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Gravitation

Field, potential, escape speed and satellites. It has shrunk by almost half since the early papers.

Questions in the bank
128
q/paper in 2025–26
0.60
Numeric answer
9%
Notes pages
6

Tier: Long tail

When you’ll see it

g on another planet, at a height or a depth, an escape speed, a satellite's speed or energy, or a period compared through Kepler's law.

How this chapter is tested

Most questions compare a quantity on one planet, at one height or in one orbit with the same quantity somewhere else. The constants cancel, so the work is in choosing the right formula and writing the ratio.

Marks are lost on distances, not on algebra. Every formula wants r, the distance from the centre: a height of R means r = 2R. A separation of 2r gets written as r, and the constant-g equations get used over a distance comparable to the earth's radius, where only energy conservation with −GMm/r works.

The chapter is set less often than in the early papers. The satellite energy relations, KE = GMm/2r and PE = −2KE, and Kepler's T² ∝ r³ answer many statement-type questions.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Newton's law, field and potential

    Add pulls as vectors; a sphere or shell acts as a point mass from outside; a system's potential energy is −Gm₁m₂/r summed over every pair.

  • g on the surface and at a height

    g = GM/R² = (4/3)πGρR on the surface; g/(1 + h/R)² at height h, close to g(1 − 2h/R) only when h is small.

  • g at a depth and the earth's spin

    g(1 − d/R) below the surface, falling to zero at the centre; rotation lowers g by ω²R cos²λ, most at the equator.

  • Escape velocity and energy conservation

    v_e = √(2GM/R) = √(2gR), independent of mass and direction; over large distances conserve KE − GMm/r.

  • Satellites and mutual orbits

    v = √(GM/r), T = 2π√(r³/GM), total energy −GMm/2r; in a binary the force uses the separation and each star its own radius.

  • Kepler's laws

    Elliptical orbits with the sun at a focus, equal areas in equal times, and T² ∝ r³/M for the central mass M.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • A height used for r

    A body 2R from the surface is 3R from the centre, so g is g/9. Read whether the distance is from the surface or the centre.

  • Depth and height formulas swapped

    Below the surface g falls as d/R; above it, as 1/(1 + h/R)². Both directions lower g, which is largest at the surface.

  • Constant-g kinematics over a large distance

    A fall from height R gives v² = gR by energy conservation, not 2gR; mgh fails when h is comparable to R.

  • Potential energy as half the total

    In orbit U = 2E, not E/2. A higher orbit has more total energy but less kinetic energy.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Gravitation notes

Drill every Gravitation question

128 questions from the bank, across 6 subtopics.

Drill the 128 questions

Drill one subtopic at a time

The 6 subtopics, in teaching order.

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