# Path of a ball thrown radially from a satellite orbiting Earth

Tags:
1. Oct 12, 2014

### khfrekek92

1. The problem statement, all variables and given/known data
A satellite has a circular orbit 500 km above earth. A ball is thrown directly downwards radially at 20 m/s. Find the path of the ball relative to the satellite.

2. Relevant equations

$$mv^2/r=GMm/r^2$$

3. The attempt at a solution
From the height of the orbit you can easily solve for the velocity:
$$mv^2/r=GMm/r^2=>v_{satellite}=sqrt{GM/r}=7667.7 m/s$$

Now I can easily tell that the ball is just going to take a slightly elliptical path relative to EARTH, however I can't quite figure out (conceptually or mathematically) what this path will take relative to the satellite moving in a circular orbit.

From what I can tell, immediately when the ball is thrown downwards, it will go in reverse (slightly) relative to the satellite because it won't be able to speed up again to the original velocity of the satellite. Any thoughts?