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'
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
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
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:
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.
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/4πmec. 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,
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
(Quotation from Physics World, January 1999, p.
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
The main report by Anderson et al in 'Physical Review Letters'
 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
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
H. Aspden, 'The Theory of Gravtitation', 1st Ed.,
(Sabberton Publications, P.O. Box 35 Southampton, England), 1960
& D. M. Eagles, Physics Letters, 41A, 423 (1972).
H. Aspden, Quantum
Uncertainties pp. 345-359 (NATO ASI Series B, vol. 162), Plenum Press,
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
Theory of Gravitation