1.Explain the difference between Gravitational Potential and Gravitational Potential Energy.

2.Derive the formulas for both using integral calculus.

Gravitational potential at any point in a gravitational field is the work done in bringing a unit mass from infinity to that point. .Gravitational potential determines the direction of motion of a body in the gravitational field of another body. 

Gravitational potential energy of a particle at a point in a gravitational field due to a body is measured by the work done in moving the particle from infinity to that point. It is equal to the product of potential at the point due to the body and the mass of the particle.

We can say that gravitational potential at a point is equal to the potential energy of the unit mass kept at that point.

 

Note: Please ask second question as a seperate query