G CONSTANT

THE CONSTANT OF GRAVITATION

An Anomaly that Challenges Orthodox Theory!

Copyright, Harold Aspden, 2000

Recently there has been a breakthrough of enormous significance on the gravity issue. Something new concerning the constancy of G has been discovered by exploration of space in the vicinity of the solar system. It has been discovered from analysis of the motion of several spacecraft used to probe regions close to our solar system that, at least up to a range of 60 A.U., there is a small additional constant rate of gravitational acceleration drawing matter towards the sun. As used here 'constant' means invariant with distance from the sun. Such a phenomenon is quite surprising as it implies a breakdown of accepted gravitational law unless one accepts that there is some dispersed gravitational influence akin to that of matter permeating the vacuum. It is as if Einstein's 'space-time' itself exhibits mass, implying that the space metric has a quite small but yet significant mass density.

This discovery leads one to imagine that space devoid of matter nevertheless does contain something akin to matter that is uniformly distributed and comprises N quasi-particles of mass m in unit volume, the expression 'quasi-particle' being used here for want of a more descriptive term, given that the scientific community has no idea what this 'something' might be.

Now what we do know about space is that it contains something which exhibits a temperature, this temperature being 2.7 K in the near vicinity of Earth. It is the temperature of the cosmic background and, from measurement of the anisotropy of the intensity of its radiation, we know that our solar system moves through that heat bath at a speed of the order of 350 km/s.

It is tempting therefore to suggest that each of those N 'quasi-particles' in unit volume has an energy quantum determined by that temperature T and Boltzmann's constant k. Given then that energy exhibits a mass property, a real mass property that gravitates, we can argue the case that space does have a real mass density, the mass density of the thermal energy.

This does not alter the primary feature of free space, its uniformity and its equilibrium with itself, which conceal its very existence save as a medium that can store energy. This medium, if devoid of thermal effects, will not exert a gravitational force on matter, just as matter does not exert force on free space. The reason is that force has to have a direction and one confronts some very difficult questions concerning the boundaries of space if the gravitating action of an enveloping and indefinitely bound mass density has to be summed to determine that direction. One simply must assume that the free space medium contrives to elude detection by somehow finding a state of equilibrium which avoids creating such a force.

The situation of special interest is that arising from the gravitational effect of the sun upon that thermal mass density. Their interaction involves gravitational energy potential, which, being a negative quantity, must offset a positive energy counterpart seated in the space medium. Accordingly, for each unit of that cosmic background of thermal energy, there is an equal negative amount of gravitational potential energy that is related to the presence of the sun. This energy has the property needed to define direction and so assert a force action on a space craft immersed in that gravitational potential energy produced by the sun's interaction with the enveloping space medium.

We may now formulate the additional gravitational force which this produces on the spacecraft. This force acting on unit mass of the spacecraft distant R from the sun is directed towards the sun and is G/R² times the mass equivalent of the total energy of the gravitational potential of that thermal mass density of space contained within a sphere of radius R centred on the sun. If the thermal energy of a 'quasi-particle' is kT and there are N such particles in unit volume of space, the thermal mass density is NkT/c². We multiply this by GM/Rc², where M is the mass of the sun, c being the speed of light in vacuo, to find the gravitational potential of unit volume of the thermal mass density. Then our task, after introducing the factor G/R², is to integrate over a range of elemental spherical shells of space to find the overall force acting on unit mass of the spacecraft.

The integral has the form (G/R²) times the integral from 0 to R of:

4πR²(GMNkT/Rc⁴)dR
which is:
2πG²MNkT/c⁴
Note that this is a force on unit mass or rate of acceleration that is in no way dependent upon R, the distance from the sun. It is a constant rate of acceleration exactly of the form observed by the NASA tests.

Note further that the value of this constant, as measured, tells us the value of N, given that we know the values of all the other terms. Now, of course, all this may seem to be hypothesis designed to give a result not dependent upon R. However, there is a converse approach to consider. Some 40 years ago [Aspden, 1960], long before NASA launched their satellites that detected this new gravitational phenomenon, the value of N was determined by a theoretical analysis of the nature of the photon. It would indeed be significant if N as predicted 40 years ago happened to have precisely the value we find from the above equation. This is in fact the case and so one must at least admit that the argument we have relied upon is substantiated by the further evidence now afforded by the NASA satellite data.

The value of N is 3.87x10³⁰ per cc. It was derived from analysis delving into the quantum properties of a space medium having everywhere an intrinsic property of determining the value of the fine-structure constant, its reciprocal 137.036 being shown to be 144π(r/d), where r is h/4πm_ec. From standard physical data r has the value 1.93x10^-11 cm and so d is determined as 6.37x10^-11 cm and, N being 1/d³, this tells us the value of N. [Aspden & Eagles, 1972]. Alternatively, for an extensive account leading to the derivation of N see the NATO ASI Series reference [Aspden, 1986].

Using this value of N and the solar mass M of 2x10³³ gm, Boltzmann's constant as 1.38x10^-16 erg/^oC, G as 6.67x10^-8 cgs. units and c as 2.998x10¹⁰ cm/s one can derive the anomalous acceleration as a function of T. It is found to be 3.69x10^-8 cms^-2 for each degree Kelvin of the general cosmic background temperature.

This may be compared with the reported anomaly in the recorded motion of three spacecraft: Pioneer 10, Pioneer 11 and Ulysses as they moved out of the solar system upon completing their main missions, that of exploring the outer planets.

"The spacecraft move as if they they were subject to a new, unknown force pointing towards the sun. This force imparts the same constant acceleration, of about 10^-7 cms^-2 to all three spacecraft, about ten orders of magnitude less than the free-fall acceleration on Earth."

(Quotation from Physics World, January 1999, p. 20).

Now, comparing this result with the theoretical value deduced above, we find that T is 2.7K, which is the temperature we measure as that of cosmic background radiation.

This author [Aspden, 1993] has, incidentally, in the periodical 'Physics Education', published bimonthly by the Institute of Physics in U.K. as inspiration for those who teach physics, already drawn attention to the fact that the 2.7K cosmic background radiation temperature is local evidence of the Principle of Conservation of Energy in the vacuum and shown how gravitational potential energy, as a deficit energy state, is balanced by the thermal energy of the vacuum. It was there explained that the energy quantum kT was used rather than 3kT/2 because the mode of thermal energy storage involves motion having only two degrees of freedom.

It may be further noted, as can be seen from that 1972 reference, that the space medium has a small residual component of energy needed to elevate it from a zero state to one in which those 'quasi-particles' satisfy an odd integer space occupancy relationship with the electron. The reason for this was the scope for their transitional involvement in the creation of virtual particles in electron and positron form. The data presented in that paper indicated that the reciprocal of the fine-structure constant would be 137.017 and not 137.036, as measured, were it not for this priming energy state. This odd integer space accommodation requirement amounts to an enhancement of about one part in 7200 and corresponds to a thermally-related speed of those 'quasi-particles' of c/7200, which, from the data presented in that paper, can be seen to be 3.2x10^-16 ergs per particle. Equating this to kT then gives a cosmic background temperature of 2.3 K. This is somewhat lower than the measured cosmic background temperature of 2.7 K in the near vicinity of Earth.

Using this lower 2.3 K temperature to determine the rate of acceleration towards the sun we get 8.48x10^-8cms^-2 and so one has reason to predict that the cosmic background temperature in the near vicinity of the sun is actually higher than the steady state background temperature prevailing in outer space. That acceleration as measured by the three space craft should reveal this and indeed it does.

The main report by Anderson et al in 'Physical Review Letters' [1998] tells us that Ulysses measured a higher anomalous acceleration rate of (12+/-3)x10^-8cms^-2 over the range of 1.3 to 5.4 astronomical units, but over the range 40 to 60 astronomical units Pioneer 10 and Pioneer 12 measured (8.09+/-0.20)x10^-8cms^-2 and (8.56+/-0.15)x10^-8cms^-2, respectively.

If the cosmic background temperature is higher in the 1.3 to 5.4 A.U. range than in the 40 to 60 A.U. range then there is a greater energy density producing an anomalous gravitational mass density in that inner range. It will affect the gravitational rate of acceleration acting on a spacecraft and make the rate of anomalous acceleration larger in that inner range.

Here then, as more data are collected from future space probes, one can see scope for research directed at proving the existence of a real space medium which exhibits quasi-mass properties owing to the effects of gravitational potential energy.

References
H. Aspden, 'The Theory of Gravtitation', 1st Ed., (Sabberton Publications, P.O. Box 35 Southampton, England), 1960
H. Aspden & D. M. Eagles, Physics Letters, 41A, 423 (1972).
H. Aspden, Quantum Uncertainties pp. 345-359 (NATO ASI Series B, vol. 162), Plenum Press, 1986.
H. Aspden, Physics Education, 28, 340 (1993).
J. D. Anderson, P. A. Lang, E. L. Lay, A. S. Liu, M. M. Nieto & S. G. Turyshev, Physical Review Letters, 81, 2858 (1998).

The above was an Essay submitted to the GRAVITY RESEARCH FOUNDATION as an entry for their YEAR 2000 COMPETITION. The author recorded his credentials as 'Dr. Harold Aspden, now retired, formerly Visiting Senior Research Fellow at Southampton University in England'. The Essay was not judged as deserving a mention in the published listing of the successful prizewinners and those deserving commendation.

******** H. Aspden August 29, 2000

If you wish now to see the next Essay in this 2000 series then press:
The Theory of Gravitation