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The question hints at an interesting tid-bit that arises in Physics, particularly in regard

to Relativity: The mass of an object figures in to any calculation of its inertia, and also

in to any calculation of the gravitational force between it and any other object. The

question is raised as to whether the object's inertial mass and its gravitational mass are

equal, and according to all the experimental and observational evidence so far, the

answer is yes, they're equal, and we only have to talk about the object's 'mass', without

making the distinction.

Assuming that that's true, then it's the object's 'mass' that increases with its speed,

and the mutual force of gravitational attraction between it and other objects changes

proportionately.

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Q: When an object accelerates to close the speed of light does its mass actually change or just its inertia if its mass increases then its gravitational force on objects should increase is this so?
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