newtonian gravitation. Knowledge of Maxwell's theory of
EM is also very helpful in many places, e.g. for supplying analogous
concepts to compare and contrast with gtr. A typical case in point: I am
about to mention "multipole moments", a concept which is best studied in
Newtonian gravitation, then Maxwell's theory of EM, then weak-field gtr.
4. Notice that in Newtonian gravitation, the field equation (Laplace's
equation) is linear; nonetheless, as I said, exact solutions suitable for
modeling our Solar System are unavailable. This is why the nineteenth
century mathematical physicists turned to perturbation analysis. In gtr,
we have the additional complication that the full field equation (the EFE)
is nonlinear, but this plays no role here because we can get away with
studying solutions to a linearized version of the EFE.
5. AE's analysis of the extraNewtonian precession of Mercury uses
linearized gtr. (Indeed, his original paper slightly precedes
Schwarzschild's discovery of the first exact solution of the full field
equations.) This is a key point because you can superimpose solutions in
a linear theory. This explains why Einstein was justified in -isolating-
the extra-Newtonian precession, the part which was observed but could not
be explained by Newtonian theory. This extra-Newtonian precession is
quite small compared to the actual precession, which is mostly
attributable to the perturbing influence of Jupiter's motion. Note that
AE studied a single test particle (modeling Mercury) in an almost
elliptical orbit about a weak-field Schwarzschild object (modeling the
Sun), which is what I mean by saying he "isolated the extraNewtonian
precession". This procedure only makes sense because of what I have just
said!
6. If you lack the assumed background in differential geometry, you will
probably find it very difficult to separate out physical/geometric
phenomena from mere coordinate artifacts. E.g. if you follow my advice
and compare AE's method in exact Schwarzschild with its weak field limit
(of course you should get the same result!), presumably working with polar
spherical type local coordinate charts, you might get confused by the
various "radii". See the "coordinate tutorial" on Baez's "Relativity on
the World Wide Web" for some help on this kind of issue. This falls under
the heading of textbook authors assuming suitable "mathematical maturity".
Similarly, beginners might get confused by the question of justifying
interpretation of parameters as "mass" or whatever. This falls under the
heading of textbook authors assuming sufficient prior experience with
simpler theories.
7. "ExtraNewtonian" deserves a small caveat because of an issue which was
raised in some "early modern" gtr textbooks (but which has since largely
been laid to rest): if the Sun had a slightly different shape from the
simplest possibility, it might acquire multipole moments sufficient to
alter some predictions from a suitable Newtonian model. Unfortunately, it
is notoriously difficult to make direct observations of the shape of the
Sun! So we study the motion of the planets, etc., and try to deduce what
we can from these; basically, it turns out that the results are consistent
with the simplest possible shape, even though this is difficult to confirm
by direct observation. This might seem circular, but here is one quick
way to see that such indirect reasoning need not be unjustifiable: note
that the effects of a nonzero quadrupole moment scale quite differently
from the extraNewtonian precession from linearized gtr which was found by
AE. This is most easily studied by deriving the precession of a test
particle in almost elliptical orbit around a static axisymmetric object
with a finite number of nonzero multipole moments (all in weak-field gtr).
I have carried out this exercise in great detail on previous occasions and
discussed the implications of the results for the question of whether
possible undiscovered solar oblateness could explain the observed motions
of various systems such as our solar system.
8. Perturbation analysis in Newtonian gravitation or gtr is usually
preferable to numerical simulation where possible, precisely because
perturbation analysis is very good at giving analytical results in a
situation which is "close" to a much simpler and well-understood
situation. Typically we get information about how various effects "scale"
with small values of perturbation parameters. This kind of result is easy
to interpret and almost always gives valuable physical insight, whereas it
can be very difficult to extract similar insight from numerical
simulations. However, if you insist on doing numerical simulation, as I
gather is the case, you need to be aware of a multitude of pitfalls which
can lead to -wildly misleading results- if you are not careful, even in
Newtonian gravitation.
9. If you want to conveniently compare predictions for the extraNewtonian
precession from various competing classical relativistic field theories of
gravitation, there is a highly developed formalism for doing this: PPN and
its derivatives. One important result from PPN is that in various precise
senses, gtr is the simplest such theory, which makes it even more striking
that gtr explains -all- current observational/experimental evidence (at
least, all the evidence everyone agrees is solid). Some competing
theories yield the same weak-field extraNewtonian precession formula as
gtr, but presumably we are not interested in a theory which explains one
more thing than Newton did, but fails to explain say the observed "Shapiro
time delay" effect! This is analogous to the point I made above, at a
lower level of structure, where assuming a suitable amount of solar
oblateness (too small to directly observe) we could perhaps after all
explain the motion of Mercury within Newtonian gravitation--- but then
we'd have a problem with the motion of Venus, and so on.
10. To set up something like PPN, you need to begin by defining some class
of theories. Inevitably, this involves making -some- assumptions,
possibly including "hidden" assumptions. If later on you with to remove
one of them (e.g. possibly different speeds of gravitational and EM
radiation), you should probably begin by setting up a more general "theory
of intertheory comparison", starting with a more general class of
theories.
OK, 'nuff said.
Suggested reading:
See a very recent post in s.p.r. where I suggested some good places to
begin studying perturbation theory in the sense of applied mathematics.
See also the gtr problem book by Press et al. for a problem on solar
oblateness versus Einstein's precession formula; compare their solution in
the back to the one I gave in the above mentioned posts to s.p.r. a few
years ago. Note that they directly compare a result from Newtonian theory
to one from weak-field gtr, without comment. Again, this is entirely
justified, but only because weak-field gtr is a linear field theory! As I
said, in my solution I worked entirely in weak-field gtr to obtain both
results, which may help some students understand that there is no "funny
business" going on here. For numerical simulations, again the textbook by
Richards is a good place to start on trying to understand "stability" in
general. Then one can consult specialized textbooks on numerical methods
for more about careful numerical integration of differential equations.
For PPN, see a survey paper by Clifford Will on the ArXiV.
"T. Essel" (hiding somewhere in cyberspace)
greywolf42
Nov19-04, 01:30 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE><tessel@tum.bot> wrote in message\nnews:cncfni\\$t38\\$1@lfa222122.richmond. edu...\n> On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)\n>\n> > In the newsgroup sci.physics.relativity I started a posting with the\n> > subject title. The purpose was how do you simulate the movement\n> > of the planets, specific the movement of Mercury.\n> >\n> > Not many people responded to my messages and as such I try in this\n> > newsgroup, maybe with a better result.\n> >\n> > The approach I take is slightly different as maybe expected and that\n> > maybe explains the low responds.\n>\n> You have asked very similar questions before in various forums including\n> s.a.r. and s.p.r., and on several previous occasions, I have gone to great\n> lengths to help you understand what gtr says about the extraNewtonian\n> precession of Mercury (and why gtr is such a satisfactory theory for\n> purposes of explaining this and a multitude of other\n> observational/experimental evidence).\n\nIt would be polite to provide a link to said statements. A google search of\nyour posts shows no matches against "Nicolaas Vroom". In fact, there is\nonly one post against your name (to Bill Kavanah), that contains the word\n"mercury" or the phrase "perturbation theory":\nhttp://www.google.com/groups?selm=cmq3is%24a2m%241%40lfa222122.richmond. edu\nAnd in this post, you again make unreferenced statements that you\'ve "posted\non this (perturbation theory) very extensively before."\n\n> Unfortunately, results have been unsatisfactory.\n\nFor whom?\n\n> But for the benefit of lurkers who may have similar\n> questions, I\'ll just restate a few general and oft-repeated observations.\n\nMere repetition is not a hallmark of either veracity or correctness.\n\n> 1. Prerequisites for discussion of this topic include some elements of\n> perturbation theory itself. This is an important body of\n> concepts/techniques in applied mathematics which applies to equations in\n> general. Once you acquire this background, you can see that similar\n> techniques are used in several places in standard textbooks on gtr:\n\nThis is true, but irrelevant to the question asked. Which was not about how\nto manipulate the details of perturbation theory, but about the physical\ncalculation of the NNPA of Mercury.\n\n{snip a bit of irrelevant detail}\n\n> 2. In addition, of course, perturbation theory is needed to follow\n> classical work (predating gtr!) within Newtonian gravitation. Here too,\n> exact solutions for multibody systems such as our Solar System are hard to\n> come by, so one attempts to find approximate solutions modeling a\n> situation "close" to a situation for which we have an exact solution (e.g.\n> Keplerian motion). This is how one tries to study analytically the effect\n> of the motion of Jupiter on the motions of the other planets, etc., within\n> the context of Newtonian gravity. This is needed in the problem at hand\n> because the theoretical problem confronting Einstein in 1916 was not to\n> explain the precession of Mercury in its orbit around the Sun, but rather\n> to explain a small residual remaining after a perturbation theory analysis\n> of a model in Newtonian gravity had explained all but a small part of the\n> observed motion.\n\nOn the contrary. The explicit, stated purpose of Einstein was to obtain\nNewcomb\'s published value (43" per century*) for the NNPA of Mercury.\nEinstein\'s primary theoretical effort (the Entwurf version of 1913) only\nresulted in a value of about 17" per century. Einstein considered this a\n"problem", and fiddled with things until he could reproduce Newcomb\'s value.\nEinstein\'s partner (Grossmann) on the other hand, remeasured the NNPA of\nMercury ... and got 18 to 28" per century**.\n\n*In order to get this value, Newcomb assumed that Mercury\'s eccentricity\nvaried during each orbit (his value was for an ephemerides, not an attempt\nto prove physical theory). Einstein\'s value does not include variations in\nMercury\'s eccentricity.\n\n** Using non-varying eccentricity.\n\n> 3. A solid background in "mathematical methods", and other prerequisites\n> for manifold theory and elementary modern differential geometry are needed\n> for both gtr and Newtonian gravitation. Knowledge of Maxwell\'s theory of\n> EM is also very helpful in many places, e.g. for supplying analogous\n> concepts to compare and contrast with gtr. A typical case in point: I am\n> about to mention "multipole moments", a concept which is best studied in\n> Newtonian gravitation, then Maxwell\'s theory of EM, then weak-field gtr.\n\nAnd totally irrelevant to the question asked.\n\n> 4. Notice that in Newtonian gravitation, the field equation (Laplace\'s\n> equation) is linear; nonetheless, as I said, exact solutions suitable for\n> modeling our Solar System are unavailable. This is why the nineteenth\n> century mathematical physicists turned to perturbation analysis. In gtr,\n> we have the additional complication that the full field equation (the EFE)\n> is nonlinear, but this plays no role here because we can get away with\n> studying solutions to a linearized version of the EFE.\n\nWhich is simply the Newtonian equation, with an added speed-of-gravity\nparameter (equal to the speed of light). One doesn\'t need "GR" for this\none. Paul Gerber did this 17 years before Einstein\'s GR.\n\n> 5. AE\'s analysis of the extraNewtonian precession of Mercury uses\n> linearized gtr. (Indeed, his original paper slightly precedes\n> Schwarzschild\'s discovery of the first exact solution of the full field\n> equations.) This is a key point because you can superimpose solutions in\n> a linear theory. This explains why Einstein was justified in -isolating-\n> the extra-Newtonian precession, the part which was observed but could not\n> be explained by Newtonian theory. This extra-Newtonian precession is\n> quite small compared to the actual precession, which is mostly\n> attributable to the perturbing influence of Jupiter\'s motion. Note that\n> AE studied a single test particle (modeling Mercury) in an almost\n> elliptical orbit about a weak-field Schwarzschild object (modeling the\n> Sun), which is what I mean by saying he "isolated the extraNewtonian\n> precession". This procedure only makes sense because of what I have just\n> said!\n\nIt makes sense simply because a finite propagation speed leads to\nprecession. Whereas assuming an infinite speed avoids precession in a 1/r^2\nforce equation.\n\n> 6. If you lack the assumed background in differential geometry, you will\n> probably find it very difficult to separate out physical/geometric\n> phenomena from mere coordinate artifacts.\n\nActually, it is simple to separate out physical phenomena that apply\nto the NNPA. Simply look at the equation that results either from GR, the\nEinstein/Grossmann "Entwurf" GR, or from any other theory with finite\ngravity speed:\n\nK pi^3\ndelta theta = -------------------------------\n(v_g)^2 a (1 - e^2)\n\nWhether using Gerber or GR, there are only three parameters needed to\ndetermine perihelion shift: semimajor axis of the planet\'s orbit (a),\neccentricity of the planet\'s orbit (e), and the speed of propagation of\ngravity. (v_g = c in GR)\nhttp://www.google.com/groups?selm=vr2941i226t8a5%40corp.supernews.com\n\ nFor GR or Gerber\'s Newtonian, the constant, K is equal to 24. For Entwurf\nGR, or standard delayed-Newtonian the constant, K, is equal to 8.\n\nYour details on the mechanics of how to make the calculation only covers how\nthe value of the constant, K, is determined. Which is not trivial,\ncertainly. But it doesn\'t address the question that was asked.\n\n{snip more irrelevant detail}\n\n> 7. "ExtraNewtonian" deserves a small caveat because of an issue which was\n> raised in some "early modern" gtr textbooks (but which has since largely\n> been laid to rest): if the Sun had a slightly different shape from the\n> simplest possibility, it might acquire multipole moments sufficient to\n> alter some predictions from a suitable Newtonian model. Unfortunately, it\n> is notoriously difficult to make direct observations of the shape of the\n> Sun!\n\nIt is straightforward, and has been done many times over the years.\nUnfortunately for GR, the directly-measured shape of the Sun is slightly\noblate ... which gives rise to between 5 to 15 seconds of arc of the "43"\nunaccounted NNPA (depending on who does the measuring).\n\n> So we study the motion of the planets, etc., and try to deduce what\n> we can from these; basically, it turns out that the results are consistent\n> with the simplest possible shape,\n\nThis is simply called ignoring the problem.\n\n> even though this is difficult to confirm\n> by direct observation. This might seem circular,\n\nIt is. Thanks for at least being honest. :)\n\n> but here is one quick\n> way to see that such indirect reasoning need not be unjustifiable: note\n> that the effects of a nonzero quadrupole moment scale quite differently\n> from the extraNewtonian precession from linearized gtr which was found by\n> AE. This is most easily studied by deriving the precession of a test\n> particle in almost elliptical orbit around a static axisymmetric object\n> with a finite number of nonzero multipole moments (all in weak-field gtr).\n> I have carried out this exercise in great detail on previous occasions and\n> discussed the implications of the results for the question of whether\n> possible undiscovered solar oblateness could explain the observed motions\n> of various systems such as our solar system.\n\nHowever, such gedanken exercises still don\'t give us any information on the\nreal solar system.\n\n{snip repetition 8, 9, and 10 of irrelevant detail}\n\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for e-mail}\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky><tessel@tum.bot> wrote in message
news:cncfni$t38$1@lfa222122.richmond.edu...
> On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)
>
> > In the newsgroup sci.physics.relativity I started a posting with the
> > subject title. The purpose was how do you simulate the movement
> > of the planets, specific the movement of Mercury.
> >
> > Not many people responded to my messages and as such I try in this
> > newsgroup, maybe with a better result.
> >
> > The approach I take is slightly different as maybe expected and that
> > maybe explains the low responds.
>
> You have asked very similar questions before in various forums including
> s.a.r. and s.p.r., and on several previous occasions, I have gone to great
> lengths to help you understand what gtr says about the extraNewtonian
> precession of Mercury (and why gtr is such a satisfactory theory for
> purposes of explaining this and a multitude of other
> observational/experimental evidence).
It would be polite to provide a link to said statements. A google search of
your posts shows no matches against "Nicolaas Vroom". In fact, there is
only one post against your name (to Bill Kavanah), that contains the word
"mercury" or the phrase "perturbation theory":
http://www.google.com/groups?selm=cmq3is%24a2m%241%40lfa222122.richmond. edu
And in this post, you again make unreferenced statements that you've "posted
on this (perturbation theory) very extensively before."
> Unfortunately, results have been unsatisfactory.
For whom?
> But for the benefit of lurkers who may have similar
> questions, I'll just restate a few general and oft-repeated observations.
Mere repetition is not a hallmark of either veracity or correctness.
> 1. Prerequisites for discussion of this topic include some elements of
> perturbation theory itself. This is an important body of
> concepts/techniques in applied mathematics which applies to equations in
> general. Once you acquire this background, you can see that similar
> techniques are used in several places in standard textbooks on gtr:
This is true, but irrelevant to the question asked. Which was not about how
to manipulate the details of perturbation theory, but about the physical
calculation of the NNPA of Mercury.
{snip a bit of irrelevant detail}
> 2. In addition, of course, perturbation theory is needed to follow
> classical work (predating gtr!) within Newtonian gravitation. Here too,
> exact solutions for multibody systems such as our Solar System are hard to
> come by, so one attempts to find approximate solutions modeling a
> situation "close" to a situation for which we have an exact solution (e.g.
> Keplerian motion). This is how one tries to study analytically the effect
> of the motion of Jupiter on the motions of the other planets, etc., within
> the context of Newtonian gravity. This is needed in the problem at hand
> because the theoretical problem confronting Einstein in 1916 was not to
> explain the precession of Mercury in its orbit around the Sun, but rather
> to explain a small residual remaining after a perturbation theory analysis
> of a model in Newtonian gravity had explained all but a small part of the
> observed motion.
On the contrary. The explicit, stated purpose of Einstein was to obtain
Newcomb's published value (43" per century*) for the NNPA of Mercury.
Einstein's primary theoretical effort (the Entwurf version of 1913) only
resulted in a value of about 17" per century. Einstein considered this a
"problem", and fiddled with things until he could reproduce Newcomb's value.
Einstein's partner (Grossmann) on the other hand, remeasured the NNPA of
Mercury ... and got 18 to 28" per century**.
*In order to get this value, Newcomb assumed that Mercury's eccentricity
varied during each orbit (his value was for an ephemerides, not an attempt
to prove physical theory). Einstein's value does not include variations in
Mercury's eccentricity.
** Using non-varying eccentricity.
> 3. A solid background in "mathematical methods", and other prerequisites
> for manifold theory and elementary modern differential geometry are needed
> for both gtr and Newtonian gravitation. Knowledge of Maxwell's theory of
> EM is also very helpful in many places, e.g. for supplying analogous
> concepts to compare and contrast with gtr. A typical case in point: I am
> about to mention "multipole moments", a concept which is best studied in
> Newtonian gravitation, then Maxwell's theory of EM, then weak-field gtr.
And totally irrelevant to the question asked.
> 4. Notice that in Newtonian gravitation, the field equation (Laplace's
> equation) is linear; nonetheless, as I said, exact solutions suitable for
> modeling our Solar System are unavailable. This is why the nineteenth
> century mathematical physicists turned to perturbation analysis. In gtr,
> we have the additional complication that the full field equation (the EFE)
> is nonlinear, but this plays no role here because we can get away with
> studying solutions to a linearized version of the EFE.
Which is simply the Newtonian equation, with an added speed-of-gravity
parameter (equal to the speed of light). One doesn't need "GR" for this
one. Paul Gerber did this 17 years before Einstein's GR.
> 5. AE's analysis of the extraNewtonian precession of Mercury uses
> linearized gtr. (Indeed, his original paper slightly precedes
> Schwarzschild's discovery of the first exact solution of the full field
> equations.) This is a key point because you can superimpose solutions in
> a linear theory. This explains why Einstein was justified in -isolating-
> the extra-Newtonian precession, the part which was observed but could not
> be explained by Newtonian theory. This extra-Newtonian precession is
> quite small compared to the actual precession, which is mostly
> attributable to the perturbing influence of Jupiter's motion. Note that
> AE studied a single test particle (modeling Mercury) in an almost
> elliptical orbit about a weak-field Schwarzschild object (modeling the
> Sun), which is what I mean by saying he "isolated the extraNewtonian
> precession". This procedure only makes sense because of what I have just
> said!
It makes sense simply because a finite propagation speed leads to
precession. Whereas assuming an infinite speed avoids precession in a 1/r^2
force equation.
> 6. If you lack the assumed background in differential geometry, you will
> probably find it very difficult to separate out physical/geometric
> phenomena from mere coordinate artifacts.
Actually, it is simple to separate out physical phenomena that apply
to the NNPA. Simply look at the equation that results either from GR, the
Einstein/Grossmann "Entwurf" GR, or from any other theory with finite
gravity speed:
K \pi^3\delta \theta =[/itex] -------------------------------
[itex](v_g)^2 a (1 - e^2)
Whether using Gerber or GR, there are only three parameters needed to
determine perihelion shift: semimajor axis of the planet's orbit (a),
eccentricity of the planet's orbit (e), and the speed of propagation of
gravity. (v_g = c in GR)
http://www.google.com/groups?selm=vr2941i226t8a5%40corp.supernews.com
For GR or Gerber's Newtonian, the constant, K is equal to 24. For Entwurf
GR, or standard delayed-Newtonian the constant, K, is equal to 8.
Your details on the mechanics of how to make the calculation only covers how
the value of the constant, K, is determined. Which is not trivial,
certainly. But it doesn't address the question that was asked.
{snip more irrelevant detail}
> 7. "ExtraNewtonian" deserves a small caveat because of an issue which was
> raised in some "early modern" gtr textbooks (but which has since largely
> been laid to rest): if the Sun had a slightly different shape from the
> simplest possibility, it might acquire multipole moments sufficient to
> alter some predictions from a suitable Newtonian model. Unfortunately, it
> is notoriously difficult to make direct observations of the shape of the
> Sun!
It is straightforward, and has been done many times over the years.
Unfortunately for GR, the directly-measured shape of the Sun is slightly
oblate ... which gives rise to between 5 to 15 seconds of arc of the "43"
unaccounted NNPA (depending on who does the measuring).
> So we study the motion of the planets, etc., and try to deduce what
> we can from these; basically, it turns out that the results are consistent
> with the simplest possible shape,
This is simply called ignoring the problem.
> even though this is difficult to confirm
> by direct observation. This might seem circular,
It is. Thanks for at least being honest. :)
> but here is one quick
> way to see that such indirect reasoning need not be unjustifiable: note
> that the effects of a nonzero quadrupole moment scale quite differently
> from the extraNewtonian precession from linearized gtr which was found by
> AE. This is most easily studied by deriving the precession of a test
> particle in almost elliptical orbit around a static axisymmetric object
> with a finite number of nonzero multipole moments (all in weak-field gtr).
> I have carried out this exercise in great detail on previous occasions and
> discussed the implications of the results for the question of whether
> possible undiscovered solar oblateness could explain the observed motions
> of various systems such as our solar system.
However, such gedanken exercises still don't give us any information on the
real solar system.
{snip repetition 8, 9, and 10 of irrelevant detail}
--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}
Nicolaas Vroom
Nov19-04, 01:31 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE><tessel@tum.bot> schreef in bericht\nnews:cncfni\\$t38\\$1@lfa222122.richmond. edu...\n> On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)\n>\n> > In the newsgroup sci.physics.relativity I started a posting with the\n> > subject title. The purpose\n>\n> question?\n>\n> > was how do you simulate the movement of the planets, specific the\n> > movement of Mercury.\n> >\n>\n> You have asked very similar questions before in various forums including\n> s.a.r. and s.p.r., and on several previous occasions, I have gone to great\n> lengths to help you understand what gtr says about the extraNewtonian\n> precession of Mercury (and why gtr is such a satisfactory theory for\n> purposes of explaining this and a multitude of other\n> observational/experimental evidence).\n\nI\'am not aware of those discussions with you but anyway thanks for\nall the detailed information regarding perturbation theory.\n\n> Unfortunately, results have been\n> unsatisfactory. But for the benefit of lurkers who may have similar\n> questions, I\'ll just restate a few general and oft-repeated observations.\n>\n> 1. Prerequisites for discussion of this topic include some elements of\n> perturbation theory itself.\n\n<SNIP>\n\nIn order to get some idea about about perturbation theory and astronomy\nI studied the following document:\n" Large-Scale Structure of the Universe and\nCosmological Perturbation Theory"\nhttp://xxx.lanl.gov/abs/astro-ph/?0112551\n\nMy previous experience with perturbation theory was\nrelated to process control.\n\nMaybe perturbation theory is the final tool that I need in order\nto solve the equations that describe the movements of the stars\nand planets (in a very acurate way ?) but first I need an answer\non a couple of questions:\n\n1) Does it make sense to transform human based observations into\ngrid based positions ?\n2) Does it make sense to remove light bending as part of those\ntransformations ?\n3) If those transformations make sense i.e. have an advantage above\nother methods then:\n4) What is the function of c within this grid or frame ?\n5) What is the function of cg within this frame ?\n6) Do I have to consider SR within this frame ?\n7) Do I need the full complexity of GR to describe the movement\nof the stars (and planets) ?\n\nIMO the answer on that question is NO because there are no\nmoving clocks involved.\n\nNicolaas Vroom\nhttp://user.pandora.be/nicvroom/\n\n\n\n> Suggested reading:\n>\n> See a very recent post in s.p.r. where I suggested some good places to\n> begin studying perturbation theory in the sense of applied mathematics.\n> See also the gtr problem book by Press et al. for a problem on solar\n> oblateness versus Einstein\'s precession formula; compare their solution in\n> the back to the one I gave in the above mentioned posts to s.p.r. a few\n> years ago. Note that they directly compare a result from Newtonian theory\n> to one from weak-field gtr, without comment. Again, this is entirely\n> justified, but only because weak-field gtr is a linear field theory! As I\n> said, in my solution I worked entirely in weak-field gtr to obtain both\n> results, which may help some students understand that there is no "funny\n> business" going on here. For numerical simulations, again the textbook by\n> Richards is a good place to start on trying to understand "stability" in\n> general. Then one can consult specialized textbooks on numerical methods\n> for more about careful numerical integration of differential equations.\n> For PPN, see a survey paper by Clifford Will on the ArXiV.\n>\n> "T. Essel" (hiding somewhere in cyberspace)\n>\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky><tessel@tum.bot> schreef in bericht
news:cncfni$t38$1@lfa222122.richmond.edu...
> On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)
>
> > In the newsgroup sci.physics.relativity I started a posting with the
> > subject title. The purpose
>
> question?
>
> > was how do you simulate the movement of the planets, specific the
> > movement of Mercury.
> >
>
> You have asked very similar questions before in various forums including
> s.a.r. and s.p.r., and on several previous occasions, I have gone to great
> lengths to help you understand what gtr says about the extraNewtonian
> precession of Mercury (and why gtr is such a satisfactory theory for
> purposes of explaining this and a multitude of other
> observational/experimental evidence).
I'am not aware of those discussions with you but anyway thanks for
all the detailed information regarding perturbation theory.
> Unfortunately, results have been
> unsatisfactory. But for the benefit of lurkers who may have similar
> questions, I'll just restate a few general and oft-repeated observations.
>
> 1. Prerequisites for discussion of this topic include some elements of
> perturbation theory itself.
<SNIP>
In order to get some idea about about perturbation theory and astronomy
I studied the following document:
" Large-Scale Structure of the Universe and
Cosmological Perturbation Theory"
http://xxx.lanl.gov/abs/astro-ph/?0112551
My previous experience with perturbation theory was
related to process control.
Maybe perturbation theory is the final tool that I need in order
to solve the equations that describe the movements of the stars
and planets (in a very acurate way ?) but first I need an answer
on a couple of questions:
1) Does it make sense to transform human based observations into
grid based positions ?
2) Does it make sense to remove light bending as part of those
transformations ?
3) If those transformations make sense i.e. have an advantage above
other methods then:
4) What is the function of c within this grid or frame ?
5) What is the function of cg within this frame ?
6) Do I have to consider SR within this frame ?
7) Do I need the full complexity of GR to describe the movement
of the stars (and planets) ?
IMO the answer on that question is NO because there are no
moving clocks involved.
Nicolaas Vroom
http://user.pandora.be/nicvroom/
> Suggested reading:
>
> See a very recent post in s.p.r. where I suggested some good places to
> begin studying perturbation theory in the sense of applied mathematics.
> See also the gtr problem book by Press et al. for a problem on solar
> oblateness versus Einstein's precession formula; compare their solution in
> the back to the one I gave in the above mentioned posts to s.p.r. a few
> years ago. Note that they directly compare a result from Newtonian theory
> to one from weak-field gtr, without comment. Again, this is entirely
> justified, but only because weak-field gtr is a linear field theory! As I
> said, in my solution I worked entirely in weak-field gtr to obtain both
> results, which may help some students understand that there is no "funny
> business" going on here. For numerical simulations, again the textbook by
> Richards is a good place to start on trying to understand "stability" in
> general. Then one can consult specialized textbooks on numerical methods
> for more about careful numerical integration of differential equations.
> For PPN, see a survey paper by Clifford Will on the ArXiV.
>
> "T. Essel" (hiding somewhere in cyberspace)
>
Nicolaas Vroom
Dec9-04, 02:02 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Nicolaas Vroom" <nicolaas.vroom@pandora.be> schreef in bericht\nnews:kOknd.29207\\$tg4.1243271@phobos.tel enet-ops.be...\n\nSNIP\n\n> but first I need an answer\n> on a couple of questions:\n>\n> 1) Does it make sense to transform human based observations into\n> grid based positions ?\n> 2) Does it make sense to remove light bending as part of those\n> transformations ?\n> 3) If those transformations make sense i.e. have an advantage above\n> other methods then:\n> 4) What is the function of c within this grid or frame ?\n> 5) What is the function of cg within this frame ?\n> 6) Do I have to consider SR within this frame ?\n> 7) Do I need the full complexity of GR to describe the movement\n> of the stars (and planets) ?\n\nNot much responds to those questions.\nStill I consider them very important and I think a must\nif you want to simulate (predict) the positions of the\nstars and planets.\n\nOne additional questions bothers me tremendously:\nWithin this grid is there any bending of space-time involved ?\nI expect if you want to visual observe the stars and planets\nthe answer is Yes.\nBut that is not the total issue.\nThe question is: if there is some form of space-time bending\ninvolved within this frame(grid) does this bending have any\ninfluence on the behaviour of the stars and planets ?\n(And how ?)\n\nNicolaas Vroom\nhttp://users.pandora.be/nicvroom/\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Nicolaas Vroom" <nicolaas.vroom@pandora.be> schreef in bericht
news:kOknd.29207$tg4.1243271@phobos.telenet-ops.be...
SNIP
> but first I need an answer
> on a couple of questions:
>
> 1) Does it make sense to transform human based observations into
> grid based positions ?
> 2) Does it make sense to remove light bending as part of those
> transformations ?
> 3) If those transformations make sense i.e. have an advantage above
> other methods then:
> 4) What is the function of c within this grid or frame ?
> 5) What is the function of cg within this frame ?
> 6) Do I have to consider SR within this frame ?
> 7) Do I need the full complexity of GR to describe the movement
> of the stars (and planets) ?
Not much responds to those questions.
Still I consider them very important and I think a must
if you want to simulate (predict) the positions of the
stars and planets.
One additional questions bothers me tremendously:
Within this grid is there any bending of space-time involved ?
I expect if you want to visual observe the stars and planets
the answer is Yes.
But that is not the total issue.
The question is: if there is some form of space-time bending
involved within this frame(grid) does this bending have any
influence on the behaviour of the stars and planets ?
(And how ?)
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Nicolaas Vroom
Dec25-04, 12:42 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>close the cavity.\nNow tie the thighs up tight to hold it all together.\nPlace breast side up in a large metal roasting pan.\nBake in 325° oven covered for 2 hours.\nRemove cover, stick a cooking thermometer deep into one of the\nbaby?s buttocks and cook uncovered till thermometer reads 190°,\nabout another hour.\n\n\n\nPro-Choice Po-Boy\n\nSoft-shelled crabs serve just as well in this classic southern delicacy.\nThe sandwich originated in New Orleans, where an abundance of abortion clinics\nthrive and hot French bread is always available.\n\n2 cleaned fetuses, head on\n2 eggs\n1 tablespoon yellow mustard\n1 cup seasoned flour\noil enough for deep frying\n1 loaf French bread\nLettuce\ntomatoes\nmayonnaise, etc.\n\nMarinate the fetuses in the egg-mustard mixture.\nDredge thoroughly in flour.\nFry at 375° until crispy golden brown.\nRemove and place on paper towels.\n\n\n\nHoliday Youngster\n\nOne can easily adapt this recipe to ham, though as presented,\nit violates no religious taboos against swine.\n\n1 large toddler or small child, cleaned and de-headed\nKentucky Bourbon Sauce (see index)\n1 large can pineapple slices\nWhole cloves\n\nPlace him (or ham) or her in a large glass baking dish, buttocks up.\nTie with butcher string around and across so that he looks like\nhe?s crawling.\nGlaze, then arrange pineapples and secure with cloves.\nBake uncovered in 350° oven till thermometer reaches 160°.\n\n\n\nCajun Babies\n\nJust like crabs or crawfish, babies are boiled alive!\nYou don?t need silverware, the hot spicy meat comes off in your hands.\n\n6 live babies\n1 lb. smoked sausage\n4 lemons\nwhole garli\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>close the cavity.
Now tie the thighs up tight to hold it all together.
Place breast side up in a large metal roasting pan.
Bake in 325° oven covered for 2 hours.
Remove cover, stick a cooking thermometer deep into one of the
baby?s buttocks and cook uncovered till thermometer reads 190°,
about another hour.
Pro-Choice Po-Boy
Soft-shelled crabs serve just as well in this classic southern delicacy.
The sandwich originated in New Orleans, where an abundance of abortion clinics
thrive and hot French bread is always available.
2 cleaned fetuses, head on
2 eggs
1 tablespoon yellow mustard
1 cup seasoned flour
oil enough for deep frying
1 loaf French bread
Lettuce
tomatoes
mayonnaise, etc.
Marinate the fetuses in the egg-mustard mixture.
Dredge thoroughly in flour.
Fry at 375° until crispy golden brown.
Remove and place on paper towels.
Holiday Youngster
One can easily adapt this recipe to ham, though as presented,
it violates no religious taboos against swine.
1 large toddler or small child, cleaned and de-headed
Kentucky Bourbon Sauce (see index)
1 large can pineapple slices
Whole cloves
Place him (or ham) or her in a large glass baking dish, buttocks up.
Tie with butcher string around and across so that he looks like
he?s crawling.
Glaze, then arrange pineapples and secure with cloves.
Bake uncovered in 350° oven till thermometer reaches 160°.
Cajun Babies
Just like crabs or crawfish, babies are boiled alive!
You don?t need silverware, the hot spicy meat comes off in your hands.
6 live babies
1 lb. smoked sausage
4 lemons
whole garli
Nicolaas Vroom
Dec25-04, 01:44 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>browned, remove and glaze,\nreturn to oven and bake 20 minutes more to form a glaze.\nCut ribs into individual pieces and serve with extra sauce.\n\n\n\nFresh Sausage\n\nIf it becomes necessary to hide the fact that you are eating\nhuman babies, this is the perfect solution.\nBut if you are still paranoid, you can substitute pork butt.\n\n5 lb. lean chuck roast\n3 lb. prime baby butt\n2 tablespoons each:\nsalt\nblack, white and cayenne peppers\ncelery salt\ngarlic powder\nparsley flakes\nbrown sugar\n1 teaspoon sage\n2 onions\n6 cloves garlic\nbunch green onions, chopped\n\nCut the children?s butts and the beef roast into pieces\nthat will fit in the grinder.\nRun the meat through using a 3/16 grinding plate.\nAdd garlic, onions and seasoning then mix well.\nAdd just enough water for a smooth consistency, then mix again.\nForm the sausage mixture into patties or stuff into natural casings.\n\n\n\nStillborn Stew\n\nBy definition, this meat cannot be had altogether fresh,\nbut have the lifeless unfortunate available immediately after delivery,\nor use high quality beef or pork roasts (it is cheaper and better to\ncut up a whole roast than to buy stew meat).\n\n1 stillbirth, de-boned and cubed\n¼ cup\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>browned, remove and glaze,
return to oven and bake 20 minutes more to form a glaze.
Cut ribs into individual pieces and serve with extra sauce.
Fresh Sausage
If it becomes necessary to hide the fact that you are eating
human babies, this is the perfect solution.
But if you are still paranoid, you can substitute pork butt.
5 lb. lean chuck roast
3 lb. prime baby butt
2 tablespoons each:
salt
black, white and cayenne peppers
celery salt
garlic powder
parsley flakes
brown sugar
1 teaspoon sage
2 onions
6 cloves garlic
bunch green onions, chopped
Cut the children?s butts and the beef roast into pieces
that will fit in the grinder.
Run the meat through using a 3/16 grinding plate.
Add garlic, onions and seasoning then mix well.
Add just enough water for a smooth consistency, then mix again.
Form the sausage mixture into patties or stuff into natural casings.
Stillborn Stew
By definition, this meat cannot be had altogether fresh,
but have the lifeless unfortunate available immediately after delivery,
or use high quality beef or pork roasts (it is cheaper and better to
cut up a whole roast than to buy stew meat).
1 stillbirth, de-boned and cubed
¼ cup
Nicolaas Vroom
Dec25-04, 01:52 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>good and hot while placing meat, vegetables, and\nfruit such as pineapples or cherries on the skewers.\nDon?t be afraid to use a variety of meats.\nGrill to medium rare,\nserve with garlic cous-cous and sautéed asparagus.\nCoffee and sherbet for desert then walnuts, cheese, and port.\nCigars for the gentlemen (and ladies if they so desire)!\n\n\n\nCrock-Pot Crack Baby\n\nWhen the quivering, hopelessly addicted crack baby succumbs to death,\nget him immediately butchered and into the crock-pot, so that any\nremaining toxins will not be fatal. But don?t cook it too long,\nbecause like Blowfish, there is a perfect medium between the poisonous\nand the stimulating. Though it may not have the same effect on your\nguests, a whole chicken cooked in this fashion is also mighty tasty.\n\n1 newborn - cocaine addicted, freshly expired, cleaned and butchered\nCarrots\nonions\nleeks\ncelery\nbell pepper\npotatoes\nSalt\npepper\ngarlic, etc\n4 cups water\n\nCut the meat into natural pieces and brown very well in olive oil,\nremove, then brown half of the onions, the bell pepper, and celery.\nWhen brown, mix everything into the crock-pot, and in 6 to 8 hours you\nhave turned a hopeless tragedy into a heartwarming meal!\n\n\n\nGeorge?s Bloody Mary\n\nDon?t shy away from this one, it is simply a cocktail variation of\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>good and hot while placing meat, vegetables, and
fruit such as pineapples or cherries on the skewers.
Don?t be afraid to use a variety of meats.
Grill to medium rare,
serve with garlic cous-cous and sautéed asparagus.
Coffee and sherbet for desert then walnuts, cheese, and port.
Cigars for the gentlemen (and ladies if they so desire)!
Crock-Pot Crack Baby
When the quivering, hopelessly addicted crack baby succumbs to death,
get him immediately butchered and into the crock-pot, so that any
remaining toxins will not be fatal. But don?t cook it too long,
because like Blowfish, there is a perfect medium between the poisonous
and the stimulating. Though it may not have the same effect on your
guests, a whole chicken cooked in this fashion is also mighty tasty.
1 newborn - cocaine addicted, freshly expired, cleaned and butchered
Carrots
onions
leeks
celery
bell pepper
potatoes
Salt
pepper
garlic, etc
4 cups water
Cut the meat into natural pieces and brown very well in olive oil,
remove, then brown half of the onions, the bell pepper, and celery.
When brown, mix everything into the crock-pot, and in 6 to 8 hours you
have turned a hopeless tragedy into a heartwarming meal!
George?s Bloody Mary
Don?t shy away from this one, it is simply a cocktail variation of
Nicolaas Vroom
Dec25-04, 02:00 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>get rid of all the leftovers in your refrigerator.\n\n1 - 2 lbs. cubed meat (human flesh, chicken, turkey, beef...)\n1 -2 lbs. coarsely chopped vegetables\n(carrots, potatoes, turnips, cauliflower, cabbage...)\nBell pepper\nonions\ngarlic\nginger\nsalt pepper, etc.\nOlive oil\nbutter\n\nBrown the meat and some chopped onions, peppers, and garilic in olive oil,\nplace in baking dish, layer with vegetables seasoning and butter.\nBake at 325° for 30 - 45 minutes.\nServe with hot dinner rolls, fruit salad and sparkling water.\n\n\n\nBébé Buffet 1\n\nShow off with whole roasted children replete with apples in mouths -\nand babies? heads stuffed with wild rice. Or keep it simple with a\nhearty main course such as stew, lasagna, or meat loaf.\n\nSome suggestions\n\nPre-mie pot pies, beef stew, leg of lamb, stuffed chicken, roast pork spiral ham,\nCranberry pineapple salad, sweet potatoes in butter, vegetable platter, tossed salad with tomato and avocado, parsley new potatoes, spinich cucumber salad, fruit salad\nBran muffins, dinner rolls, soft breadsticks, rice pilaf, croissants\nApple cake with rum sauce, frosted banana nut bread sherbet, home made brownies\nIced tea, water, beer, bloody marys, lemonade, coffee\n\nThe guests select food, beverages, silverware... everything from the buffet table.\nThey move to\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>get rid of all the leftovers in your refrigerator.
1 - 2 lbs. cubed meat (human flesh, chicken, turkey, beef...)
1 -2 lbs. coarsely chopped vegetables
(carrots, potatoes, turnips, cauliflower, cabbage...)
Bell pepper
onions
garlic
ginger
salt pepper, etc.
Olive oil
butter
Brown the meat and some chopped onions, peppers, and garilic in olive oil,
place in baking dish, layer with vegetables seasoning and butter.
Bake at 325° for 30 - 45 minutes.
Serve with hot dinner rolls, fruit salad and sparkling water.
Bébé Buffet 1
Show off with whole roasted children replete with apples in mouths -
and babies? heads stuffed with wild rice. Or keep it simple with a
hearty main course such as stew, lasagna, or meat loaf.
Some suggestions
Pre-mie pot pies, beef stew, leg of lamb, stuffed chicken, roast pork spiral ham,
Cranberry pineapple salad, sweet potatoes in butter, vegetable platter, tossed salad with tomato and avocado, parsley new potatoes, spinich cucumber salad, fruit salad
Bran muffins, dinner rolls, soft breadsticks, rice pilaf, croissants
Apple cake with rum sauce, frosted banana nut bread sherbet, home made brownies
Iced tea, water, beer, bloody marys, lemonade, coffee
The guests select food, beverages, silverware... everything from the buffet table.
They move to
Nicolaas Vroom
Dec25-04, 02:45 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Whole fresh pre-mie; eviscerated, head, hands and feet removed\nOnions, bell pepper, celery\n½ cup wine\nRoot vegetables of choice (turnips, carrots, potatoes, etc) cubed\n\nMake a crust from scratch - or go shamefully to the frozen food section\nof your favorite grocery and select 2 high quality pie crusts (you\nwill need one for the top also).\nBoil the prepared delicacy until the meat starts to come off the bones.\nRemove, de-bone and cube; continue to reduce the broth.\nBrown the onions, peppers and celery.\nAdd the meat then season, continue browning.\nDe-glaze with sherry, add the reduced broth.\nFinally, put in the root vegetables and simmer for 15 minutes.\nAllow to cool slightly.\nPlace the pie pan in 375 degree oven for a few minutes so bottom crust is not soggy,\nreduce oven to 325.\nFill the pie with stew, place top crust and with a fork, seal the crusts together\nthen poke holes in top.\nReturn to oven and bake for 30 minutes, or until pie crust is golden brown.\n\n\n\nSudden Infant Death Soup\n\nSIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.\nIts free, you can sell the crib, baby clothes, toys, stroller... and so easy to\nprocure if such a lucky find is at hand (just pick him up from the crib and\nhe?s good to go)!\n\nSIDS victim, cleaned\n½ cup cooking oil\nCarrots\nonions\nbroccoli\nwhole cabbage\nfresh green beans\npotato\nturnip\ncelery\ntomato\n½ stick butter\n1 cup cooke\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Whole fresh pre-mie; eviscerated, head, hands and feet removed
Onions, bell pepper, celery
½ cup wine
Root vegetables of choice (turnips, carrots, potatoes, etc) cubed
Make a crust from scratch - or go shamefully to the frozen food section
of your favorite grocery and select 2 high quality pie crusts (you
will need one for the top also).
Boil the prepared delicacy until the meat starts to come off the bones.
Remove, de-bone and cube; continue to reduce the broth.
Brown the onions, peppers and celery.
Add the meat then season, continue browning.
De-glaze with sherry, add the reduced broth.
Finally, put in the root vegetables and simmer for 15 minutes.
Allow to cool slightly.
Place the pie pan in 375 degree oven for a few minutes so bottom crust is not soggy,
reduce oven to 325.
Fill the pie with stew, place top crust and with a fork, seal the crusts together
then poke holes in top.
Return to oven and bake for 30 minutes, or until pie crust is golden brown.
Sudden Infant Death Soup
SIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.
Its free, you can sell the crib, baby clothes, toys, stroller... and so easy to
procure if such a lucky find is at hand (just pick him up from the crib and
he?s good to go)!
SIDS victim, cleaned
½ cup cooking oil
Carrots
onions
broccoli
whole cabbage
fresh green beans
potato
turnip
celery
tomato
½ stick butter
1 cup cooke
Nicolaas Vroom
Dec25-04, 03:24 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>salt\ncrab boil\n\nBring 3 gallons of water to a boil.\nAdd sausage, salt, crab boil, lemons and garlic.\nDrop potatoes in, boil for 4 minutes.\nCorn is added next, boil an additional 11 minutes.\nPut the live babies into the boiling water and cover.\nBoil till meat comes off easily with a fork.\n\n\n\nOven-Baked Baby-Back Ribs\n\nBeef ribs or pork ribs can be used in this recipe,\nand that is exactly what your dinner guests will assume!\nAn excellent way to expose the uninitiated to this highly misunderstood\nyet succulent source of protein.\n\n2 human baby rib racks\n3 cups barbecue sauce or honey glaze (see index)\nSalt\nblack pepper\nwhite pepper\npaprika\n\nRemove the silverskin by loosening from the edges,\nthen stripping off.\nSeason generously, rubbing the mixture into the baby?s flesh.\nPlace 1 quart water in a baking pan, the meat on a wire rack.\nBake uncovered in 250° oven for 1½ hours.\nWhen browned, remove and glaze,\nreturn to oven and bake 20 minutes more to form a glaze.\nCut ribs into individual pieces and serve with extra sauce.\n\n\n\nFresh Sausage\n\nIf it becomes necessary to hide the fact that you are eating\nhuman babies, this is the perfect solution.\nBut if you are still paranoid, you can substitute pork butt.\n\n5 lb. lean chuck roast\n3 lb. prime baby butt\n2 tablespoons each:\nsalt\nblack, white and cayenne peppers\ncelery salt\ngarlic powder\nparsley flakes\nbrown sugar\n1 teaspoon sage\n2 onions\n6 cloves garlic\nbunch green onions, chopped\n\nCut the children?s butts and the beef roast into pieces\nthat will fit in the grinder.\nRun the meat through using a 3/16 grinding plate.\nAdd garlic, onions and seasoning then mix well.\nAdd just enough water for a smooth consistency, then mix again.\nForm the sausage mixture into patties or stuff into natural casings.\n\n\n\nStillborn Stew\n\nBy definition, this meat cannot be had altogether fresh,\nbut have the lifeless unfortunate available immediately after delivery,\nor use hi\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>salt
crab boil
Bring 3 gallons of water to a boil.
Add sausage, salt, crab boil, lemons and garlic.
Drop potatoes in, boil for 4 minutes.
Corn is added next, boil an additional 11 minutes.
Put the live babies into the boiling water and cover.
Boil till meat comes off easily with a fork.
Oven-Baked Baby-Back Ribs
Beef ribs or pork ribs can be used in this recipe,
and that is exactly what your dinner guests will assume!
An excellent way to expose the uninitiated to this highly misunderstood
yet succulent source of protein.
2 human baby rib racks
3 cups barbecue sauce or honey glaze (see index)
Salt
black pepper
white pepper
paprika
Remove the silverskin by loosening from the edges,
then stripping off.
Season generously, rubbing the mixture into the baby?s flesh.
Place 1 quart water in a baking pan, the meat on a wire rack.
Bake uncovered in 250° oven for 1½ hours.
When browned, remove and glaze,
return to oven and bake 20 minutes more to form a glaze.
Cut ribs into individual pieces and serve with extra sauce.
Fresh Sausage
If it becomes necessary to hide the fact that you are eating
human babies, this is the perfect solution.
But if you are still paranoid, you can substitute pork butt.
5 lb. lean chuck roast
3 lb. prime baby butt
2 tablespoons each:
salt
black, white and cayenne peppers
celery salt
garlic powder
parsley flakes
brown sugar
1 teaspoon sage
2 onions
6 cloves garlic
bunch green onions, chopped
Cut the children?s butts and the beef roast into pieces
that will fit in the grinder.
Run the meat through using a 3/16 grinding plate.
Add garlic, onions and seasoning then mix well.
Add just enough water for a smooth consistency, then mix again.
Form the sausage mixture into patties or stuff into natural casings.
Stillborn Stew
By definition, this meat cannot be had altogether fresh,
but have the lifeless unfortunate available immediately after delivery,
or use hi
Nicolaas Vroom
Dec25-04, 03:28 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>If you want to simulate the movement of galaxies\nstars or planets then one very important\nquestion to answer is what is "timewise" the basis\nof your simulation.\nIMO there are two possibilities.\nIn both cases you start by selecting a reference point\n(or origin) and a time t0 (or a now)\n\nThe first possibility is based on what you see.\nThat means you place yourself at the origin and you\nobserve the positions of the planets. Those positions\nare the starting point of your simulation.\nThe second possibility is identical as the first, but the\nstarting position of the simulation is not the observed\nposition but the predicted position at the time t0 (now)\n\nThat means if a certain star is 1 light min away, you\ndo not take the observed position, but the predicted\nposition 1 min in the future from the observed position.\n\nIMO this is the correct way to do your simulation\nbecause you are comparing more apples with apples.\n\nThe next question to answer is what should be\nthe origin of your simulation.\nIMO the Sun is better than the Earth,\nand even better is the centre of our Galaxy (than the Sun).\nThe reason is that a clock at the centre of Our Galaxy\nis more stable as one at the Sun (or Earth)\n\nThe next question to answer is how should you\nobserve the positions of the stars.\nIMO you should use a grid of synchronised clocks,\nall at equal nearest distance, with one clock at your\norigin.\nIf you place yourself at the origin than you will see\nthat all clocks at the same distance will run the same\ntimeperiod delta t behind.\nFor example a clock at 1 light minute will run 1 minute\nbehind.\n\nThe next, and most important, question to answer\nis what are the rules that describe the movement\nof the stars (or objects) assuming you have selected\nthe second possibility.\n\nHopes this helps in the discussion.\n\nFor a 3D picture of the galaxies and to study\nthe grid See:\nhttp://www.astro.utu.fi/EGal/elg/ELG3D.html\nNo 8 is the Milky Way Galaxy\nNo 32 is the Andromeda Galaxy\nIt is not clear if this 3D picture represents\npossibility 1 or 2.\n\n\nNicolaas Vroom\nhttp://users.pandora.be/nicvroom/\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>If you want to simulate the movement of galaxies
stars or planets then one very important
question to answer is what is "timewise" the basis
of your simulation.
IMO there are two possibilities.
In both cases you start by selecting a reference point
(or origin) and a time t0 (or a now)
The first possibility is based on what you see.
That means you place yourself at the origin and you
observe the positions of the planets. Those positions
are the starting point of your simulation.
The second possibility is identical as the first, but the
starting position of the simulation is not the observed
position but the predicted position at the time t0 (now)
That means if a certain star is 1 light min away, you
do not take the observed position, but the predicted
position 1 min in the future from the observed position.
IMO this is the correct way to do your simulation
because you are comparing more apples with apples.
The next question to answer is what should be
the origin of your simulation.
IMO the Sun is better than the Earth,
and even better is the centre of our Galaxy (than the Sun).
The reason is that a clock at the centre of Our Galaxy
is more stable as one at the Sun (or Earth)
The next question to answer is how should you
observe the positions of the stars.
IMO you should use a grid of synchronised clocks,
all at equal nearest distance, with one clock at your
origin.
If you place yourself at the origin than you will see
that all clocks at the same distance will run the same
timeperiod \delta t behind.
For example a clock at 1 light minute will run 1 minute
behind.
The next, and most important, question to answer
is what are the rules that describe the movement
of the stars (or objects) assuming you have selected
the second possibility.
Hopes this helps in the discussion.
For a 3D picture of the galaxies and to study
the grid See:
http://www.astro.utu.fi/EGal/elg/ELG3D.html
No 8 is the Milky Way Galaxy
No 32 is the Andromeda Galaxy
It is not clear if this 3D picture represents
possibility 1 or 2.
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Nicolaas Vroom
Dec25-04, 04:16 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>limb, rack, or roast\nPotatoes, carrot\nOil\ncelery\nonions\ngreen onions\nparsley\ngarlic\nsalt, pepper, etc\n2 cups beef stock\n\nMarinate meat (optional, not necessary with better cuts).\nSeason liberally and lace with garlic cloves by making incisions,\nand placing whole cloves deep into the meat.\nGrease a baking pan, and fill with a thick bed of onions,\ncelery, green onions, and parsley.\nPlace roast on top with fat side up.\nPlace uncovered in 500° oven for 20 minutes, reduce oven to 325°.\nBake till medium rare (150°) and let roast rest.\nPour stock over onions and drippings, carve the meat and\nplace the slices in the au jus.\n\n\n\nBisque à l?Enfant\n\nHonor the memory of Grandma with this dish by utilizing her good\nsilver soup tureen and her great grandchildren (crawfish, crab or\nlobster will work just as well, however this dish is classically\nmade with crawfish).\n\nStuffed infant heads, stuffed crawfish heads, stuffed crab or lobster shells;\nmake patties if shell or head is not available\n(such as with packaged crawfish, crab, or headless baby).\nFlour\noil\nonions\nbell peppers\ngarlic salt, pepper, etc.\n3 cups chicken stock\n2 sticks butter\n3 tablespoons oil\n\nFirst stuff the heads, or make the patties (see index)\nthen fry or bake.\nSet aside to drain on paper towels.\nMake a roux with butter, oil and flour,\nbrown vegetables in the roux, then add chicken stock and\nallow to simmer for 20 minutes.\nAdd the patties or stuffed heads, and some loose crawfish,\nlobster, long piglet, or what have you.\nCook on low for 15 minutes, then allow it to set for at least\n15 minutes more.\nServe over steamed rice; this dish is very impressive!\n\n\n\nStuffed Cabbage Rolls\n\nBabies really can be found under a cabbage leaf -\nor one can arrange for ground beef to be found there instead.\n\n8 large cabbage leaves\n1 lb. lean ground newborn human filets, or ground chuck\nOnions\npeppers\ncelery\nga\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>limb, rack, or roast
Potatoes, carrot
Oil
celery
onions
green onions
parsley
garlic
salt, pepper, etc
2 cups beef stock
Marinate meat (optional, not necessary with better cuts).
Season liberally and lace with garlic cloves by making incisions,
and placing whole cloves deep into the meat.
Grease a baking pan, and fill with a thick bed of onions,
celery, green onions, and parsley.
Place roast on top with fat side up.
Place uncovered in 500° oven for 20 minutes, reduce oven to 325°.
Bake till medium rare (150°) and let roast rest.
Pour stock over onions and drippings, carve the meat and
place the slices in the au jus.
Bisque à l?Enfant
Honor the memory of Grandma with this dish by utilizing her good
silver soup tureen and her great grandchildren (crawfish, crab or
lobster will work just as well, however this dish is classically
made with crawfish).
Stuffed infant heads, stuffed crawfish heads, stuffed crab or lobster shells;
make patties if shell or head is not available
(such as with packaged crawfish, crab, or headless baby).
Flour
oil
onions
bell peppers
garlic salt, pepper, etc.
3 cups chicken stock
2 sticks butter
3 tablespoons oil
First stuff the heads, or make the patties (see index)
then fry or bake.
Set aside to drain on paper towels.
Make a roux with butter, oil and flour,
brown vegetables in the roux, then add chicken stock and
allow to simmer for 20 minutes.
Add the patties or stuffed heads, and some loose crawfish,
lobster, long piglet, or what have you.
Cook on low for 15 minutes, then allow it to set for at least
15 minutes more.
Serve over steamed rice; this dish is very impressive!
Stuffed Cabbage Rolls
Babies really can be found under a cabbage leaf -
or one can arrange for ground beef to be found there instead.
8 large cabbage leaves
1 lb. lean ground newborn human filets, or ground chuck
Onions
peppers
celery
ga
Nicolaas Vroom
Dec25-04, 05:03 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>garlic\nbunch green onions, chopped\n\nCut the children?s butts and the beef roast into pieces\nthat will fit in the grinder.\nRun the meat through using a 3/16 grinding plate.\nAdd garlic, onions and seasoning then mix well.\nAdd just enough water for a smooth consistency, then mix again.\nForm the sausage mixture into patties or stuff into natural casings.\n\n\n\nStillborn Stew\n\nBy definition, this meat cannot be had altogether fresh,\nbut have the lifeless unfortunate available immediately after delivery,\nor use high quality beef or pork roasts (it is cheaper and better to\ncut up a whole roast than to buy stew meat).\n\n1 stillbirth, de-boned and cubed\n¼ cup vegetable oil\n2 large onions\nbell pepper\ncelery\ngarlic\n½ cup red wine\n3 Irish potatoes\n2 large carrots\n\nThis is a simple classic stew that makes natural gravy,\nthus it does not have to be thickened.\nBrown the meat quickly in very hot oil, remove and set aside.\nBrown the onions, celery, pepper and garlic.\nDe-glaze with wine, return meat to the pan and season well.\nStew on low fire adding small amounts of water and\nseasoning as necessary.\nAfter at least half an hour, add the carrots and potatoes,\nand simmer till root vegetables break with a fork.\nCook a fresh pot of long grained white rice.\n\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>garlic
bunch green onions, chopped
Cut the children?s butts and the beef roast into pieces
that will fit in the grinder.
Run the meat through using a 3/16 grinding plate.
Add garlic, onions and seasoning then mix well.
Add just enough water for a smooth consistency, then mix again.
Form the sausage mixture into patties or stuff into natural casings.
Stillborn Stew
By definition, this meat cannot be had altogether fresh,
but have the lifeless unfortunate available immediately after delivery,
or use high quality beef or pork roasts (it is cheaper and better to
cut up a whole roast than to buy stew meat).
1 stillbirth, de-boned and cubed
¼ cup vegetable oil
2 large onions
bell pepper
celery
garlic
½ cup red wine
3 Irish potatoes
2 large carrots
This is a simple classic stew that makes natural gravy,
thus it does not have to be thickened.
Brown the meat quickly in very hot oil, remove and set aside.
Brown the onions, celery, pepper and garlic.
De-glaze with wine, return meat to the pan and season well.
Stew on low fire adding small amounts of water and
seasoning as necessary.
After at least half an hour, add the carrots and potatoes,
and simmer till root vegetables break with a fork.
Cook a fresh pot of long grained white rice.
Nicolaas Vroom
Dec25-04, 05:10 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Simmer for half an hour keeping the stock thick.\nRemove the carcass and add the vegetables slowly to the stock,\nso that it remains boiling the whole time.\nCover the pot and simmer till vegetables are tender\n(2 hours approximately).\nContinue seasoning to taste.\nBefore serving, add butter and pasta,\nserve piping with hot bread and butter.\n\n\n\nOffspring Rolls\n\nSimilar to Vietnamese style fried rolls, they have lots of meat\n(of course this can consist of chicken, beef, pork, or shrimp).\nWho can resist this classic appetizer; or light lunch served with\na fresh salad? Versatility is probably this recipe?s greatest virtue,\nas one can use the best part of a prime, rare, yearling, or the\nmorticians occasional horror: a small miracle stopped short by a\ndrunk driver, or the innocent victim of a drive-by shooting...\n\n2 cups finely chopped very young human flesh\n1 cup shredded cabbage\n1 cup bean sprouts\n5 sprigs green onion, finely chopped\n5 cloves minced garlic\n4-6 ounces bamboo shoots\nSherry\nchicken broth\noil for deep frying (1 gallon)\nSalt\npepper\nsoy & teriyaki\nminced ginger, etc.\n1 tablespoon cornstarch dissolved in a little cold water\n1 egg beaten\n\nMake the stuffing:\nMarinate the flesh in a mixture of soy and teriyaki sauces\nthen stir fry in hot oil for till brown - about 1 minute, remove.\nStir-fry the vegetables.\nPut the meat back into the wok and adjust the seasoning.\nDe-glaze with sherry, cooking off the alcohol.\nAdd broth (optional) cook a few more minutes.\nAdd the cornstarch, cook a few minutes till thick,\nthen place th\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Simmer for half an hour keeping the stock thick.
Remove the carcass and add the vegetables slowly to the stock,
so that it remains boiling the whole time.
Cover the pot and simmer till vegetables are tender
(2 hours approximately).
Continue seasoning to taste.
Before serving, add butter and pasta,
serve piping with hot bread and butter.
Offspring Rolls
Similar to Vietnamese style fried rolls, they have lots of meat
(of course this can consist of chicken, beef, pork, or shrimp).
Who can resist this classic appetizer; or light lunch served with
a fresh salad? Versatility is probably this recipe?s greatest virtue,
as one can use the best part of a prime, rare, yearling, or the
morticians occasional horror: a small miracle stopped short by a
drunk driver, or the innocent victim of a drive-by shooting...
2 cups finely chopped very young human flesh
1 cup shredded cabbage
1 cup bean sprouts
5 sprigs green onion, finely chopped
5 cloves minced garlic
4-6 ounces bamboo shoots
Sherry
chicken broth
oil for deep frying (1 gallon)
Salt
pepper
soy & teriyaki
minced ginger, etc.
1 tablespoon cornstarch dissolved in a little cold water
1 egg beaten
Make the stuffing:
Marinate the flesh in a mixture of soy and teriyaki sauces
then stir fry in hot oil for till brown - about 1 minute, remove.
Stir-fry the vegetables.
Put the meat back into the wok and adjust the seasoning.
De-glaze with sherry, cooking off the alcohol.
Add broth (optional) cook a few more minutes.
Add the cornstarch, cook a few minutes till thick,
then place th
Nicolaas Vroom
Dec25-04, 05:33 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>hour, add the carrots and potatoes,\nand simmer till root vegetables break with a fork.\nCook a fresh pot of long grained white rice.\n\n\n\nPre-mie Pot Pie\n\nWhen working with prematurely delivered newborns (or chicken) use sherry;\nred wine with beef (buy steak or roast, do not pre-boil).\n\nPie crust (see index)\nWhole fresh pre-mie; eviscerated, head, hands and feet removed\nOnions, bell pepper, celery\n½ cup wine\nRoot vegetables of choice (turnips, carrots, potatoes, etc) cubed\n\nMake a crust from scratch - or go shamefully to the frozen food section\nof your favorite grocery and select 2 high quality pie crusts (you\nwill need one for the top also).\nBoil the prepared delicacy until the meat starts to come off the bones.\nRemove, de-bone and cube; continue to reduce the broth.\nBrown the onions, peppers and celery.\nAdd the meat then season, continue browning.\nDe-glaze with sherry, add the reduced broth.\nFinally, put in the root vegetables and simmer for 15 minutes.\nAllow to cool slightly.\nPlace the pie pan in 375 degree oven for a few minutes so bottom crust is not soggy,\nreduce oven to 325.\nFill the pie with stew, place top crust and with a fork, seal the crusts together\nthen poke holes in top.\nReturn to oven and bake for 30 minutes, or until pie crust is golden brown.\n\n\n\nSudden Infant Death Soup\n\nSIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.\nIts free, you can sell the crib, baby clothes, toys, stroller... and so easy to\nprocure if such a lucky find is at hand (just pick him up from the crib an\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>hour, add the carrots and potatoes,
and simmer till root vegetables break with a fork.
Cook a fresh pot of long grained white rice.
Pre-mie Pot Pie
When working with prematurely delivered newborns (or chicken) use sherry;
red wine with beef (buy steak or roast, do not pre-boil).
Pie crust (see index)
Whole fresh pre-mie; eviscerated, head, hands and feet removed
Onions, bell pepper, celery
½ cup wine
Root vegetables of choice (turnips, carrots, potatoes, etc) cubed
Make a crust from scratch - or go shamefully to the frozen food section
of your favorite grocery and select 2 high quality pie crusts (you
will need one for the top also).
Boil the prepared delicacy until the meat starts to come off the bones.
Remove, de-bone and cube; continue to reduce the broth.
Brown the onions, peppers and celery.
Add the meat then season, continue browning.
De-glaze with sherry, add the reduced broth.
Finally, put in the root vegetables and simmer for 15 minutes.
Allow to cool slightly.
Place the pie pan in 375 degree oven for a few minutes so bottom crust is not soggy,
reduce oven to 325.
Fill the pie with stew, place top crust and with a fork, seal the crusts together
then poke holes in top.
Return to oven and bake for 30 minutes, or until pie crust is golden brown.
Sudden Infant Death Soup
SIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.
Its free, you can sell the crib, baby clothes, toys, stroller... and so easy to
procure if such a lucky find is at hand (just pick him up from the crib an
Nicolaas Vroom
Jan27-05, 03:02 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>This responds is partly written as a reply of the thread:\n"non-GR theories of Gravity" initiated by Phillip Helbig.\n\n"Nicolaas Vroom" <nicolaas.vroom@pandora.be> schreef in bericht\nnews:Nfjzd.10044\\$_C2.478443@phobos.tele net-ops.be...\n> If you want to simulate the movement of galaxies\n\n> IMO there are two possibilities.\n> In both cases you start by selecting a reference point\n> (or origin) and a time t0 (or a now)\n>\n> The first possibility is based on what you see.\n> That means you place yourself at the origin and you\n> observe the positions of the planets. Those positions\n> are the starting point of your simulation.\n> The second possibility is identical as the first, but the\n> starting position of the simulation is not the observed\n> position but the predicted position at the time t0 (now)\n\nThis second possibilty is the prefered strategy\nbut things are not that simple.\n\nIn order to calculate the predicted positions at time t0\nyou need a model.\n\nOne model can be Newton\'s Law.\nThe most important parameter of Newton\'s Law are\nthe masses of all the objects included in your simulation.\nIn order to calculate those masses you need as many\nas possible observations of all your objects.\nYou need a set of estimated values for all your masses\nand a set of initial positions (*) for your simulation.\nWith those two sets of information and with Newton\'s law\nyou can calculate the observed positions at the time\nof those observations.\nAnd you can calculate an overall error factor.\n\nNext you can do the same for a different set of estimated\nvalues for all your masses and you can again\ncalculate an overall error factor.\n\nAnd again.\n\nThe set of estimated masses with the smallest overall\nerror factor is the best.\n\n(*) Your simulation starts with a set of initial positions\nall at the same moment. Very often that set is not available\nbecause most probably all you observations are\nat a different moment. That means you have to calculate\nthose initial positions with the masses based on your\nbest estimate.\nThis makes this whole exercise very complex.\n\nA different model can be MOND.\nMOND stands for (Milgrom\'s?) Modified Newton Dynamics.\nAs the name explains MOND is based on Newton\'s Law\nslightly modified with at least one additional parameter.\nIf you want to use MOND you have to estimate this parameter\nand a set of masses for all the objects included.\nAgain you have to calculate an overall error factor\nand the smallest overall error factor gives the best estimates.\n\nMOND is a better theory than Newton\'s Law if the final\noverall error factor using MOND is the smallest of the two.\n\nIn principle you can also use a different model.\n\nFor example you can use Newton\'s Law modified\nwith a parameter which takes into account that\nNewton\'s Law does not act instantaneous.\nAgain you have to calculate an overall\nerror factor and the story repeats it self.\n\n(It should be mentioned that each of those\n3 theories gives different mass estimates)\n\nFor example you can use GR\n\nHopes this helps.\n\n> Nicolaas Vroom\n> http://users.pandora.be/nicvroom/\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>This responds is partly written as a reply of the thread:
"non-GR theories of Gravity" initiated by Phillip Helbig.
"Nicolaas Vroom" <nicolaas.vroom@pandora.be> schreef in bericht
news:Nfjzd.10044$_C2.478443@phobos.telenet-ops.be...
> If you want to simulate the movement of galaxies
> IMO there are two possibilities.
> In both cases you start by selecting a reference point
> (or origin) and a time t0 (or a now)
>
> The first possibility is based on what you see.
> That means you place yourself at the origin and you
> observe the positions of the planets. Those positions
> are the starting point of your simulation.
> The second possibility is identical as the first, but the
> starting position of the simulation is not the observed
> position but the predicted position at the time t0 (now)
This second possibilty is the prefered strategy
but things are not that simple.
In order to calculate the predicted positions at time t0
you need a model.
One model can be Newton's Law.
The most important parameter of Newton's Law are
the masses of all the objects included in your simulation.
In order to calculate those masses you need as many
as possible observations of all your objects.
You need a set of estimated values for all your masses
and a set of initial positions (*) for your simulation.
With those two sets of information and with Newton's law
you can calculate the observed positions at the time
of those observations.
And you can calculate an overall error factor.
Next you can do the same for a different set of estimated
values for all your masses and you can again
calculate an overall error factor.
And again.
The set of estimated masses with the smallest overall
error factor is the best.
(*) Your simulation starts with a set of initial positions
all at the same moment. Very often that set is not available
because most probably all you observations are
at a different moment. That means you have to calculate
those initial positions with the masses based on your
best estimate.
This makes this whole exercise very complex.
A different model can be MOND.
MOND stands for (Milgrom's?) Modified Newton Dynamics.
As the name explains MOND is based on Newton's Law
slightly modified with at least one additional parameter.
If you want to use MOND you have to estimate this parameter
and a set of masses for all the objects included.
Again you have to calculate an overall error factor
and the smallest overall error factor gives the best estimates.
MOND is a better theory than Newton's Law if the final
overall error factor using MOND is the smallest of the two.
In principle you can also use a different model.
For example you can use Newton's Law modified
with a parameter which takes into account that
Newton's Law does not act instantaneous.
Again you have to calculate an overall
error factor and the story repeats it self.
(It should be mentioned that each of those
3 theories gives different mass estimates)
For example you can use GR
Hopes this helps.
> Nicolaas Vroom
> http://users.pandora.be/nicvroom/
Nicolaas Vroom
Feb1-05, 01:31 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nThis responds is partly written as a reply of the thread:\n"non-GR theories of Gravity" initiated by Phillip Helbig.\n\n"Nicolaas Vroom" <nicolaas.vroom@pandora.be> schreef in bericht\nnews:Nfjzd.10044\\$_C2.478443@phobos.tele net-ops.be...\n> If you want to simulate the movement of galaxies\n\n> IMO there are two possibilities.\n> In both cases you start by selecting a reference point\n> (or origin) and a time t0 (or a now)\n>\n> The first possibility is based on what you see.\n> That means you place yourself at the origin and you\n> observe the positions of the planets. Those positions\n> are the starting point of your simulation.\n> The second possibility is identical as the first, but the\n> starting position of the simulation is not the observed\n> position but the predicted position at the time t0 (now)\n\nThis second possibilty is the prefered strategy\nbut things are not that simple.\n\nIn order to calculate the predicted positions at time t0\nyou need a model.\n\nOne model can be Newton\'s Law.\nThe most important parameter of Newton\'s Law are\nthe masses of all the objects included in your simulation.\nIn order to calculate those masses you need as many\nas possible observations of all your objects.\nYou need a set of estimated values for all your masses\nand a set of initial positions (*) for your simulation.\nWith those two sets of information and with Newton\'s law\nyou can calculate the observed positions at the time\nof those observations.\nAnd you can calculate an overall error factor.\n\nNext you can do the same for a different set of estimated\nvalues for all your masses and you can again\ncalculate an overall error factor.\n\nAnd again.\n\nThe set of estimated masses with the smallest overall\nerror factor is the best.\n\n(*) Your simulation starts with a set of initial positions\nall at the same moment. Very often that set is not available\nbecause most probably all you observations are\nat a different moment. That means you have to calculate\nthose initial positions with the masses based on your\nbest estimate.\nThis makes this whole exercise very complex.\n\nA different model can be MOND.\nMOND stands for (Milgrom\'s?) Modified Newton Dynamics.\nAs the name explains MOND is based on Newton\'s Law\nslightly modified with at least one additional parameter.\nIf you want to use MOND you have to estimate this parameter\nand a set of masses for all the objects included.\nAgain you have to calculate an overall error factor\nand the smallest overall error factor gives the best estimates.\n\nMOND is a better theory than Newton\'s Law if the final\noverall error factor using MOND is the smallest of the two.\n\nIn principle you can also use a different model.\n\nFor example you can use Newton\'s Law modified\nwith a parameter which takes into account that\nNewton\'s Law does not act instantaneous.\nAgain you have to calculate an overall\nerror factor and the story repeats it self.\n\nSee also my postings in the thread\nRe: Perihelion of Mercury with classical mechanics ?\nin sci.astro\n\n(It should be mentioned that each of those\n3 theories gives different mass estimates)\n\nFor example you can use GR\n\nHopes this helps.\n\n> Nicolaas Vroom\n> http://users.pandora.be/nicvroom/\n\n\n\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>This responds is partly written as a reply of the thread:
"non-GR theories of Gravity" initiated by Phillip Helbig.
"Nicolaas Vroom" <nicolaas.vroom@pandora.be> schreef in bericht
news:Nfjzd.10044$_C2.478443@phobos.telenet-ops.be...
> If you want to simulate the movement of galaxies
> IMO there are two possibilities.
> In both cases you start by selecting a reference point
> (or origin) and a time t0 (or a now)
>
> The first possibility is based on what you see.
> That means you place yourself at the origin and you
> observe the positions of the planets. Those positions
> are the starting point of your simulation.
> The second possibility is identical as the first, but the
> starting position of the simulation is not the observed
> position but the predicted position at the time t0 (now)
This second possibilty is the prefered strategy
but things are not that simple.
In order to calculate the predicted positions at time t0
you need a model.
One model can be Newton's Law.
The most important parameter of Newton's Law are
the masses of all the objects included in your simulation.
In order to calculate those masses you need as many
as possible observations of all your objects.
You need a set of estimated values for all your masses
and a set of initial positions (*) for your simulation.
With those two sets of information and with Newton's law
you can calculate the observed positions at the time
of those observations.
And you can calculate an overall error factor.
Next you can do the same for a different set of estimated
values for all your masses and you can again
calculate an overall error factor.
And again.
The set of estimated masses with the smallest overall
error factor is the best.
(*) Your simulation starts with a set of initial positions
all at the same moment. Very often that set is not available
because most probably all you observations are
at a different moment. That means you have to calculate
those initial positions with the masses based on your
best estimate.
This makes this whole exercise very complex.
A different model can be MOND.
MOND stands for (Milgrom's?) Modified Newton Dynamics.
As the name explains MOND is based on Newton's Law
slightly modified with at least one additional parameter.
If you want to use MOND you have to estimate this parameter
and a set of masses for all the objects included.
Again you have to calculate an overall error factor
and the smallest overall error factor gives the best estimates.
MOND is a better theory than Newton's Law if the final
overall error factor using MOND is the smallest of the two.
In principle you can also use a different model.
For example you can use Newton's Law modified
with a parameter which takes into account that
Newton's Law does not act instantaneous.
Again you have to calculate an overall
error factor and the story repeats it self.
See also my postings in the thread
Re: Perihelion of Mercury with classical mechanics ?
in sci.astro
(It should be mentioned that each of those
3 theories gives different mass estimates)
For example you can use GR
Hopes this helps.
> Nicolaas Vroom
> http://users.pandora.be/nicvroom/
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