Gimagine two artitcial satellites obating earth at the same distance one satellite has a greater man than the other one. What it true about there motion

Question

Gimagine two artitcial satellites obating earth at the same distance one satellite has a greater man than the other  one. What it true about there motion

anonymous · Answer

Do you mean that one has a greater mass than the other one?

If so, then the force of gravity in the satellite with greater mass is greater than that with the other one. And since the force of gravity supplies the centripetal $F_c$ making the satellites to orbit, you have the following equation that will lead us to a neat conclusion about their motion.

$F_c = F_g$

$\frac{mv^2}{r}=G\frac{mM}{r^2}$

$\frac{v^2}{r}=G\frac{M}{r^2}$ <-- mass $m$ cancels out.

$v^2=G\frac{M}{r}$ <-- Multiply both sides by $r$.

$v=\sqrt{G\frac{M}{r}} $ <-- Take the square root of both sides.

You can see here that their velocity is the same, independent of their masses, provided that they are orbiting the same planet of mass $M$ and the distance $r$ of the two from it is the same.