Gravitation Part 1

What these notes cover

These notes cover gravitational fields for Cambridge International A Level Physics (9702): Newton’s law of gravitation, gravitational field strength and its inverse-square variation with distance, gravitational field lines, the null point between the Earth and the Moon, why g is slightly smaller at the equator than at the poles, and satellites in circular orbits, including orbital speed, angular velocity, kinetic energy, period and geostationary orbits. They include worked examples and past-paper questions.

Key formulas and definitions

• Newton’s law of gravitation: two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of their separation: F = GMm / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻².
• A gravitational field is a region in which a mass experiences a force. Gravitational field strength is the force per unit mass: g = F / m.
• For a point mass or a uniform sphere: g = GM / r², so g follows an inverse-square law with distance from the centre (doubling r makes g one quarter as large).
• Gravitational field lines point radially inwards towards the mass, because gravity is always attractive. Close to the Earth’s surface the field is approximately uniform.
• Between the Earth and the Moon there is a null point where the two fields are equal and opposite, so the resultant field strength is zero.
• g is slightly smaller at the equator than at the poles, because the Earth is not a perfect sphere and because, at the equator, part of the gravitational force provides the centripetal force for the Earth’s rotation.
• For a satellite in a circular orbit, gravitational force provides the centripetal force: GMm / r² = mv² / r, giving v = √(GM / r) and T² = (4π² / GM) r³.
• A geostationary satellite orbits above the equator, from west to east, with a period of 24 hours, so it stays above the same point on the Earth’s surface.