Gravitational potential (V)
Gravitational Fields - OCR A-Level Physics
Key Definition
Gravitational potential (V)
The work done per unit mass to move a test mass from infinity to that point in the field. Units: $J kg^{-1}$.
The work done per unit mass to move a test mass from infinity to that point in the field. Units: $J kg^{-1}$.
$$V = -\frac{GM}{r}$$
- 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 always negative because gravity is attractive. Work must be done against gravity to move a mass away, so moving from infinity ($V = 0)$ to any point requires negative work.
- V is a scalarA quantity with magnitude only and no direction (e.g. mass, time, temperature). quantity (no direction, just a value at each point).
- At infinity, $V = 0 (the reference point)$.
- Closer to the mass, V becomes more negative (a deeper potential well).
- Equipotential surfacesSurfaces on which the gravitational potential is the same everywhere; no work is done moving along them. are surfaces where V is constant. No work is done moving along an equipotential.
- Field lines are always perpendicular to equipotential surfaces.
- g = -$\Delta$V / $\Delta$r (field strength equals the negative potential gradient).
Common Mistake
MEDIUM
Wrong: Forgetting the negative sign in $V = -GM/r$ and getting a positive 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..
Right: 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 ALWAYS negative (or zero at infinity). If you calculate a positive value for V, you have missed the negative sign.
Right: 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 ALWAYS negative (or zero at infinity). If you calculate a positive value for V, you have missed the negative sign.