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Gravitational Energy

Part of the Mechanics section of Coddy's Physics journey. Lesson 91 of 97.

Far from the ground, mgh\relax mgh no longer works. A mass at distance rr from the centre has:

U=−GMmrU = -\frac{GMm}{r}

The zero is very far away, so UU is negative everywhere else.

UU climbs toward zero as rr grows, and U⋅rU \cdot r is the same at every distance. Moving out takes the work ΔU=U2−U1\Delta U = U_2 - U_1.

A graph of gravitational potential energy U against distance r from the surface radius R outward: U starts at minus GMm over R and rises toward zero without reaching it

U is negative and climbs toward zero as r grows.

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Challenge

A probe 2 planet radii from a planet's centre has a potential energy of −30 GJ-30\ \mathrm{GJ} (−3×1010 J-3 \times 10^{10}\ \mathrm{J}). Find its potential energy UU when it is 3 planet radii from the centre.

Try it yourself

Physics diagram: planet, path, satellite

Solve for UU

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

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