Gravity & Momentum: Direction's Role in Observation

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tommac
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does the direction of movement play a role in the gravitational effect on a distant observer.

Given two masses of equal rest mass. One traveling away from an observer and one traveling towards an observer both traveling at the same speed. Will both exert the same amount of gravity on the observer?
 
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Whatever i write here may be all crap.

If you consider slow speeds I don't think it will make much of a difference but maybe as the speeds increase "gravitational waves" ,as all other types of waves , may undergo the doppler effect.

But i don't think that's going to happen, gravity is just too different.
 
In classical gravity, no it will not matter. In General Relativity, it can. If the masses are really, really heavy, like black holes, or if they move close to the speed of light, yes, it will make a difference.

In linearized gravity, which is a good approximation for just about anything that isn't close to event horizon, a mass behaves like a charge in that a moving mass generates a so-called gravitomagnetic field. Just like magnetic field can deflect moving charges, gravitomagnetic field can deflect moving masses.