- #26

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That might be an interesting exercise. I think the best approximation so far for time dilation of multiple masses is the equation I gave in #16 along with the provisos and limitations mentioned. Simply sum or integrate all the all the potentials of the points masses and insert the total potential into the gravitational time dilation equation.Right, it would only follow if all of the masses and observers are static. That would not be so with an orbitting smaller body, true, where kinetic properties would also need to be accounted for, but I am not considering that, only static contributions. Perhaps you could think of the smaller body as accelerated upon a constantly accelerating platform. If a smaller body were added to the larger one, say a star, then it would be held up by the same process that holds up the star, the internal pressures. The overall reason I am considering only static bodies is not to determine some multiple body orbital problem, which would be extremely complex, but rather to integrate all of the point masses of a static non-rotating sphere of uniform density to find the overall time dilation at some r by considering the contributions of the time dilations for all of the static point masses that make it up.