Derive an expression for gravitational potential?

If a body is taken from the surface of the earth to a point at a height ‘h’ above the surface of the earth, then r_i = R and r_f = R + h then,

ΔU = GMm [1/R – 1/(R+h)]

ΔU = GMmh/R(R + h)

When, h<<R, then, R + h = R and g = GM/R².

On substituting this in the above equation we get,

Gravitational Potential Energy ΔU = mgh

When a body of mass (m) is moved from infinity to a point inside the gravitational influence of a source mass (M) without accelerating it, the amount of work done in displacing it into the source field is stored in the form of potential energy this is known as gravitational potential energy. It is represented with the symbol Ug.

The equation for gravitational potential energy is:

⇒ GPE = m⋅g⋅h

Where,

• m is the mass in kilograms,
• g is the acceleration due to gravity (9.8 on Earth)
• h is the height above the ground in meters