(A Level) Gravitational fields

Learning objectives

Define gravitational field strength as force per unit mass, and represent gravitational fields with field lines, radial around a point mass and uniform close to the Earth's surface.

Use Newton's law of gravitation F = Gm₁m₂/r², treating a uniform sphere as a point mass at its centre.

Derive g = GM/r² from Newton's law of gravitation, and explain why g hardly changes over heights that are small compared with the Earth's radius.

Analyse circular orbits by setting GMm/r² equal to mv²/r or mrω², show that T² ∝ r³, and describe a geostationary orbit: 24-hour period, west-to-east motion, directly above the Equator.

Define the gravitational potential at a point as the work needed per kilogram to bring a small mass there from infinity, and use φ = −GM/r and Ep = −GMm/r for point masses, explaining why both are negative.