Gravitational Potential and Potential Energy

Gravitational potential is one of the most important — and most commonly misunderstood — concepts in A-Level Physics. While gravitational field strength tells you about the force a mass would experience, gravitational potential tells you about the energy associated with a position in a gravitational field.

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Gravitational Potential

Gravitational potential V at a point in a gravitational field is defined as the work done per unit mass in bringing a small test mass from infinity to that point.

$V = -\frac{GM}{r}$V=−rGM​

where:

• V is the gravitational potential (J kg⁻¹)
• G is the gravitational constant (6.674 × 10⁻¹¹ N m² kg⁻²)
• M is the mass creating the field (kg)
• r is the distance from the centre of mass M to the point (m)

The units of gravitational potential are joules per kilogram (J kg⁻¹).

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Why Is Gravitational Potential Negative?

This is crucial. Gravitational potential is always negative (or zero at infinity). Here is why: