The satellite moves around the planet in a circular orbit at low altitude at a speed of 6 km / s

The satellite moves around the planet in a circular orbit at low altitude at a speed of 6 km / s. What is the radius of the planet if the acceleration of gravity on its surface is 7.2 m / s2?

v = 6 km / s = 6000 meters per second – the speed with which the satellite moves around the planet;

g = 7.2 meters per second squared – the acceleration of gravity on the surface of this planet.

It is required to determine r (kilometer) – the radius of this planet.

According to the problem statement, the satellite moves in a circular orbit at low altitude. Then, since the satellite moves only under the influence of the gravity of the planet, then the acceleration of free fall is the centripetal acceleration of the satellite:

g = a (q) = v ^ 2 / r, hence:

r = v ^ 2 / g = 60002 / 7.2 = 36,000,000 / 7.2 = 5,000,000 meters = 5,000 kilometers.

Answer: the radius of the planet is 5000 kilometers.