Gravitational field and potential
g = G M / r2 and V = -G M / r
Field strength follows 1/r^2, potential follows 1/r, and gravitational potential is negative when zero is at infinity.
Know the equation
| Symbol | Quantity | Unit |
|---|---|---|
| g | gravitational field strength | N/kg |
| G | gravitational constant | N m2/kg2 |
| M | mass producing the field | kg |
| r | distance from the centre of the mass | m |
| V | gravitational potential | J/kg |
| W | work done or potential energy change | J |
Rearrangements
- M = g r2 / G
- r = sqrt(G M / g)
- M = -V r / G
- d(W) = m d(V)
Apply it — mark your own working
Work each one out on paper first, then reveal the mark scheme and tick the marks you actually earned. That is exactly how you should mark past papers.
Calculate the gravitational potential at a distance 7.0 x 106 m from the centre of Earth. Use M(Earth) = 5.97 x 1024 kg and G = 6.67 x 10−11 N m2/kg2.
Do the calculation on paper first — then mark it.
An 800 kg satellite is moved from radius 6.8 x 106 m to radius 7.2 x 106 m from Earth's centre. Calculate the minimum work required. Use M(Earth) = 5.97 x 1024 kg and G = 6.67 x 10−11 N m2/kg2.
Do the calculation on paper first — then mark it.
Where the marks get lost
- Measuring r from the surface instead of from the centre of the spherical body.
- Dropping the negative sign from gravitational potential. Potential becomes less negative as an object is moved away.
- Using 1/r2 for potential; only field strength has the inverse-square dependence.
Exam tip: Keep the signs until the final line. Raising a satellite makes V increase from a more negative value to a less negative value, so the required work is positive.
Still losing marks on the calculations?
I'll go through your working line by line and show you exactly where the marks are — your first lesson is free.