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PIONEER ANOMALY AND COSMIC DECREASE OF GRAVITY
The modified Hubble-law

By Louis Nielsen
http://www.rostra.dk/louis

THE PIONEER-ANOMALY.
When all known forces acting on the Pioneer spacecrafts are taken into
consideration, a very small but unexplained force remains. It appears
to cause a constant sunward acceleration for both spacecraft.
It is observed that the Pioneer spacecrafts has a negative
acceleration-anomaly about
a(anomaly) = 8*10^(-10) m/s^2.

COSMIC DECREASE OF GRAVITY. THE MODIFIED HUBBLE-LAW.
In the following considerations about a modified Hubble-law where the
Hubble-function H(T) is determined by a decreasing gravitational
‘constant’ G according to the relation:

(1)  H(T) = - (dG/dT)*(1/G) = (1/3)*(1/T)

In equation (1) (dG/dT) is the time derivative of the variable
decreasing gravitational ‘constant’ G and T is the actual age of the
Universe.
The mathematical connection between H(T) and T gives a hyperbola
curve.

The modified Hubble-law is given by:

(2)  v(T) = H(T)*D(T)

In equation (2) v(T) is the radial velocity of an object at the time T
the actual age of the Universe and D(T) is the distance from an
observer to the object at the time T.

By differentiation of the velocity in equation (2) we get the
acceleration a(T) of the object at the time T when it is in a distance
D(T). We get:

(3)  a(T) = (- 2/9)* (D(T)/T^2)

From equation (3) we see that the acceleration a(T) is negative. The
velocity v(T) of the object is decreasing.

We can rewrite equation (3) so we have a relationship between a(T),
v(T) and T. We get:

(4)  a(T) = (-2/3)* (v(T)/T)

From equation (4) we see that the negative acceleration, the
deceleration, of a given object is inversely proportional to the
actual age T of the Universe and directly proportional to the actual
velocity v(T).

If T = 13*10^9 years = 4.1*10^17 sec and v(T) = 1*10^7 m/s (greater
than the real velocity) then we get a very small value for the
acceleration a(T) given by:

(5)   a(T) = - 0.2*10^(-10) m/s^2

The value in (5) is of the order of the measured acceleration-anomaly.

Is the observed acceleration-anomaly of the Pioneer Probes caused by a
cosmic decrease of the gravitational ‘constant’ and maybe explained by
the above considerations?

Best regards
Louis Nielsen
Denmark
http://www.rostra.dk/louis