Quote:
Originally Posted by Zuts
Gravity travels at a finite speed, the speed of light. In a binary system the companion star did not appear out of nothing, the mass has been there for ever.
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I agree, this is well said. We do not have to worry about "if something happens.." because nothing (in terms of sudden change of mass) will ever happen, so the centre of mass will remain where it was.. Even in the case of explosion of the star, the centre of mass will stay where it has been (because of preservation of momentum).
But when we have relativistic cas (asimetric explosion, for example) gravity waves could be generated.. and then we will have to worry about t e speed of light because this will change the state of the system and there will be a sudden change of the centre of gravity that will propagate at the speed of light.
Quote:
Originally Posted by Zuts
As the bodies orbit each other the center of mass for a n body system will change at the speed of light.
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This is something we have to think about more carefully..
In the closed system the preservation of momentum law (again) says that the centre of mass should not change at all (and not at the speed of light, but rather its position should be "updated" at the speed of light).
I think the momentum preservation works in the same way regardless of gravity propagates with finite or infinite speed...
It may turn out that we do not have to take c into account at all.