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I would like to ask about gravitational mass. I know inertial mass is changing by motion (speed) according to $m=\frac{m_o}{(1-v^2/c^2)^{1/2}}$ And also that is inertial mass which sits in $E=mc^2$. If the statements above is correct, now how about gravitational mass? Does it change with motion (speed)? And what mass should be used for general gravitational formula $F=\frac{GmM}{r^2}$? should we use $m_o$ (rest mass) regardless of speed of the object? Or should we use $m=\frac{m_o}{(1-v^2/c^2)^{1/2}}$ to substitute in $F=\frac{GmM}{r^2}$? In other words does mass equivalence principle (inertial mass=gravitational mass) hold in high speeds?

Qmechanic
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Ebi
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    It is generally the convention to use rest mass to be "the mass" of an object, see here. – Charlie Aug 04 '20 at 10:40
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    Is the concept of relativistic mass that brings you here. I am sure you will get a nice answer. This is again a demonstration that the concept of relativistic mass can be handled by the persons who already know what it is. Basically nothing than a formal trick to feel back in classical mechanics and therefore abused (hopefully less and less) by teachers, popular media, and professionals, too. – Alchimista Aug 04 '20 at 10:47
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  • Relativistic/inertial mass is a failed concept. It makes mass directional - is that really what you want? 2. You cannot use the Newtonian gravitational formula with either special relativity or general relativity, however you define your mass.
    • – m4r35n357 Aug 04 '20 at 10:51
  • @m4r35n357 Thanks for your response. Could you please elaborate why "cannot use the Newtonian gravitational formula with either special relativity or general relativity, however you define your mass"? – Ebi Aug 04 '20 at 11:00
  • For the Newtonian gravitational formula subquestion (v3) see https://physics.stackexchange.com/q/122319/2451 – Qmechanic Aug 04 '20 at 11:23
  • @Ebi Special and General Relativity are completely separate theories to Newtonian physics, and have their own (different) formulas and relationships. You have to learn them in their own right, you can't just combine parts of one theory with parts of another. Does that help? – m4r35n357 Aug 04 '20 at 13:18