Hohmann transfer
The most fuel-efficient two-burn manoeuvre for moving between two circular orbits; uses a half-ellipse as the transfer path.
Definition
A Hohmann transfer orbit is an elliptical trajectory that touches the inner circular orbit at its periapsis and the outer circular orbit at its apoapsis. The spacecraft makes two engine burns: the first accelerates it from the inner orbit onto the transfer ellipse, and the second — half an orbit later — circularises it into the outer orbit. The total velocity change (Δv) is the minimum possible for a two-impulse transfer between coplanar circular orbits.
Walter Hohmann, a German civil engineer and amateur rocketry enthusiast, published the idea in 1925 in his book Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies). His calculation showed that interplanetary travel was energetically feasible — a revolutionary insight at a time when most scientists considered space travel fantasy. Every Mars mission, every geostationary satellite insertion, and every orbit-raising manoeuvre uses Hohmann's geometry or a close variant.