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.
[3 marks]
Total for this question: 3
All equation deep-dives
Gravitational field and potential
Fields and capacitors
AQA 7408
In the data booklet
ORIGINAL
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.
Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works
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.
Q1
Do the calculation on paper first — then mark it.
Q2
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.
[4 marks]
Total for this question: 4
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.
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