Hohmann Transfer
Two-burn transfer between circular Earth orbits: Δv₁, Δv₂, total, and time of flight.
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The engineering
The Hohmann transfer is the cheapest two-burn route between coplanar circular orbits: burn once to stretch your orbit's far side out to the target radius, coast half an ellipse, burn again to circularize. LEO to GEO costs about 3.9 km/s split roughly 2.4/1.5 — the number that sizes every GTO upper stage and satellite apogee motor.
It's optimal only up to a radius ratio of about 11.94 (beyond that a bi-elliptic detour wins, slowly) and it assumes coplanar orbits — plane changes are so expensive they get combined into the apogee burn, which is why launch sites near the equator charge a premium. Note both burns *add* energy when going up; coming down, the same magnitudes act as brakes.
Where this math comes from
Walter Hohmann was a city building-official in Essen who did celestial mechanics by night; his 1925 book 'Die Erreichbarkeit der Himmelskörper' proved the tangent-ellipse transfer minimal years before any rocket could fly one. He'd worked it out by 1912 but published into the small, fervent spaceflight-society world that Oberth's 1923 book had electrified.
The maneuver stayed theory until the space age made it plumbing: every GEO comsat since Syncom (1963–64) rides a Hohmann-style geostationary transfer orbit, Mariner 4's 1964–65 Mars trajectory was a near-Hohmann interplanetary version, and 'Hohmann window' is why Mars missions leave in herds every 26 months.
- 1925Walter HohmannProves the minimum-energy two-impulse transfer.
- 1923Hermann OberthThe book that made orbital mechanics a movement.
- 1964NASA / Hughes Syncom 3GTO — the Hohmann transfer as commercial routine.
- 1965JPL Mariner 4Near-Hohmann trajectory reaches Mars.
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