question on gravitational field interaction

[VinPhys]

If 2 masses are moving apart or towards each other, does the force of gravity between them vary relativistically? If a gravitational field propagates at C, and a mass originating the field is moving relative to another mass, then is a Lorentz factor needed to describe their gravitational interaction?

That is:

The Force of attraction given by the simple Newtonian equation:

Can be rewritten by substituting:

 

 

If this is mathematically correct, then 2 objects moving away from each other at velocity greater than C should experience repulsive (or anti) gravity, and in a galaxy where there are many mass pairs where v2/c2 is non-trivial, there will be stronger than expected gravitational attraction.

Can the cumulative gravitational force on an object be approximated by the sum of pairwise forces of relativistic gravity where each pairwise force is a function of the relative velocity between masses?

[MigL]

You are mixing up Newtonian gravity with relativistic gravity.

 

Relativistic gravity is explaned by GR and is a geometric theory, not a field based theory.

( Although AJB will probably correct me again that geometry IS the field )

[studiot]

 

You are mixing up Newtonian gravity with relativistic gravity.

 

Agreed.

 

Don't forget that General Relativity (which deals with gravity) operates in 4D Minkowski space.

 

In Newtonian physics (that you are describing) the gravitational effect and contant G is due to mass density in 3D space.

 

In General Relativity these effects are due to momentum density in 4D Minkowski space.

Edited April 23, 2014 by studiot

[ajb]

You are mixing up Newtonian gravity with relativistic gravity.

That is exactly the problem here.

 

In Newtonian gravity it is only the mass of the objects, which would be understood as the rest mass of the objects that matters. When we pass to general relativity the energy does matter.