Hohmann Transfer Orbit
The Hohmann transfer is the most fuel-efficient two-impulse maneuver for moving a spacecraft between two circular orbits. A prograde burn at the inner orbit raises the apoapsis to the outer orbit; a second burn at arrival circularizes the orbit. Despite being the slowest transfer, it uses the least propellant — the fundamental tradeoff of orbital mechanics.
Δv₁ = √(μ/r₁) · (√(2r₂/(r₁+r₂)) − 1) Δv₂ = √(μ/r₂) · (1 − √(2r₁/(r₁+r₂)))
The maneuver
Named after Walter Hohmann, who described it in 1925, the Hohmann transfer uses two engine burns to move between two coplanar circular orbits. The transfer orbit is an ellipse tangent to both the inner and outer circles. It is the most fuel-efficient two-impulse transfer between circular orbits.
Delta-v
The first burn (Δv₁) is prograde at the periapsis of the transfer ellipse, raising the spacecraft’s apoapsis to the outer orbit. The second burn (Δv₂) is prograde at the apoapsis, circularizing the orbit. The total Δv is the sum of both burns and determines the propellant required via the Tsiolkovsky rocket equation.
Transfer time
The transfer takes exactly half the orbital period of the transfer ellipse: T = π · √((r₁+r₂)³ / (8μ)). For an Earth-to-Mars transfer, this is about 8.5 months. For LEO to GEO, about 5.25 hours.
Trade-offs
The Hohmann transfer minimizes fuel but maximizes transfer time. For faster transfers, bi-elliptic transfers or continuous-thrust spirals can be used, but at higher Δv cost. In practice, launch windows are also constrained by planetary alignment.
Presets
LEO to GEO: Low Earth orbit (400 km altitude) to geostationary orbit (35,786 km altitude). Earth to Mars: Earth’s orbit (1 AU) to Mars orbit (1.524 AU) around the Sun. Earth to Moon: LEO to lunar orbit distance. LEO to MEO: Low orbit to GPS satellite altitude (~20,200 km).