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?
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$\begingroup$ Related: physics.stackexchange.com/q/9371/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Jun 6, 2014 at 5:41
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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).
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:
But if we will add Anti-Earth at same distance from moon as earth it will look like this:
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)
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$\begingroup$ That what I don't ask ... I write my question in different word: If we have three entity 1)earth 2) moon 3) anti-earth and anti earth has same mass and same diameter as earth( means anti earth is carbon copy of earth except that it is made of anti material). Now what I am trying to say is if at first anti earth is not present and we measure center of gravity between earth and moon and now we add anti earth in this scenario. Moon is same distance from both earth and anti earth now then center of gravity will now change or not? $\endgroup$ Commented Mar 23, 2014 at 18:23
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$\begingroup$ @user43004 so you mean that if earth and anti-earth are rotating around each other and moon is between them? $\endgroup$– user21420Commented Mar 23, 2014 at 18:41
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$\begingroup$ Yes that what i mean now what will be scenario? $\endgroup$ Commented Mar 23, 2014 at 19:40
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$\begingroup$ @user43004 I have edited my answer (I have added results of that scenario in my answer) $\endgroup$– user21420Commented Mar 23, 2014 at 19:45