The Einstein field equation for gravity uses the stress-energy tensor, rather than just mass, to determine the gravitational force acting between two bodies. When spacetime curvature is small and relative velocities are much less than the speed of light, this force is well-approximated by Newton's law of gravity (F = G*M1*M2/R^2)(adsbygoogle = window.adsbygoogle || []).push({});

My question is, how is the force modified when the bodies' relative velocity approaches the speed of light? I presume the other terms in the stress-energy tensor (T11, T12, etc.) would come into play, but I am not sure exactly how. Would the bodies' relative motion amplify (or reduce?) the gravitational force that each one feels from the other?

To clarify, I'm not thinking of curved spacetimes such as near a black hole. This would be a case where spacetime is still nearly flat, only with high relative velocity, such as a spacecraft approaching a planet at nearly the speed of light. Does the planet's gravity well appear any stronger or weaker due to the craft's velocity?

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# Gravitational Force between Moving Bodies

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