How a Hohmann Transfer Orbit Works

June 16, 2026 5 min read

A Hohmann transfer is the cheapest two-burn way to move a spacecraft between two circular orbits. You fire your engine once to stretch the circular orbit into an ellipse that just touches the destination, coast half a lap, then fire again to circularize at the new altitude. Two short burns, one long free coast, minimum fuel.

It is named for Walter Hohmann, a German structural engineer who worked out the math in his spare time and published it in his 1925 book Die Erreichbarkeit der Himmelskorper ("The Attainability of the Celestial Bodies"). He did the foundational calculations between 1911 and 1915, decades before any rocket could reach orbit. A century later, essentially every communications satellite and every Mars probe still rides a Hohmann ellipse to get where it is going.

The geometry: one ellipse tangent to both orbits

Picture two circles around Earth: a low parking orbit and a high target orbit. The Hohmann transfer connects them with a single ellipse that is tangent to the inner circle at its lowest point (periapsis) and tangent to the outer circle at its highest point (apoapsis). Because the ellipse kisses each circle exactly once, both burns are purely along-track speed changes, which is the most propellant-efficient way to add energy.

The transfer ellipse has a semi-major axis equal to the average of the two orbital radii: a = (r1 + r2) / 2. That single fact, plus the conservation of energy, is enough to compute the entire maneuver. The spacecraft spends exactly half of the ellipse's orbital period coasting from the first burn to the second, which is why a Hohmann transfer is sometimes called a "half-orbit" transfer.

The engine that does the work: the vis-viva equation

The whole maneuver runs on one beautiful formula, the vis-viva ("living force") equation, which gives orbital speed at any distance from the central body:

v = sqrt( mu * (2/r - 1/a) )

Here mu is the gravitational parameter (the mass of the central body times the gravitational constant G), r is your current distance, and a is the semi-major axis of whatever orbit you are on. Plug in the circular orbit (where a = r) and you get circular speed; plug in the transfer ellipse and you get the speed you need at each end. The delta-v for each burn is simply the difference between those two speeds.

Working it through gives the two classic Hohmann formulas:

delta-v1 = sqrt(mu/r1) * ( sqrt(2*r2/(r1+r2)) - 1 )
delta-v2 = sqrt(mu/r2) * ( 1 - sqrt(2*r1/(r1+r2)) )

The total cost is just delta-v_total = delta-v1 + delta-v2. Both burns add speed when you climb to a higher orbit. (Counterintuitively, the higher orbit is the slower one, so the second burn is still a speed-up relative to where the ellipse left you.) Our Hohmann transfer calculator does this arithmetic for any pair of orbits and central bodies.

A worked example: from the ISS to geostationary orbit

Suppose you want to raise a spacecraft from the International Space Station's orbit (about 420 km altitude) up to geostationary orbit at 35,786 km, where a satellite circles once per day and appears to hang motionless over a fixed spot on the equator. The numbers come out like this:

First burn (raise apoapsis to GEO altitude): roughly 2.4 km/s
Coast: a free half-lap lasting about 5 hours 15 minutes
Second burn (circularize at GEO): about 1.5 km/s
Total: roughly 3.9 km/s of delta-v

This is exactly how communications satellites reach their slots. The launch vehicle drops the satellite into a Geostationary Transfer Orbit (GTO), which is literally a Hohmann ellipse with perigee near 200 to 400 km and apogee at GEO altitude. The satellite then fires its onboard apogee-kick motor to circularize. Real missions combine that apogee burn with a plane change to cancel the inclination inherited from the launch site, and they do it at apogee on purpose, because the spacecraft is moving slowest there and an inclination change costs the least where speed is lowest.

Scaling up: the journey to Mars

The same ellipse works around the Sun. An Earth-to-Mars Hohmann transfer is a heliocentric ellipse with perihelion at Earth's orbit (1 AU) and aphelion at Mars's orbit (1.524 AU). The departure burn adds about 2.94 km/s to Earth's 29.78 km/s orbital speed, and the arrival burn near Mars is about 2.65 km/s, for roughly 5.6 km/s of heliocentric delta-v. The coast lasts about 259 days, close to nine months.

Because both planets keep moving, you cannot launch whenever you like. Mars has to be about 44 degrees ahead of Earth at departure so that it arrives at the rendezvous point at the same moment the spacecraft does, 180 degrees around the Sun. That alignment recurs only on Mars's synodic period:

1 / | 1/T_Earth - 1/T_Mars | = 1 / | 1 - 1/1.881 | ~ 2.14 years ~ 780 days

That is the famous "every 26 months" Mars launch window. Every Mars mission in history, from Mariner 4 in 1965 to Perseverance in 2021, has launched inside one of these narrow recurring windows; miss it and you wait over two years.

The trade-off: cheapest, but not fastest

A Hohmann transfer minimizes fuel, but it maximizes travel time among reasonable trajectories. The coast time is locked by the ellipse's geometry, so the only way to arrive sooner is to spend dramatically more propellant on a steeper, higher-energy path. For Earth to Mars, cutting the trip in half can demand on the order of ten times the fuel. That is the fundamental speed-versus-fuel bargain of spaceflight, and it is why crewed Mars architectures wrestle so hard with closing the loop on propellant.

The Hohmann transfer is also not always the absolute champion. When the destination orbit is more than about 11.94 times the radius of the starting orbit, a three-burn bi-elliptic transfer can actually use less total delta-v, trading a much longer flight time for fuel savings. For everything inside that ratio, including the LEO-to-GEO case, Hohmann's century-old two-burn ellipse remains the provably optimal answer, and the workhorse of orbital mechanics.

Frequently Asked Questions

Why does a Hohmann transfer use exactly two burns?

The two circular orbits are connected by a single ellipse that touches each one at one point. The first burn places the spacecraft onto that transfer ellipse, and the second burn at the far end reshapes the ellipse back into a circle at the new altitude. Two tangent points means two along-track burns, which is the minimum and most fuel-efficient option for moving between coplanar circular orbits.

How long does a Hohmann transfer take?

The coast time is exactly half the orbital period of the transfer ellipse, set entirely by its geometry. Raising from the ISS to geostationary orbit takes about 5 hours 15 minutes, while an Earth-to-Mars transfer around the Sun takes roughly 259 days, about nine months. You cannot speed it up without switching to a higher-energy, more fuel-hungry trajectory.

What is the vis-viva equation and why does it matter here?

The vis-viva equation, v = sqrt(mu * (2/r - 1/a)), gives orbital speed at any distance r for an orbit with semi-major axis a. It lets you compute the speed needed at each end of the transfer ellipse and the local circular speeds, and the delta-v for each burn is just the difference between them. It is the single tool that turns the geometry into concrete fuel numbers.

Is the Hohmann transfer always the most fuel-efficient option?

It is the cheapest two-burn transfer between coplanar circular orbits as long as the target radius is less than about 11.94 times the starting radius. Beyond that ratio, a three-burn bi-elliptic transfer can use slightly less total delta-v at the cost of a much longer flight time. For common cases like LEO to GEO, the Hohmann transfer is provably optimal.