Consider a body of mass M at the point C. Let P be a point at a distance r from C. To calculate the gravitational potential at P consider two points A and B. The point A, where the unit mass is placed is at a distance x from C.

The gravitational field at A is **E = GM/x ^{2}**

The work done in moving the unit mass from A to B through a small distance dx is **du = dv = -E.dx**

Negative sign indicates that work is done against the gravitational field.

**dv = – GM/x ^{2} dx**

The work done in moving the unit mass from the point P to infinity is:

**∫ dv = – ^{∞}∫_{r} GM/x^{2} dx**

**So, v = – GM/r**

The gravitational potential is negative, since the work is done against the field. (i.e) the gravitational force is always attractive.