Work required to move a mass away from two others

[BOAS]

Hi

1. Homework Statement

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.

Homework Equations

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

$W_{grav} = - U$

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?

 

[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.

 

[BOAS]

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.

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?

 

[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.