Calculating Time to Overtake a Satellite in Orbit

[Symstar]

Homework Statement

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?

Homework Equations

Fg=G*m1m2/r^2

The Attempt at a Solution

$$F_g=m\frac{v^2}{r}$$
$$G\frac{m_1m_E}{r^2}=m\frac{v^2}{r}$$
$$G\frac{m_E}{r}=v^2$$
$$v=\sqrt{G\frac{m_E}{r}}$$

v_sat=31577.92 m/s
v_shut=31621.43 m/s

v_shut 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?

 

[D H]

What did I do wrong?

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

 

[Symstar]

Silly mistake, thanks for the help!