A centripetal force of 220 N acts on a 1,800-kg satellite moving with a speed of 5,100 m/s in a circular orbit around a planet. What is the radius of its orbit?

Answer 1

Hi Adrienne, let's talk centripetal force! A centripetal force is a "center-seeking force," and, from what we know about uniform circular motion, a force pointing inwards to the center of a circle is necessary for an object to revolve! In this case, our uniform circular motion is the circular orbit of the satellite.

From uniform circular motion, we know that the centripetal force required to keep an object of mass m revolving at speed v and radius r is

F_cent = mv²/r.

The problem gives us F_cent = 220 N, so all that is left for us is to solve for r with a little algebra:

r = mv²/F_cent

Substituting m = 1800 kg, v = 5100 m/s as well gives

r = 2.1 × 10⁸ m.