Apollo 11 Moon Landing – Mathematics of Orbital Mechanics

On 20 July 1969, humans landed on the Moon. The trajectory was computed using Newton’s laws and Kepler’s laws, with mid‑course corrections solved by numerical integration. The translunar injection required precise velocity: 10,848 m/s from Earth orbit. The lunar module’s descent used a ‘powered descent initiation’ point calculated to minimise fuel. All navigation used the mathematics of conic sections and perturbation theory. The astronauts carried a slide rule and a sextant for backup. Without celestial mechanics, Apollo would have been impossible.