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Conjecture: 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 to


r = radius of galaxy
m = mass of galaxy within radius r

giving


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 radius.

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 graphs.

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.

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