Question

A spacecraft is in orbit around a planet. The radius of the orbit is 2.9 times the radius of the planet (which is R = 71498 km). The gravitational field at the surface of the planet is 24 N/kg. What is the period of the spacecraft's orbit? [Hint: You don't need any more data about the planet to solve the problem.]

Answer 1

Well, what the gravitational force at the orbit? It must be
\[ \frac{24}{2.9^2} \ N/kg \]

Answer 2

From that you can find the speed of the spacecraft. And you can calculate separately the circumference of the orbit. Therefore the time required to complete one orbit.