<h3><u>Question: </u></h3>
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
<h3><u>Answer:</u></h3>
The equation for the speed of a satellite orbiting in a circular path around the earth depends upon the mass of Earth.
Option c
<h3><u>
Explanation:
</u></h3>
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
.
Gravitational force between Earth and Satellite: ![F_{G} = \frac{G \times M_e \times M_s}{R^2}](https://tex.z-dn.net/?f=F_%7BG%7D%20%3D%20%5Cfrac%7BG%20%5Ctimes%20M_e%20%5Ctimes%20M_s%7D%7BR%5E2%7D)
Centripetal force of Satellite :![F_C = \frac{M_s \times V^2}{R}](https://tex.z-dn.net/?f=F_C%20%3D%20%5Cfrac%7BM_s%20%5Ctimes%20V%5E2%7D%7BR%7D)
Where G = Gravitational Constant
= Mass of Earth
= Mass of satellite
R= Radius of satellite’s circular orbit
V = Speed of satellite
Equating
, we get
Speed of Satellite ![V =\frac{\sqrt{G \times M_e}}{R}](https://tex.z-dn.net/?f=V%20%3D%5Cfrac%7B%5Csqrt%7BG%20%5Ctimes%20M_e%7D%7D%7BR%7D)
Thus the speed of satellite depends only on the mass of Earth.