3.7.2.3
Gravitational potential is always negative
Gravitational Fields & Orbits — AQA A-Level Physics
Key Definition
Gravitational potential — The work done per unit mass in bringing a test mass from infinity to a defined point. Symbol: V. Units: J kg⁻¹.
$$V_g = -\frac{GM}{r}$$
- Gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. is defined as zero at infinity.
- Since gravitational force is attractive, work must be done on a mass to move it to infinity. This means V is negative at all finite distances from a mass.
- Closer to a mass, V is more negative (lower). Further away, V becomes less negative (higher), approaching zero at infinity.
- V is a scalar quantityA quantity that has magnitude (size) only. It has no direction.. This is different from g, which is a vector.
- Near the Earth's surface, the familiar $GPE = mgh applies. For large distances$, use the full gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. equation.
Common Mistake
MEDIUM
Students often: Forgetting the negative sign in gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. calculations.
Instead: V is always negative near a mass. Only drop the sign if the question asks for 'change in' potential (magnitude). Keep the negative sign when stating potential at a point.
Instead: V is always negative near a mass. Only drop the sign if the question asks for 'change in' potential (magnitude). Keep the negative sign when stating potential at a point.