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Suppose that there are two bodies A and B in a vacuum with equal rest mass M and at a distance D apart. The universal law of gravitation states that, if each is at rest relative to the other, the acceleration of one towards the the other is $\frac{MG}{D^2}$ where $G$ is a constant depending only on the units of time, distance and mass employed in the calculation.

Suppose now that body A at time $T$ is still a distance $D$ from body B but that its velocity as observed by B is directly away from B and of scalar value $V$. Is there a formula for the acceleration of A as viewed by B in terms of $M$, $G$, $D$ and $V$?

Thomas Fritsch
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Kelly McKennon
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    For the Newtonian formalism of gravity, the magnitude of the acceleration is not velocity-dependent. – HDE 226868 Feb 15 '16 at 16:29
  • @HDE226868… Is this known by experiment to be true, even for very high velocities? – Kelly McKennon Feb 15 '16 at 17:13
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    Possible duplicates: http://physics.stackexchange.com/q/47783/2451 and links therein. – Qmechanic Feb 15 '16 at 18:09
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    Regarding your follow-up question to HDE226868, at very high velocities (a significant fraction of the speed of light), the Newtonian model of gravity produces inaccurate results, and you need to use general relativity. – Red Act Feb 15 '16 at 19:03

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The rate of acceleration is independent of the rate of motion so this formula still applies even when the two objects are moving relative to each other. The only time you need to use a different formula is when you need to take general relativity into account such as when figuring out how Gravity bends light.

Anders Gustafson
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  • I take it then that I may infer from your answer that either (1) the question is avoided in special relativity or (2) the answer produced from the fundamental principles of special relativity is independent of the direction of the world-line of the body A? – Kelly McKennon Feb 15 '16 at 20:23