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Gravity mechanism predicts G to within 1.7%

  1. Jul 1, 2004 #1
    Proof that gravity constant G = (3/4)(H^2)/[(pi)(density)e^3]

    The acceleration of matter outwards in the big bang is a force (Newton's 2nd law) requiring a reaction (Newton's 3rd law). The reaction is the inward directed force of gravity carried by the fabric of space.

    Proof of 1.7% accuracy: http://www.wbabin.net/physics/cook2.htm

    Background info: http://members.lycos.co.uk/nigelbryancook/


    Nugent, Physical Review Letters (v75 p394), cites decay of nickel-63 from supernovae, obtaining H = 50 km/sec/Mps (where 1 Mps = 3.086x10^22 m). The density of visible matter at our local time has long been known to be 4x10^-28 kg/m3. However, White and Fabian in the March 1995 Monthly Notices of the Royal Astronomical Society, using the Einstein Observatory satellite data, estimate that invisible gas increases this density by 15%.

    Using these data, G = 3(H^2)/[pi(e^3)ρ] = 6.783x10^-11 Nm^2kg^-2, within 1.65% of the physical measurement for G of 6.673x10^-11 Nm^2kg^-2. (http://members.lycos.co.uk/nigelbryancook/)


    ‘Electronic Universe’ article (Electronics World, Vol. 109, No. 1804) proves G = 3(H^2)/(4 pi ρ). [Ref: http://cdsweb.cern.ch/search.py?f=author&p=Cook,+N and http://www.wbabin.net/physics/cook1.htm.

    H is the Hubble constant and ρ is the density of universe responsible for causing gravity by the inward reaction of 377-ohm physical space to the outward big bang; pi is the mathematical constant. Considering the density, it is highest at early times and thus density increases in the observable space-time trajectory, as we look further into the past with increasing distance.

    But the increasing spread of matter with increasing distance partly offsets this increase, as proven when we put the observed Hubble equation (v = Hr) into the mass continuity equation and solve it. For spherical symmetry, dx = dy = dz = dr. Hence: dρ/dt = -div.(ρv) = -div.(ρHr) = 3d(ρHr)/dr = -3ρH. Solving dρ/dt = -3ρH by rearranging, integrating, then using exponentials to get rid of the natural logarithms (resulting from the integration) gives the increased density to be ρe^(3Ht), where e is Euler’s constant (2.718 ...). In the absence of gravitational retardation (i.e. with the cause of gravity as inward reaction of space to the outward big bang), H = 1/t when H = v/r = c/(radius of universe) = 1/t, where t is the age of the universe, so e^(3Ht) = e^3 = 20.1 and observed G = 3(H^2)/[4pi(e^3)ρ].
    Last edited: Jul 24, 2004
  2. jcsd
  3. Jul 1, 2004 #2

    You might want to speak to these people then.

    Maybe you could speak directly to the graviton issue( refute Witten's claim, and place his derivation here as I am interested, even if it had to be a generalization for now) and detail how this would have been dismissed?

  4. Jul 2, 2004 #3
    Newton's third law of motion is that every action has a reaction, and the reaction to the big bang is the inward force of gravity. Along the visible space-time trajectory, whereby distance = speed of light x time (and gravity goes at light speed too), the Hubble law contains a true constant.

    (If we ignore the visible space-time trajectory, and try to calculate how far the stars are away after the light has travelled to us, then their distances will be further so the "constant" is not constant when considering absolute distances at a fixed time say 20 gigayears after big bang.)

    But on the space-time trajectory, where we deal with true observables which control gravity, it is constant because there v/r = constant = H.

    Now this constant implies acceleration into the past (greater distances), a = dv/dt = d(Hr)/dt = Hv = H(Hr). The acceleration of mass implies force (F=ma). Newton's third law of motion is that every action has a reaction, and the reaction to the big bang is the inward force of gravity.

    The physical space which causes this inward force is well described in electromagnetism.
  5. Jul 2, 2004 #4
    Thanks for taking the time and care in those explanations.

    One thing that really gave me a hard time was understanding the idea of the innate nature of curvature in the cosmos, but this becomes really easy once finding the Friedman equations and the curvature parameters.

    What also made this very easy to understand was the reality that gravity could indeed become very strong, and hence the nature of curvature much more defined?( you would have to correct here if this is wrong)

    So what happened and we now have to explain this gap in our thinking

    There are a lot of things happening in terms of expansion, at the same time this is happening?
  6. Jul 3, 2004 #5
    The Hubble constant is real in the space-time trajectory which we observe, and in which gravity travels at light speed along with visible light. The Hubble constant (H) says that observed (visible) velocity (v) from Doppler red shift of galaxy clusters is proportional to the distances of those galaxies (d), or v = Hr. Because distance r is proportional to time past, t, the rate of change of observable velocity with respect to observable time is the acceleration a = dv/dt = d(Hr)/dt = Hv = HHr. Newton’s third law states that the mass accelerating away from us is a force which has an equal and opposite reaction upon the fabric of space, causing the downward push, gravity.

    In "quantum gravity" there is the problem that the carrier particles, which are hypothetical but have nevertheless been named "gravitons" (which makes many people think that they have been observed), have to borrow energy using the Heisenberg uncertainty principle.

    The uncertainty principle says that the amount of uncertainty in the energy (and thus mass, by Einstein's E=mc^2) of the carrier particle is inversely proportional to the time that the energy is "borrowed".

    Since the distance the carrier particle can go is at most the speed of light multiplied by that time, it follows that there is a limiting range for quantum forces. This works well for short-ranged nuclear forces, but not for gravity and electromagnetism. In addition, for electromagnetism the QED force theory for short ranges (ignoring the distance limit) predicts 137 times the observed force as given by the Coulomb law.

    At present the official approach is to state that that the force carrier particles in electromagnetism and gravity have "no rest mass". Because they are never at rest, this is a little bit irrelevant, but if they had no transit mass then they would have no energy and thus would have an infinite range. The problem then is that, without mass, they would have no momentum to impart and would be unable to cause force.

    Quite apart from these issues, the quantum force field theory for electromagnetism offers no explanation for attractive forces in terms of how momentum is exchanged, and offers no explanation for the differences in force strengths between electromagnetism, gravity and the strong nuclear force.

    If you do the QED calculation, it gives you a force 137 times stronger than electromagnetism. This is equal to the strong nuclear force. In order to get the electromagnetic force using the official procedure, you divide this force by the factor 137 derived empirically by comparison with Coulomb's law. In order to get gravity, you divide by a still larger empirical factor, around 10^40, based upon Newton's law.

    My work is concerned with the mechanisms for the forces by way of imparting momentum.

    If you drop an apple, it gains momentum apparently from nowhere as it accelerates downward. This violates the law of conservation of momentum until you have a gravity proof which explains what is giving it momentum and why.

    As Feynman said, to imagine that the particles know a formula, and can look around them, see the masses and calculate them accurately, then move in accordance to the law, is a little bit hocus pocus. The law is useful, and Einstein's modification in general relativity to conserve the potential energy of the gravitational field, predicts that light is deflected by gravity twice as much as slow moving objects. It also introduces time dilation as a result of gravity, and so on.

    The only problem with general relativity is the lack of a mechanism, which means that it uses Newton's (really Laplace's) constant "G" without question. When we find that the mechanism for gravity is the equal and opposite reaction of space to the force from the acceleration of matter outwards in the big bang, we find that the furthest objects will not be slowed down, violating the gross application of general relativity to cosmology.

    I predicted this via the letters page of the October 1996 issue of "Electronics World" about two years before Saul Perlmutter discovered it using CCD computerised observations of distant supernova redshifts.
  7. Jul 3, 2004 #6
    In bold I higlighted your statement because as a student here, I wondered about the propogation question Michael brought up in regards to LIGO, and your statement.

    In essence, the relevance of gravitational waves is understood, so if we progress here in terms of the massless particles, photon as a interactive entity, and we see where such gravitational waves this too, then why not this interaction between the two? What are we really saying? We have chosen them to represent, as carriers.

    So your feelings about photon in respect of Gravitational Radiation and then I read through statements in regards to Hocus pocus of Feynmen?

    What is strange to me then is the way in which such quantum geoemtry might have something to say about this issue using discription of photons long and short and how would we tackle this in face of such propogation.

    To disavow credibility to answering orbital probabilites in face of gravitational wave generation as well why could we not have married the two into a quantum geometry. Even strings saids it is to fuzzy at that measurement, yet there are interactive capabilties in the issue of Glast that are truly forth coming?
    Last edited: Jul 3, 2004
  8. Jul 3, 2004 #7
    The "hocus pocus" expression is Feynman's, used in the final chapter of his book to describe the renormalisation of QED, the empirically necessary mathematical division by infinity to cancel infinity out, and so forth. It seems quite fair.

    String theory is a little bit speculative still. I agree with gravitational radiation theory as predicted by general relativity. This is an effect of the acceleration of neutral/uncharged mass, whereas photon radiation comes from the acceleration of charges.
  9. Jul 3, 2004 #8
    The discriptive pathways used in Feynmen's Toy models are very instructive.

    That we add this feature to a very dynamcial movement in the universe does not remove pathways from the iteractions taking place in that cosmo. I think we can add this feature to the questions of Quantum geometry, and seeing your efforts, spark something else for me in terms of the "esoteric,":) on self similarity that was given in terms of isometric relationships(Rydberg atoms), that have been toted as bogus. I find these very relevant(?) from my own perspective, to the cosmological and quantum world of association, inherent in orbital discriptions. Coincidence?



    This is speculation. But the topological feature of these varying states of progression needed some model for consideration, and from a interactive state, how would you do that if you had not considered the overall dynamics?

    Could we not add new toy model discriptions here to Feynmen model approaches? Photon graviton interaction? :smile:
    Last edited: Jul 3, 2004
  10. Jul 3, 2004 #9
    Well, I'm saying continuous emission and absorption of energy carries the energy which causes electromagnetic forces. This results from the continuous spin of particles, which has no time variation so the frequency is zero (no oscillations per second). Spinning something which is symmetric does not create oscillating waves, just continuous energy emission. Planck's theory describes the quantum emission from charges jumping between energy levels in an atom, which is a different situation from continuous emission from a spinning charged particle.

    As for the ether, I think that Professor H.A. Wilson puts it best in the 1959 4th edition of his book Modern Physics, which I quoted somewhere on the Physics Forums. Wilson, a brilliant nuclear physicist, pointed out that a vacuum has a magnetic permeability (in the equation of magnetic force) and an electric permittivity (in Coulomb's law of electric force), and that the no one has ever observed a space in which these values were zero.

    Because a space empty of physical properties has never been observed, it is unscientific to make up theories about it. When you hold two magnets with the poles nearby and feel the attraction or repulsion force between them, you do not need to theorise that magic occurs. If you observe a physical force being transmitted through "empty space" then you can measure properties of space.

    A particle ether, which is what a graviton mechanism would amount to - stripped of hocus pocus - would scatter photons of light in a diffuse pattern, rather than allow the smooth deflection of starlight by gravity which is actually observed during solar eclipses. In addition, a graviton particle ether would be likely to slow down planets and cause continuous drag on moving particles. The "Higgs Boson", a hyped-up particle ether invented by Peter Higgs in the early 1960s to explain inertial mass, is a bit too speculative and vague to convincingly explain what it sets out to do.

    The problem with maths, if you study the history of applied mathematics, is that it is very hard to do anything for the first time. Once people have beaten a track, it is a different story. If you go to a standard mathematician, they will try to solve a problem using standard methods, ie, obvious methods, quickly. These guys are good at speed solutions needed to get A grades, but it's another story altogether when years of dedicated trial-and-error work is needed.

    They don't have the imagination or dedication to follow up radical new ideas, so they all bunch up on one or two main roads, like superstrings (10 dimensions), and the entanglement interpretation of QED. Since they tend to get side-jobs as Referees for scientific journals, you find - surprise, surprise - that only these rain roads are illuminated with street lamps. The successful native paths are left in the dark (censored out).

    The only way of getting these problems past the suppression barriers is to put in effort to first make the proofs clear and then probably to pay to publish them as notices in mainstream publications. I'd be happy with an energy field in space composed of equal positive and negative electromagnetic fields. When you put an electron near a proton to form a hydrogen atom, the result is neutrally charged, but in fact the energy of the positive and negative fields in the surrounding space does not cease to exist, only the net electric field becomes zero, and the mass-energy remains in the positive and negative fields.

    A similar effect occurs in Young's double slit experiment, where energy arrives at the dark fringes out of phase, cancelling. When you calculate the energy for a few bright and dark fringes on the screen, the energy arriving in the bright areas is proportional to sin^2 x, where x is the scaled distance along the screen. Integrating this, you find that half the energy ends up in bright fringes and half in dark fringes. The dark fringes are produced by photons cancelling each other by interference. What happens to the energy, then, that lands up in the dark fringes?

    David A. Chalmers wrote a paper in the Feb 1997 issue of the journal Science World, in which he made holes in the dark fringes of a screen, using a 0.5 milliwatt red laser as the light source, and detected light passing through the dark fringes. It seems that unless there is a hole for the light to go through, the "cancelled" light energy is simply absorbed by the screen as non-oscillatory electromagnetic energy. The light areas are merely places where the uncancelled light is received and can be reflected back.

    To describe the 377 ohm fabric of space as a sea of normally cancelled-out positive and negative field energy, with a mass (given by m = energy divided by the square of the velocity of light) would be more sensible than speculating about unobserved gravitons or Higgs particles.

    The energy field, while having a zero electric charge because of the equal positive and negative charges in the universe, nevertheless has mass and its interacting with moving particles would be to resist changes in velocity, ie, to cause inertia and momentum. Hence we would get Newton's laws.
    Last edited: Jul 4, 2004
  11. Jul 4, 2004 #10

    Here are H.A. Wilson's remarks on the nature of space:

    "It has been supposed that empty space has no physical properties but only geometrical properties. No such empty space without physical properties has ever been observed, and the assumption that it can exist is without justification. It is convenient to ignore the physical properties of space when discussing its geometrical properties, but this ought not to have resulted in the belief in the possibility of the existence of empty space having only geometrical properties... It has specific inductive capacity and magnetic permeability." - Professor H.A. Wilson, FRS, Modern Physics, Blackie & Son Ltd, London, 4th ed., 1959, p. 361.

    Basically, we don't need to get involved in ether particles speculation, we can use measured properties of the fabric of space which carry magnetic force we can feel between magnets to prove that measurable properties of a physical medium in the fabric of space, "empty space", exist. Measurable properties are scientific, so the fabric of space is a physical reality. Nobody has ever discovered a space in which the electromagnetic permittivity and permeability are zero, so an "empty space" is purely speculation. A vacuum conveys magnetic forces. We measure this as the permeability of a vacuum.
    Last edited: Jul 4, 2004
  12. Jul 4, 2004 #11
    There is a interesting set of questions that come up in regards to background versus non background, and the way in which we describe the nature of this reality. By the respective tendencies, of LG or Strings this becomes specific.

    If going through the issues of GR, it was evident that such graduation in thinking would have moved the discussion of the gauss field , with coordinates measures understood in those magnetic fields, yet it was part and parcel of this graduation to understand that it was to leave Euclidean perspectives. So we recognized the curvture properties in the issues of gravity where none could have existed with the normal definitions of Euclidean?

    I have become confused bewteen your correspondance to the ether in context of the derivation of gravitational waves and further extension in the carrier as the graviton.

    If such a "pattern" is to disavow the photon in our recognitions of the work laid out for us in the historical determinations(em considerations), then I would have to ask if the interferometer has somehow been removed from this process?

    It was well evident to me that we are not talking about the esoteric nature of the medium, but of logical evdeince of energy being transferred to other means and propogation through the cosmos. The recognition of the spacetime fabric as well.

    So this takes us further to the question of Dimension then and its measure in regards to TEV measures. The Gap in the sense of the blackhole not only questioned the cosmological significance of the nature of this curvature but also what possibilties can exist, in the nature of the colliders.

    Does this seem consistent and respective of your post.

    Here is link for consideration

    I am still very green here
    Last edited: Jul 4, 2004
  13. Jul 4, 2004 #12
    Yes, it does seem consistent. If we agree that space has specific properties, the vacuum is physical reality. If you have a cubic metre of space in a vacuum, it is not an imaginary non-existent geometrical construction, but has measurable physical qualities (characteristic impedance, permittivity, permeability, and conductive velocity, c). The 19th century physics journals, and the internet of today, are both found to be loaded with hypothetical models and speculative particles which fill the vacuum. Einstein was at one stage praised for dismissing them in 1905, although he restored what he called an "ether" 1920 in his inaugural lecture at Leyden University, describing a physical space with properties of a continuum as well as electromagnetic properties.

    General relativity indicates, by the successful prediction of the smooth deflections of photons of starlight by the sun's strong gravity as seen during eclipses, that the fabric of space is not particulate. It is difficult to imagine how particles causing gravity could interact with particles (photons) of light without particle-particle scatter occurring.

    Electromagnetic theory says the impedance of the vacuum is a fixed 377 ohms, which is highly significant as radiation is only resisted once regardless of distance travelled in space (although particles diverge as they travel outwards, the individual photon is not retarded in proportion to distance travelled). The resistance of anything composed of particles is proportional to distance (thus, ohms/metre). A fixed, once-only impedance is different from the drag you get in particle fluids, so the fabric of space in general relativity is described as an "ideal fluid". After space is forced to flow around a particle, it continues doing so without resistance. You then have to apply force to stop the particle moving, to break down the wave flowing around it.

    The properties of matter such as inertia and momentum therefore accord with the properties of a space continuum implied by electromagnetism and general relativity.
    Last edited: Jul 4, 2004
  14. Jul 4, 2004 #13


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    Nigel, I notice nobody tells in the thread that your prediction is one to get G from a measurement of Hubble constant, not from first principles. Have they even read your webpage?
  15. Jul 4, 2004 #14
    The proof is a proof from first principles employing observable facts such as laws of motion, density, and the motion of stars which you mean when you refer to the Hubble "constant". I start with the observed facts. Your question says that the mathematical proof for the cause of gravity is a connection between the Hubble constant and Laplace's constant G.

    The important fact at stake is the mechanism explaining the connection, published seven years ago. The numerical connection made last week is further evidence that the proof is correct. By accounting fully for gravity, it excludes the possibility that there is another cause at work, such as a partial contribution to gravitation by mysterious "dark matter".

    The Hubble constant is often falsely stated as being the velocity divided by the distance, but the distance will increase while the light comes to us.

    Therefore, the observed constant is the velocity divided by the travel time of the light (this time is equal to the apparent observed distance divided into the velocity of light, not the actual distance where the star is now).

    The crucial distinction is that the observable fact, namely velocity being proportional to travel time, implies acceleration.

    You will notice that v/t is constant for continuous acceleration, and in fact has units of acceleration. In the frame of reference in which we see the stars, therefore, the Hubble recession is an acceleration of matter away from us in all directions. By Newton's 2nd Law, force = mass multiplied by acceleration, so there is a force in the observable space-time. By Newton's 3rd law, there is a reaction inwards. The calculation shows this is gravity.

    When you calculate the effect of this on the fabric of space, you get gravity. There is no possibility that gravity is a law of nature as well as being the result of the mechanism here, because it would then be double its measured strength.
    Last edited: Jul 4, 2004
  16. Jul 4, 2004 #15
    Newton's mechanics which includes:
    -the gravity law;
    -the 3rd law;
    -the 2nd law;
    -the 1st law;
    is inaccurate and here is whyIt is one of my sites on geocities . I'm not spaming. I'm just trying to sell what nobody is willing to buy.

    Try the law of lever.
  17. Jul 5, 2004 #16

    They're accurate enough for my purposes!
  18. Jul 5, 2004 #17
    Here's another 'objection' people sometimes make. In 1948, Dr Edward Teller took a breather from promoting his hydrogen bomb design for the benefit of the human race, and wrote a paper attacking a suggestion by Dirac that the gravity constant G varies with time.

    Teller "showed" that any increase in G in the past would - because the fusion rate depends on gravitational compression in the sun - have meant the oceans were boiling when life was supposed to be evolving.

    In fact, like his false hydrogen bomb design (only corrected by mathematician Stanislaw Ulam in 1951), his objection was false.

    As the gravity constant G increases, so would the the Coulomb law (which is about 10^40 times stronger).

    The increase in nuclear fusion in the sun due to the rising gravitational compression of the core would be offset by the rising Coulomb repulsion between protons.

    So you don't get what Teller predicted. (Just as well they didn't need his hydrogen bomb design of 1948! Although I admire his promotion of unpopular civil defence countermeasures and deterrence against the Soviet Union.)

    In order to fuse two nuclei (all nuclei have positive charge), you need to force them close enough together against electrostatic repulsion that the short-ranged strong nuclear force attracts them.

    Therefore, you always have the issue that a variation in the Coulomb electromagnetic force offsets a variation in the gravitational compression force, whatever stars you consider.

    Other people claim that G cannot vary because of properties of rocks dated by radioactive decay of uranium into lead, or similar. These claims fall down for the same reason. If there is any link between the mechanisms of different fundamental forces, then the dating of the rock's by decay products suffers from the issue that the force controlling the decay rate (the strong nuclear force or weak nuclear force, depending on the type of radioactivity) would vary. If you assume without proof one thing is constant in order to "disprove" the variation of something, the reasoning is circular!

    Basically, ridicule is not a very scientific approach. It is better to look for what is positive than political-type "shoot the messenger" activities!
    Last edited: Jul 5, 2004
  19. Jul 5, 2004 #18
    as far as i know G is called newton's constant.
  20. Jul 5, 2004 #19
    Give credit where it is due, Newton's Principia does not mention G, which was introduced by Laplace in the 18th century!
  21. Jul 5, 2004 #20
    Newton's three "Laws" of motion are observations, and in that sense not inaccurate. His gravity law is correct for the situation I analyse in my papers and obtain the mechanism of gravity from. Einstein's law states that the Ricci tensor is equal to 4 times pi times the energy tensor for the limiting everyday case (EXACTLY equivalent to Newton's Law), but a term subtracted from the Ricci tensor changes the result to 8 pi times the energy tensor in the case of light speed. Thus starlight passing near the sun experiences an acceleration of a = 2MG/r^2, whereas an apple dropped only a = MG/r^2. This difference in 1919 validated Einstein. His work in using tensors to account for the conservation of gravitational potential energy is brilliant. However, it lacks a mechanism for gravitation.

    Since you object to Newton, let's see what he actually said:

    Newton’s Principia corrected English translation from the Latin (revised 2nd edition, 1713).

    Preface dated 8 May 1686 Trinity College to first edition, Newton ends: ‘I heartily beg that what I have here done may be read with forbearance; and that my labours in a subject so difficult may be examined, not so much with the view to censure, as to remedy their defects.’ (Interesting, when you consider that Hooke had earlier ridiculed Newton’s arrogant paper on light; pointing out an error and humiliating him. Was Newton paranoid, or genuinely trying to avert censure? Today’s historian simply says ‘Newton was humble’.)

    Definitions: 1. Mass = density x volume, 2. Momentum = velocity x mass, 3. Inertia = force opposing acceleration of mass, 4. Force = action causing the acceleration of mass, 5. Centripetal force = force directed from all directions towards a point.

    ‘[Def.8] ... I here design only to give a mathematical notion of those forces, without considering their physical causes and seats.’

    Scholium: ‘... I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion... II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure... III. Place is a part of space which a body takes up... The motion of the whole is the same with the sum of the motions of the parts... IV. Absolute motion is the translation of a body from one absolute place into another...’

    ‘The effects which distinguish absolute from relative motion, are the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative...’

    'Axioms, or Laws of Motion: Law I. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

    [Adapted from René Descartes’ Principia Philosophiae of 1644, where Descartes discussed ‘rules of Nature’, writing: ‘If at rest we do not believe it is ever set in motion, unless it is impelled thereto by some cause. Nor that there is any more reason if it is moved, why we should think that it would ever of its own accord, and unimpeded by anything else, interrupt this motion.’]

    'Projectiles continue in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity.

    [Compare this ‘observation’ with Aristotle’s actual mechanism for the projectile, whereby some type of ether – air was not understood – moves around a moving object as a wave that pushes the arrow onwards, causing inertial resistance and momentum.]

    'A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotation, otherwise than it is retarded by the air. [A spinning top is not retarded by the air to any significant extent, but by heat friction of the point or bearing in motion.] The greater bodies of the planets and comets, meeting with less resistance in freer spaces, preserve their motions both progressive and circular for a much longer time.

    ‘Law II. The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. ...

    ‘Law III. To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. ... If you press a stone with your finger, the finger is also pressed by the stone. ... the changes of the velocities made towards contrary parts are inversely proportional to the bodies.’

    [i.e., momentum conservation means v2/v1 = m1/m2. This is very important, correcting the gross error in Descartes’ second ‘law of Nature’ of 1647. Descartes had written: ‘1. If two bodies have equal mass and velocity before they collide then both will be reflected by the collision, and will retain the same speeds they possessed beforehand. 2. If two bodies have unequal masses, then upon collision the lighter body will be reflected and its new velocity become equal to that of the heavier one. The velocity of the heavier body remains unchanged.’ This latter is wrong.]

    Book I. The Motion of Bodies. ‘Section II. The Determination of Centripetal Forces. Proposition 1. Theorem 1. The areas which revolving bodies describe by radii drawn to an immovable centre of force ... are proportional to the times on which they are described. For suppose the time to be divided into equal parts ... suppose that a centripetal force acts at once with a great impulse, and, turning aside the body from the right line... in equal times, equal areas are described... Now let the number of those triangles be augmented, and their breadth diminished in infinitum ... Q.E.D.’

    [Newton proves this using a Euclid-style geometric diagram instead of using differential calculus. The proof could be ridiculed by a bigot as being wishy-washy as it assume that it is permissible to treat a true elliptical orbit as if it is composed of lots of triangles with the force being assumed to act discretely as lots of small discrete impulses (causing each deflection of the planet towards the sun), instead of a continuously acting force! (By the same bigotry, you could deny that the exponential curve and sine curve are composed of lots of steps from a TEM wave charging a capacitor or going through inductor.) Newton nowhere writes the F=mMG/r2 law. Laplace introduced G in the eighteenth century. Planet speed, v = (circumference of orbit, 2 pi R)/(time taken for orbit, T). By Kepler’s third law, T squared over R cubed is constant. Hence centripetal acceleration (velocity squared over radius) for gravity does as the inverse square of radius. (Newton did not know the mass of the earth or sun very well and like Catt, didn’t get involved with anything which he felt might censure him as a charlatan, falling down only with the particle nature of light, false non-adiabatic equation for speed of sound, and other trifling factual errors.)]

    Book III. The System of the World (In Mathematical Treatment). General Scholium. ‘... Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets ... But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. ... And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the classical bodies, and of our sea.'

    In bold print I have highlighted Newton's statement "...I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis..." which I agree with and have used myself in proof of the mechanism of gravity, based upon observables (including Hubble expansion).

    Those who deny the observed Hubble expansion are refusing to put their eye to the telescope to see the redshift, or to check the red-shifted spectra for signs of scattering or tiring of light. Only one observable mechanism for the red-shift is proved, and that is the Doppler shift implying motion. The red-shifted spectra do not show the scattering which would indicate that the cause of the red-shift is dust scattering, not do they show any evidence for a red-shift which is greater at some frequencies than others (as would be implied by a tired light hypothesis, if the low energy frequencies got tired faster than higher frequencies). There is no scientific evidence and no scientific explanation for any cause beyond the Doppler effect and gravitational redshift. And since we know the masses of constant energy supernovae, their increasing redshifts with distance imply increasing Doppler velocity. This is scientific observation.
    Last edited: Jul 5, 2004
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