Question

Jupiter has a mass of 1.9*1027 kg and a radius of 69,900 km. G = 6.67*10-11 Nm2 /kg2 a. Find the acceleration due to gravity at its surface b. Find the speed of a satellite orbiting at a height of 10,000 km above its surface c) Find the cetripetal acceleration of the satellite

Answer 1

Mass of Jupiter is

Radius of Jupiter is

The gravitational force on an object of mass m at a distance r away from the center of planet, outside the planet is

(a)

The surface of the planet is at distance r=R from the center of the planet

By Newton's second law, force F acting on mass m accelerates the mass by amount a=F/m

So, the acceleration of an object of mass m at the surface of Jupiter is

Substituting given values

(b)

The satellite is distance above the surface of Jupiter.

The distance of satellite from the center of Jupiter is

Let m be the mass of the satellite, the gravitational force on the satellite is

Given the satellite is orbiting, let v be the speed of the satellite in the orbit. The centripetal acceleration required to keep the satellite in orbit is

The gravitational force provide the necessary centripetal force

Substituting values

(c)

The centripetal acceleration is