# How gravitational potential energy depends upon the difference in heights of initial and final position?

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Gravitational potential energy is zero at infinity and decreases as the distance decreases.

This is because**gravitational force exerted on the body** by the earth is attractive.

Hence gravitational potential energy(U) is negative.

U = -

This is because

Hence gravitational potential energy(U) is negative.

U = -

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Let M = Mass of planet

m = mass of body

r = distance of body from the center of the planet

The word**Potential energy **defined only for conservative force field.

So the change in**Potential energy (dU) **of a system corresponding to a conservative internal force is given by

dU = F.dr x cos(180) {since the displacement is anti- parallel to the gravitational pull}

⇒ =

⇒ =

⇒ ΔU =

⇒ ΔU =

⇒ ΔU =

which proves that gravitational potential depends on the difference of the initial and final heights of the body.

m = mass of body

r = distance of body from the center of the planet

The word

So the change in

dU = F.dr x cos(180) {since the displacement is anti- parallel to the gravitational pull}

⇒ =

⇒ =

⇒ ΔU =

⇒ ΔU =

⇒ ΔU =

which proves that gravitational potential depends on the difference of the initial and final heights of the body.