Respuesta :
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 [tex]F_{G} = F_{C}[/tex].
Gravitational force between Earth and Satellite: [tex]F_{G} = \frac{G \times M_e \times M_s}{R^2}[/tex]
Centripetal force of Satellite :[tex]F_C = \frac{M_s \times V^2}{R}[/tex]
Where G = Gravitational Constant
[tex]M_e[/tex]= Mass of Earth
[tex]M_s[/tex]= Mass of satellite
R= Radius of satellite’s circular orbit
V = Speed of satellite
Equating [tex]F_G = F_C[/tex], we get
Speed of Satellite [tex]V =\frac{\sqrt{G \times M_e}}{R}[/tex]
Thus the speed of satellite depends only on the mass of Earth.
