Anom Accel of Pioneer 10 for v>(GM/r)^1/2

The Anomalous Acceleration of Pioneer 10 toward the sun of
about 10^-8cm/sec^2
at various distances r from the sun can be associated with
the fact that the velocity of the spacecraft is greater than the
orbital velocity the
spacecraft would have in a circular orbit at the same distance.
A rationale for this coincidence is given below.

The speed of the craft,now 12km/sec according to Pioneer
home page was about 36.67km/sec as it passed Jupiter while
29km per sec relative to the sun when it was on earth
orbiting the sun.
If the spacecraft was in orbit around the sun at a distance
r from
the sun it would have an orbital velocity of v from
GM/r^2=v^2/r
So its orbital velocity at a distance r can be compared to its
actual
velocity v*_r compared to v_r.
The hypothesis is proposed that the mass of objects is
proportional
to the total number of protons and neutrons in the object and to
the transverse speed
of the object wrt its attractive center eg the center of the
earth for objects on the
earth or in orbit around the earth, and the sun, for planets and
other
objects like the spacecraft beyond the earth's orbit.
The Pioneer 10 spacecraft is moving almost completely
radially away
from the sun such that the sine of the angle between its
trajectory and a radial line
to the sun is very small eg .001.
The spacecraft is also free to rotate.
According to this hypothesis there would be change in the
attraction
of the spacecraft to the sun proportional to the difference
between
(GM/r)^1/2 and v*_r. If r=10^12 then
((6.67)(10^-11)(1.99)(10^30)/(10^12))^1/2=3.66(10^3.5)=11.57km/se
c
about and the speed of the craft was probably more.


The attractive mass of an object on the earth directed to
the
center of the earth is assumed to be due to electrostatic dipole
inside protons and neutrons of length 10^-18 meters so that
(6.67)(10^-11) times [(1.67)(10^-27)]^2 = (9)(10^9)(es)^2 if
s=(.9)(10-18) is the gravitational force between two protons
one
meter apart represented as the force between two electrostatic
dipoles one meter part and colinearly and attractively oriented.
And so the gravitational force between the sun and the earth
could be written as the force between radially oriented dipoles:
GmM/R^2 = 9(10^9)mM[6.02)(10^26)]^2 times kK times s*S*
times
(2.56) times 10-38 divided by R^2 where the dipoles are es* and
eS* and e=1.6(10^-19)Coul.;this implies kKs*S*=
(.0079)10^(-61-11+38) =
10^-36 approximatelySince the Sun is .75H+.25He so that 1.75kg
of
Sun contains 6.02 times 10^26 molecules each of which contains
on
average 1.75 protons+neutrons so 1kg of the gaseous Sun
contains 6.02 times 10^26 protons+neutrons in a volume that is
larger of course than that of 1 kg of a solid planet; but 1kg of
any planet or the Sun contains the same number of
protons+neutrons. There are about 2(10^30) kg in the Sun. Hence
the Sun contains 6.02 times 10^26 times M or 12 times 10^56 and
the Earth contains 6.02 times 10^26 times m or 3.59 times 10^51
unit dipoles in the Earth. The total dipoles a
1.2(10^57)k(s)RS* and 3.59(10^51)K(S)Rs*.
Hence . Now RkS* and RKs* are the magnitudes of the dipoles
associated with the Sun and planet respectively where R varies
from around 1.5(10^11)meters 10^10 to 10^13 meters. But we also
know that the Earth's dipoles cannot be much larger than atomic
nuclei about 10^-15meters =RKs* that Ks*=10^-26 which implies
kS*=10^-10 and also RkS*= 10^(-10+11) so the dipoles on the
Sun are 10 meters in length or
the amount of charge in each dipole is more than e=^-19 etc.
We assume, following the Wilson Bartlett relation between
angular momentum and gravity,
that dipoles in protons and neutrons on planets that produce
their attraction to the sun is
due to the orbital speed of the planets and so a part of the
planet, like the spacecraft, when moving apart from the planet
at
a different speed
will have its dipoles change and so its attractive mass will
change.
see http://www.bestweb.net/~sansbury