Pioneer and the solar system

The quantification changes the Newton's law . The acceleration is given
by A= -a-GM/rr . a=Hc and H is the Hubble's constant . This formula is given
by an equation , which is in the site http://perso.orange.fr/claude.morichon
in the paragraph " Newton's law" . This formula gives a potential
U=ar -GM/r , and with this potential the dark matter is completely out ,
and the problem of Pioneer is resolved .
Therefore it is necessary to confirm this formula . If this formula
is good we have a displacement of the perihelion of the planets , which is
given by 6,28 abb/GM multiplied by the square root of 1-ee . e is the
eccentricity , b the half axis and M the mass of the sun .
For Mercury we have 7" per century . It is not good for the Relativity
..But it is necessary to have a new examination of the action of the other
planets . It seems we have equalization .
Perhaps if we use Jupiter it is possible to have a verification of the
formula , but the complete calculation is hard .

marie-morichon wrote:

The quantification changes the Newton's law . The acceleration is given
by A= -a-GM/rr . a=Hc and H is the Hubble's constant . This formula is given
by an equation , which is in the site http://perso.orange.fr/claude.morichon
in the paragraph " Newton's law" . This formula gives a potential
U=ar -GM/r , and with this potential the dark matter is completely out ,
and the problem of Pioneer is resolved .

http://perso.orange.fr/claude.morich...itation-01.htm

The equation on your page is

acceleration = (GM/r^2) [ 1 + GM/r^2 * 1/a]

The deviation from Newton's law is:

anomalous acceleration = (Gm/r^2)^2 * 1/a

= (GM)^2 / (a*r^4)

If 'a' is a constant, the anomaly should fall as the
fourth power of the distance, but the observed
anomaly is constant. To explain that, you need
to show that your value 'a' decreases as the fourth
power of the distance of the craft from the Sun:

a = k / r^4

where k is a constant. The value would be

k = (GM)^2 / a_P

where a_P is the Pioneer anomaly or 8.74*10^-8 m/s^2
and GM is the value for the Sun.

George