Gravitational Potential Energy: It is the energy an object possesses due to its position in a gravitational field. It is defined as the work done against gravity in moving an object from a reference point to its current position. The gravitational potential energy of an object increases as it is lifted to a higher position in a gravitational field, and decreases as it is lowered to a lower position. The higher an object is above the reference point, the more gravitational potential energy it has.

Formula of Gravitational Potential Energy

The formula for gravitational potential (PE) Energy is:

PE = mgh

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

Expression for Gravitational Potential Energy at Height (h)

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

⇒ Note: 

• The weight of a body at the centre of the earth is zero due to the fact that the value of g at the centre of the earth is zero.
• At a point in the gravitational field where the GPE is zero, the gravitational field is zero.

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By Team Learning Mantras