🌍 Hohmann Transfer Orbit

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

The most fuel-efficient way to move a spacecraft between two circular orbits using just two engine burns.

Moving a spacecraft from one circular orbit to a different one — say, from low Earth orbit up to geostationary orbit — doesn't mean simply thrusting outward. The Hohmann transfer is the classic, fuel-optimal solution: fire the engine once to enter an elliptical transfer orbit whose closest point touches the starting orbit and farthest point touches the destination orbit, coast along that ellipse, then fire the engine a second time at arrival to circularize into the final orbit.

Each burn changes speed, not direction, and both happen at points where the transfer ellipse is tangent to the circular orbits — that tangency is exactly what makes the maneuver efficient, since it means each burn only needs to change speed, without also needing to change the direction of travel.

The vis-viva equation — the same relationship underlying both circular orbital velocity and this transfer orbit calculation — gives the speed at any point of any orbit (circular or elliptical) purely from the central body, the orbit's size, and the distance at that point, which is what lets this calculation find the transfer ellipse's speed at both its endpoints.

Key formula

Vis-viva: v = √(μ × (2/r − 1/a))
Burn 1 = |v_transfer,departure − v_circular,initial|
Burn 2 = |v_circular,final − v_transfer,arrival|

Variables

a

semi-major axis of the transfer ellipse — the average of the initial and final orbital radii

Notes & limitations

• A Hohmann transfer is fuel-optimal for a two-burn transfer between circular orbits, but not necessarily the fastest — it takes exactly half an orbit of the transfer ellipse to complete, which for a large orbit change (like Earth to Mars) can mean a coast of many months.
• This assumes both orbits are in the same plane — a real transfer between differently-inclined orbits needs an additional plane-change maneuver, which typically costs significant extra delta-v not included here.