Answer to Question #116040 in Astronomy | Astrophysics for Joana

Question

Two satellites are at the same distance from the Earth. If one of the satellites has a mass of (m) and the other has mass of (2m), which one will have the smaller acceleration?

Answer 1

Use the universal gravitation law to calculate the acceleration due to gravity. The planet with mass M attracts an object with mass m located at a distance R+h from the planet's centre. On the other hand, the body is subjected to the acceleration due to gravity g:

$$G\frac{Mm}{(R+h)^2}=mg,\\ \space\\ g=\frac{GM}{(R+h)^2}.$$

As we see, the acceleration does not depend on mass of the satellites.