Physics Problem: Magnitude of the gravitational force

Question

A 1,120-kg satellite is in a circular orbit around a planet. The satellite travels with a constant speed of 3,960 m/s.

The radius of the circular orbit is 3.80 × 10^6 m.
Determine the magnitude of the gravitational force exerted on the satellite by the planet.

 

Please Explain how you got your answer and what formula you used. Thanks.

Answer 1

Note that for a circular orbit, the gravity force matches the centripetal force which is F = mv²/r.

 

For the given satellite it is

 

F = mv²/r = (1120 kg)(3960 m/s)² / (3.80×10⁶ m) ≈ 4600 N

 

Note that the final units are Newtons and that I only kept two significant digits because that is the accuracy of the least accurate piece of information, the orbital radius.