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View Full Version : Dynamic stability of an Earth Ring

AA Institute
Oct11-04, 03:52 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>\n\nSuppose an asteroid by a distant future engineering achievement has\nbeen captured into orbit around the Earth.\nNow suppose we want to carve it out by detonating a series of missiles\nthat incrementally hollow their way into the body of such an asteroid.\nThe material excavated out of the body would create a thin ring system\naround the Earth, as I try to illustrate here:-\n\nhttp://uk.geocities.com/aa_spaceagent/restricted/earth-ring.html\n\nMy main concern with such a project is one of SAFETY. I\'d like to know\nwhat a *safe* perigee (minimum) altitude would be necessary to prevent\norbital decay of ring material. I don\'t want any material from my\nhypothetical ring system coming down toward the Earth under any\ncircumstances. Would the ring material be contained in a narrow plane\nof fixed orbital incline, or would it scatter over time?\n\nQUESTION: I am under pressure to demonstrate by way of a mathematical\nmodel the dynamical stability of such a ring system, composed of small\nparticles being gravitationally influenced by the Earth and the Moon\nby way of "3 body problem".\n\nWhat are the analytical equations necessary to help demonstrate\n*theoretically* that such ring particles would indeed be stable in\ntheir orbital paths around the Earth? Or if not, how would I be able\nto show this?\n\nI would sincerely appreciate all help, as this is quite *pivotal* to\nmy research on this article.\n\nThanks for any support.\nAbdul Ahad\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Suppose an asteroid by a distant future engineering achievement has
been captured into orbit around the Earth.
Now suppose we want to carve it out by detonating a series of missiles
that incrementally hollow their way into the body of such an asteroid.
The material excavated out of the body would create a thin ring system
around the Earth, as I try to illustrate here:-

http://uk.geocities.com/aa_spaceagent/restricted/earth-ring.html

My main concern with such a project is one of SAFETY. I'd like to know
what a *safe* perigee (minimum) altitude would be necessary to prevent
orbital decay of ring material. I don't want any material from my
hypothetical ring system coming down toward the Earth under any
circumstances. Would the ring material be contained in a narrow plane
of fixed orbital incline, or would it scatter over time?

QUESTION: I am under pressure to demonstrate by way of a mathematical
model the dynamical stability of such a ring system, composed of small
particles being gravitationally influenced by the Earth and the Moon
by way of "3 body problem".

What are the analytical equations necessary to help demonstrate
*theoretically* that such ring particles would indeed be stable in
their orbital paths around the Earth? Or if not, how would I be able
to show this?

I would sincerely appreciate all help, as this is quite *pivotal* to
my research on this article.

Thanks for any support.
Abdul Ahad
AA Institute
Oct11-04, 01:06 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>\n\nabdul.ahad@ntlworld.com (AA Institute) wrote in message\n\n&gt; Would the ring material be contained in a narrow plane\n&gt; of fixed orbital incline, or would it scatter over time?\n&gt;\n&gt; QUESTION: I am under pressure to demonstrate by way of a mathematical\n&gt; model the dynamical stability of such a ring system, composed of small\n&gt; particles being gravitationally influenced by the Earth and the Moon\n&gt; by way of "3 body problem".\n&gt;\n&gt; What are the analytical equations necessary to help demonstrate\n&gt; *theoretically* that such ring particles would indeed be stable in\n&gt; their orbital paths around the Earth? Or if not, how would I be able\n&gt; to show this?\n&gt;\n\nBefore anyone spends too much time on this, I should mention that I\nhave since done some independent research and posted my findings on\nanother group in the sci.space category:-\n\n"... I hereby report that a ring system that is not oriented along the\nEarth\'s equator, which is emanating\nfrom a non-circular orbit of an asteroid, will scatter its particles\nat the fastest rate, and no Earth orbiting ring system could ever be\nformed in those circumstances. This is mainly due to the differential\nrates of precession of each ring particle\'s orbital nodes owing to the\nun-even (oblate) mass distribution of the Earth.\n\nOn the other end of the scale, a perfectly circular, concentric system\nof ring particles orbiting exactly co-planer with the Earth\'s\nequatorial plane has a very short term (a couple of years at most)\nchance of staying together in a ring formation. That\'s assuming an\norbital altitude of 40,000 km above the equator. However, such a\nparticulate ring system is then subject to two kinds of external\nperturbing influences: that coming from the Sun and that from the\nMoon, acting along the ecliptic plane and the plane of the Moon\'s\norbit, respectively. The combined effects of both these forces will\ncause the ring material to scatter into a \'band\' of +/- 15 degrees\ngeocentric latitude (30 degree spread around the equatorial plane)\nover several years.\n\nThe final conclusion is therefore no stable ring system would be\npossible around the Earth in the long term, hence any excavation\ndebris carved out of an Earth orbiting asteroid will require serious\ncontainment/safe disposal. Thus, such an orbital engineering project\nis not going to be viable around the Earth." - A. Ahad.\n\n\nIn addition, I am working on a short paper that will hopefully better\nillustrate the scattering of such a ring system over time, on my\nwebsite,\nhere:-\n\nhttp://uk.geocities.com/aa_spaceagent/restricted/earth-ring-dynamics.html\n\nBest,\nAbdul\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>abdul.ahad@ntlworld.com (AA Institute) wrote in message

> Would the ring material be contained in a narrow plane
> of fixed orbital incline, or would it scatter over time?
>
> QUESTION: I am under pressure to demonstrate by way of a mathematical
> model the dynamical stability of such a ring system, composed of small
> particles being gravitationally influenced by the Earth and the Moon
> by way of "3 body problem".
>
> What are the analytical equations necessary to help demonstrate
> *theoretically* that such ring particles would indeed be stable in
> their orbital paths around the Earth? Or if not, how would I be able
> to show this?
>

Before anyone spends too much time on this, I should mention that I
have since done some independent research and posted my findings on
another group in the sci.space category:-

"... I hereby report that a ring system that is not oriented along the
Earth's equator, which is emanating
from a non-circular orbit of an asteroid, will scatter its particles
at the fastest rate, and no Earth orbiting ring system could ever be
formed in those circumstances. This is mainly due to the differential
rates of precession of each ring particle's orbital nodes owing to the
un-even (oblate) mass distribution of the Earth.

On the other end of the scale, a perfectly circular, concentric system
of ring particles orbiting exactly co-planer with the Earth's
equatorial plane has a very short term (a couple of years at most)
chance of staying together in a ring formation. That's assuming an
orbital altitude of 40,000 km above the equator. However, such a
particulate ring system is then subject to two kinds of external
perturbing influences: that coming from the Sun and that from the
Moon, acting along the ecliptic plane and the plane of the Moon's
orbit, respectively. The combined effects of both these forces will
cause the ring material to scatter into a 'band' of +/- 15 degrees
geocentric latitude (30 degree spread around the equatorial plane)
over several years.

The final conclusion is therefore no stable ring system would be
possible around the Earth in the long term, hence any excavation
debris carved out of an Earth orbiting asteroid will require serious
containment/safe disposal. Thus, such an orbital engineering project
is not going to be viable around the Earth." - A. Ahad.


In addition, I am working on a short paper that will hopefully better
illustrate the scattering of such a ring system over time, on my
website,
here:-

http://uk.geocities.com/aa_spaceagent/restricted/earth-ring-dynamics.html

Best,
Abdul