# Work required to move a mass away from two others

1. Dec 4, 2014

### BOAS

Hi

1. The problem statement, all variables and given/known data

At a certain instant, the earth, the moon, and a stationary 1490kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84×10^5km in length. What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and moon? You can ignore any gravitational effects due to the other planets or the sun.

2. Relevant equations

$U = -G \frac{m_{1}m_{2}}{r}$

$W_{grav} = - U$

3. The attempt at a solution

I am confused by this question. I haven't done a question like this involving three masses before. I don't really know where to get started but I have a thought;

Do I need to find the center of mass of the Earth and the Moon, and treat that as a single mass for which i'm moving the satellite from?

2. Dec 4, 2014

### BvU

Yes, well, it's a given that they are at 3.84 x 105 km away. All you need to look up is their mass.

3. Dec 4, 2014

### BOAS

Is it the center of mass of all three that I need to find, or the center of mass of the earth and the moon?

4. Dec 4, 2014

### BvU

Check with your relevant equation. No common center of mass there. You can simply add potential caused by earth to that caused by moon.