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LearnCambridge97022025–2027Paper 4 · A Level Structured QuestionsGravitational fields
Paper 4 · Module

Gravitational fields

2 subtopics≈ 75 min in total
Start the module: Gravitational force and field strengthOpen graphing calculator

  1. Gravitational force and field strength

    Every pair of point masses attracts with a force F=GMmr2F=\dfrac{GMm}{r^2}, where G=6.67×10−11G=6.67\times10^{-11} N m² kg⁻². A uniform sphere acts as if its mass were at its centre. Gravitational field strength is force per unit mass, g=Fm=GMr2g=\dfrac Fm=\dfrac{GM}{r^2}, an inverse-square law. Near Earth's surface, gg is nearly constant because height changes are tiny compared with Earth's radius.

    ≈ 35 min

  2. Gravitational potential and orbits

    Gravitational potential is the work done per unit mass bringing a small mass from infinity: φ=−GMr\varphi=-\dfrac{GM}r. It is zero at infinity and negative everywhere else, because gravity is attractive. A mass mm has potential energy Ep=−GMmrE_p=-\dfrac{GMm}r. For a circular orbit, gravity provides the centripetal force, giving v2=GMrv^2=\dfrac{GM}r and T2=4π2GMr3T^2=\dfrac{4\pi^2}{GM}r^3. A geostationary satellite orbits above the equator with a period of 2424 hours.

    ≈ 40 min