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.