Question

The equation for the speed of a satellite in a circular orbit around the earth depends on mass. Which mass?

Answer 1

Question:

The equation for the speed of a satellite in a circular orbit around the Earth depends on mass. Which mass?

a. The mass of the sun

b. The mass of the satellite

c. The mass of the Earth

Answer:

The equation for the speed of a satellite orbiting in a circular path around the earth depends upon the mass of Earth.

Option c

Explanation:

Any particular body performing circular motion has a centripetal force in picture. In this case of a satellite revolving in a circular orbit around the earth, the necessary centripetal force is provided by the gravitational force between the satellite and earth. Hence $F_{G} = F_{C}$.

Gravitational force between Earth and Satellite: $F_{G} = \frac{G \times M_e \times M_s}{R^2}$

Centripetal force of Satellite :$F_C = \frac{M_s \times V^2}{R}$

Where G = Gravitational Constant

$M_e$= Mass of Earth

$M_s$= Mass of satellite

R= Radius of satellite’s circular orbit

V = Speed of satellite

Equating  $F_G = F_C$, we get  

Speed of Satellite $V =\frac{\sqrt{G \times M_e}}{R}$

Thus the speed of satellite depends only on the mass of Earth.