Calculating the Total Work Done by Gravity

[Simon777]

Homework Statement

A satellite in a circular orbit around the Earth with a radius 1.011 times the mean radius of the Earth is hit by an incoming meteorite. A large fragment (m = 83.0 kg) is ejected in the backwards direction so that it is stationary with respect to the Earth and falls directly to the ground. Its speed just before it hits the ground is 355.0 m/s. Find the total work done by gravity on the satellite fragment. RE 6.37·10^3 km; Mass of the earth= ME 5.98·10^24 kg.

Homework Equations

Gravitational PE= (-GmM)/R

The Attempt at a Solution

Delta PE= PE intial - PE final

= (-(6.67x10^-11) (83kg) (5.98x10^24kg))/((1.011) (6.37x10^3)) - (-(6.67x10^-11) (83kg) (5.98x10^24kg))/(6.37x10^3)

= 5.65x10^10J

This is incorrect and I have tried for hours to get something to work so any help would be greatly appreciated.

 

[gneill]

Something happened to your orders of magnitude. I think you're result is about 1000x to big. Check your math.

You can save yourself a lot of digit pushing if you do some of the algebra symbolically ahead of time:

Let r = 1.011; M = Mass of Earth; R = radius of Earth; m = mass of fragment;

$$\Delta E = \left(\frac{G M m}{R} - \frac{G M m}{r R}\right) = \frac{G M m}{R}\left(1 - \frac{1}{r}\right)$$

 

[Simon777]

Something happened to your orders of magnitude. I think you're result is about 1000x to big. Check your math.

You can save yourself a lot of digit pushing if you do some of the algebra symbolically ahead of time:

Let r = 1.011; M = Mass of Earth; R = radius of Earth; m = mass of fragment;

$$\Delta E = \left(\frac{G M m}{R} - \frac{G M m}{r R}\right) = \frac{G M m}{R}\left(1 - \frac{1}{r}\right)$$

That does make it easier, thank you. Using it, I still end up with 5.65x10^10J. Perhaps one of my terms is wrong. This is what I used:
M=5.98·10^24 kg
G=6.67x10^-11
m=83.0kg
R= 6.37·10^3 km
r= 1.011

 

[gneill]

Convert your Earth radius to meters!

 

[Simon777]

Convert your Earth radius to meters!

I can't believe I wasted all that time because I overlooked something so basic as units. Thank you so much for helping me realize this. I was over thinking it and thought I needed to factor something else in.