# Satellite / force of gravity

1. Oct 9, 2008

### Symstar

1. The problem statement, all variables and given/known data
You are an astronaut in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 20 km behind it.

How long will it take to overtake the satellite if you reduce your orbital radius by 1.1 km?

2. Relevant equations
Fg=G*m1m2/r^2

3. The attempt at a solution
$$F_g=m\frac{v^2}{r}$$
$$G\frac{m_1m_E}{r^2}=m\frac{v^2}{r}$$
$$G\frac{m_E}{r}=v^2$$
$$v=\sqrt{G\frac{m_E}{r}}$$

vsat=31577.92 m/s
vshut=31621.43 m/s

vshut relative to satellite = 43.51 m/s

v=d/t => t=d/v

t = 20,000m / 43.51m/s = 459.66s = 0.13 hr

This is, however, the wrong answer. What did I do wrong?

2. Oct 9, 2008

### D H

Staff Emeritus
The satellite 400 km above the Earth, not 400 km from the center of the Earth.

3. Oct 9, 2008

### Symstar

Silly mistake, thanks for the help!