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Mass is said to be a source of gravity (I think:p), but if I were to travel into space. Would it change with respect to someone on earth? Since the gravity changes in space, but does it affect the change of mass? I mean since mass is its source, then the mass should affect it and not it.. Am I thinking right?

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No. Mass stays constant and never changes even in "zero gravity" environments.

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    $\begingroup$ Please consider extending your answer, otherwise make it a comment. $\endgroup$
    – rmhleo
    Feb 16 '16 at 20:04

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