# Universal Gravitation

Momentum09

## Homework Statement

Given: The universal gravitational constant G = 6.67 E-11, the mass of the earth M = 5.98E24, and its radius R = 6.7 E6. How much work must an external force do on the satellite to move it from a circular orbit of radius 2R to 3R, if its mass is 2000kg? Answer in Joules.

## Homework Equations

I know that E = -GMm/2r, where M is the mass of the earth and m = satellite.

## The Attempt at a Solution

So I calculated the total energy in each radii,
for 2R, -GMm/4R
for 3R, -GMm/6R
then I subtract one from the other to get the net energy change. I don't know what to do after that. Please help. Thank you!

## Answers and Replies

Staff Emeritus
Gold Member
There is a considerably simpler way of doing this. The work done in moving an object from one orbit to another is:

$$W=\int_{r_1}^{r_2} F(r) dr$$

EDIT: Sorry forgot to say that your method is fine for potential energy not total mechanical energy as you have used.

Last edited:
Momentum09
thank you so much! :)

Homework Helper
There is a considerably simpler way of doing this. The work done in moving an object from one orbit to another is:

$$W=\int_{r_1}^{r_2} F(r) dr$$

EDIT: Sorry forgot to say that your method is fine for potential energy not total mechanical energy as you have used.

Actually, I think he is ok. The kinetic energy at radius R is GMm/(2R). The potential is -GMm/R. So the sum is, as he states, -GMm/(2R).

Staff Emeritus
Gold Member
Was just the procedure in the attempt at the solution that made me think it was total mechanical energy.

ttt359
I have the exact same question. This is one of the method that I used:
E intial = Ki + Ui = 0 + (-GMm/2R)
E final = Kf + Uf = (1/2)(GMm/3R) + (-GMm/3R)
then Work = E final - E intial

this make sense right? Then why it doesn't work

I also try the integrate method, but nothing work! Can somebody please tell me why?
and how to fix it?

Homework Helper
If it's in orbit at radius 2R, how can Ki=0?

ttt359
ok, so Ki is not = O; Then why is it the integration method didn't work either?