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) = (G * M_e * M_s)/(R^2)`

Centripetal force of Satellite :
`F_C = (M_s * 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 =(√(G * M_e))/(R)`

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