Chapter 7 — Gravitation

Gravitation is the force of attraction between all material objects in the universe, inversely proportional to the square of the distance between them. Newton's law of universal gravitation governs both terrestrial and celestial phenomena, with the gravitational constant G = 6.67×10⁻¹¹ N m²/kg².

Chapter 7 explores gravitational forces governing planetary and terrestrial motion. It covers Kepler's laws of planetary motion, Newton's universal law of gravitation (F = Gm₁m₂/r²), the gravitational constant G (experimentally determined by Cavendish), acceleration due to gravity at Earth's surface and varying with altitude/depth, gravitational potential energy, escape speed (11.2 km/s from Earth), orbital mechanics of satellites, and energy conservation in orbital systems. The chapter bridges historical observations from Ptolemy through Copernicus to Newton's comprehensive gravitational framework.

1. 01All planets move in elliptical orbits with the Sun at one focus; the line joining a planet to the Sun sweeps equal areas in equal times; and the square of orbital period is proportional to the cube of semi-major axis (Kepler's laws)
2. 02Gravitational force: F = Gm₁m₂/r² where G = 6.67×10⁻¹¹ N m²/kg²; independent of intervening matter and the nature of objects
3. 03Acceleration due to gravity decreases with altitude: g(h) ≈ g(1 − 2h/Rₑ) for h << Rₑ and decreases with depth: g(d) = g(1 − d/Rₑ)
4. 04Gravitational potential energy at distance r from Earth's center: W(r) = −GMₑm/r; total mechanical energy of orbiting satellites is negative
5. 05Escape speed from Earth's surface: vₑ = √(2GMₑ/Rₑ) = √(2gRₑ) ≈ 11.2 km/s; independent of projectile mass or direction
6. 06A uniform spherical shell exerts gravitational force on external objects as if all mass is concentrated at the centre; exerts zero force on internal objects