Gravitational fields and orbital motion

Learning objectives

State Newton's law of gravitation F = GMm/r² and apply it to point masses and to uniform spheres whose mass may be treated as concentrated at the centre

Define gravitational field strength as the force per unit mass, calculate it from g = GM/r², and explain why it is numerically equal to the acceleration of free fall at that point

Apply the condition for a circular orbit to satellites and planets, obtaining orbital speed v = √(GM/r) and orbital period, and verify Kepler's third law T² ∝ r³ from orbital data

(HL) Define gravitational potential as Vg = −GM/r and gravitational potential energy as Ep = −GMm/r, and explain why both quantities are negative and tend to zero at infinite separation

(HL) Relate gravitational field strength to the potential gradient through g = −ΔVg/Δr, and sketch and interpret field lines and equipotential surfaces for one mass and for two masses

(HL) Calculate escape speed from vesc = √(2GM/r), analyse the total energy of a body in a circular orbit as ET = −GMm/2r, and determine the energy needed to transfer a satellite between orbits