Question

The orbital speed of a satellite moving in a circular orbit around the earth is $v_o$. If another satellite having half the mass of the first satellite has to revolve in some orbit, then determine its orbital speed.

Answer 1

Orbital velocity :

The velocity of a satellite moving around a central body is given by $v=\sqrt{\frac{GM}{R}}$where G= gravitational constant, M is the mass of the central body, and R is the radius of the orbit.

Given data :

The orbital speed of satellite 1 =$v_o$

Let $m_1$ be the mass of satellite 1

For another satellite, let mass be $m_2$

Given, $m_2=\raisebox{1ex}{$m_1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

From the above formula, we can see that orbital speed is independent of the mass of the satellite. It depends only on the mass of the central body and the radius of the orbit.

Thus, the orbital speed of the second satellite is the same as that of the first, which is $v_o$.