Two objects of equal mass m are separated by a distance r. Which expression gives the gravitational potential at the point P mid way between the two objects?

Question

The answer shows as -4Gm/r, but I can't see where this comes from.

Answer 1

Midway between the two objects, you add the gravitational potentials due to each object. The distance to each object is r/2.

The PE due to each separate mass is
-Gm/(r/2) = -2Gm/r

Double that for two objects at the same distance, and you have the "book" answer.

Note that "gravitational potential" is gravitational potential energy per unit mass placed at that location. The units are joules per kg