# Geosynchronous orbit

## Homework Statement

1. One of Jupiter's moons has a mass of 4.80E+23 kg and a radius of 3000.0 km. How high above the surface of the moon should a satellite of mass 183.0 kg be so that it undergoes geosynchronous orbit about the moon? The rotational period of the moon is 0.2639 days.

2. How fast must the satellite be moving so that it maintains the geosynchronous orbit?

3. The moon will also travel in uniform circular motion in small circles due to the presence of the satellite. Using the fact that the period of motion for the moon is the same as the period of motion for the satellite, find the radius of motion for the moon.

i dont know

## The Attempt at a Solution

I dont know how to star it

Andrew Mason
Science Advisor
Homework Helper

## Homework Statement

1. One of Jupiter's moons has a mass of 4.80E+23 kg and a radius of 3000.0 km. How high above the surface of the moon should a satellite of mass 183.0 kg be so that it undergoes geosynchronous orbit about the moon? The rotational period of the moon is 0.2639 days.

2. How fast must the satellite be moving so that it maintains the geosynchronous orbit?

3. The moon will also travel in uniform circular motion in small circles due to the presence of the satellite. Using the fact that the period of motion for the moon is the same as the period of motion for the satellite, find the radius of motion for the moon.

i dont know

## The Attempt at a Solution

I dont know how to star it

1. Work out the relationship between speed, v, of the satellite and the radius of orbit, r by analysing the force/acceleration. (If the satellite is moving in a circle of radius r, and speed v, what is the centripetal acceleration? What supplies that acceleration? What is the formula for calculating that central force/acceleration?)

2. How is the speed of the satellite related to the period of rotation and the radius, r? Substitute that expression for v into the relationship in 1.

AM