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If we put earth like planet made up of antimatter (same mass of earth, same diameter etc..) with same distance from moon as current distance between earth and moon then center of gravity of moon and earth will change or not? Why?

Qmechanic
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user43004
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In short, answer is no. Gravity center won't change. For example imagine electron and positron. After measuring I will get that Mass of electron and positron are same: $9.10938291 × 10^{-31}$ $kg$. So electron and positron have same mass but different charges (Charge of electron is $-1.60217657 × 10^{-19}$ $coulombs$ and charge of positron is $1.60217657 × 10^{-19}$ $coulombs$). Charges have no effect on gravity center. And if mass is same why should gravity center change. (Gravitational Force depends on mass (and radius) $F=G\frac{Mm}{r^2}$)

Here's image of Hydrogen and Anti-Hydrogen atom (Only Charges are different not masses).

enter image description here

So in conclusion Anti-Earth and Anti-Moon will have same gravity center as normal Earth and Moon.

EDIT: Center of gravity of earth and moon is:

enter image description here

But if we will add Anti-Earth at same distance from moon as earth it will look like this:

enter image description here

And Center of gravity of this system will be at moon (Because Anti-Earth have same mass (Particle and its Anti-Particle have same mass), radius and distance from moon as Earth. But it will be Until Earth will meet Anti-Earth and they will annihilate).

(Sorry for my very poor drawing)