So, here's problem 43:
It asks for the acceleration of the bodies' centre of mass when they are a distance of apart.
Here's a more rigourous mathematical approach:
The centre of mass can be found using ; with this, we can find the second derivative of with respect to time, giving:
So, now we compute the gravitational force which can give the values of and :
So, acceleration of C.M is:
Therefore the acceleration,