The gravitational mass of the an object is variable depending
on the surrounding matter distribution. So that its total
gravitational potential energy is equal to its rest mass.
From the conjecture, for any mass m
So for most masses the effective gravitational constant is
Small numerical constants are omitted for simplicity.
The conjecture gives an alternative solution of the flatness
problem of cosmology, as can be seen from equation (2).
For a mass as big as a galaxy equation (1) should be amended
r = radius of galaxy
m = mass of galaxy within radius r
or from (2)
Equation (5) predicts a reduction in the effective gravitational
constant for masses of high m / r ratio.
For ‘ordinary’ masses the m / r ratio
is insignificant compared to ,
but for galaxies it is significant.
For a star orbiting a galaxy at radius r, with
m being the mass of the galaxy within radius r
So stars moving at a constant velocity at different radii
means a constant m / r ratio.
Equation (5) predicts this constant ratio in the following
way. For any given radius r, if the mass within this
radius is such that the m / r value is higher than
an average value (k), then the effective gravitational constant
is lowered. This allows rotating matter to drift away from
the centre, thus reducing the m / r ratio at this
If m / r < k (for any given radius r)
then the effective gravitational constant is higher than average
attracting more matter to within this radius, increasing the
m / r ratio at this radius.
In this way a constant m / r ratio for spiral galaxies
can be maintained for different r, resulting in the
constant velocity of stars and the flat shape of the rotation
A reduction in the value of G at the centre of galaxies,
equation (5), may lead to the phenomenon of active galactic
nuclei and the emergence of jets.