Question

A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R=1.9 x 10⁷ m.  The mass of the planet is M = 4.4 x 10²⁴ kg. 

Part (a) Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite.

Part (b) Express the magnitude of the centripetal acceleration a, of the satellite in terms of the speed of the satellite v, and R. 

Part (c) Express the speed v in terms of G, M and R. 

Part (d) Calculate the numerical value of v, in m/s.