The Hohmann Transfer: Why It's Everywhere in Spaceflight
If you've ever watched a NASA mission and someone said "they're doing a Hohmann transfer to get to Mars," they were describing the most-used trick in orbital mechanics. It's also one of the simplest. Walter Hohmann published the idea in 1925, and it remains the workhorse of low-thrust orbital maneuvers.
The basic idea
A Hohmann transfer is the most fuel-efficient way to move a spacecraft between two circular orbits in the same plane, using only two engine burns. The spacecraft leaves its current orbit, enters an elliptical "transfer orbit" that touches both the original and the target orbit, then performs a second burn at the other end to circularize.
That's it. Two burns. One ellipse. Done.
Why is it efficient?
Hohmann transfers minimize the total delta-v (change in velocity) needed for the maneuver. There's a more efficient option called a bi-elliptic transfer for very large orbit changes (typically when the ratio of final to initial altitude is more than ~11.5), but for the vast majority of real missions — Starlink shell changes, lunar transfers, even some Mars transfers — the Hohmann is optimal.
The cost you pay is time. The transfer takes longer than alternative trajectories. For commercial constellations (where every second of fuel matters), that's fine. For crewed missions, sometimes a faster trajectory is worth the extra fuel.
The math, briefly
For a transfer from circular orbit radius $r_1$ to circular orbit radius $r_2$, with $r_2 > r_1$:
First burn (at $r_1$): speed up to the transfer orbit's apogee velocity
$$\Delta v_1 = \sqrt{\frac{\mu}{r_1}} \left(\sqrt{\frac{2 r_2}{r_1 + r_2}} - 1\right)$$
Second burn (at $r_2$): speed up to the new circular orbit velocity
$$\Delta v_2 = \sqrt{\frac{\mu}{r_2}} \left(1 - \sqrt{\frac{2 r_1}{r_1 + r_2}}\right)$$
Where $\mu$ is Earth's standard gravitational parameter ($3.986 \times 10^{14}$ m³/s²).
The total delta-v is the sum. For a low Earth orbit (400 km) to geosynchronous transfer orbit (35,786 km), that comes out to about 2.5 km/s — roughly the delta-v of a Falcon 9 second stage. This is why GEO missions can be done with moderate-sized rockets, but only with multiple burns.
Real-world examples
Starlink shell changes. SpaceX routinely uses Hohmann transfers to raise Starlink satellites from their initial drop-off orbit (~300 km) to their operational orbit (~550 km). The satellites do this with their onboard krypton-ion thrusters over the course of weeks.
Lunar transfers. Most missions to the Moon (Apollo, Artemis, most lunar orbiters) use a Hohmann-like transfer to reach lunar distance. The Apollo missions didn't use a pure Hohmann because they needed a free-return trajectory (in case the engine failed). But the basic idea — elliptical transfer to the Moon, then circularize at lunar distance — is Hohmann.
Mars transfers. A pure Hohmann transfer to Mars is one of the standard reference trajectories. It opens every 26 months (when Earth and Mars are in the right alignment) and takes about 9 months. NASA's Mars missions all use Hohmann or near-Hohmann transfers for the trans-Mars injection.
Geostationary satellites. Every commercial GEO satellite uses a Hohmann transfer from GTO (geostationary transfer orbit, the elliptical orbit the launch vehicle drops them in) to GEO. The satellite's apogee kick motor fires at the high point of the GTO to circularize.
When NOT to use Hohmann
A pure Hohmann transfer isn't always the right choice:
- Out-of-plane maneuvers. If the target orbit is in a different plane (different inclination), you need a combined plane change and Hohmann, or a more complex trajectory. Plane changes are very expensive in delta-v.
- Crewed missions with deadlines. When you need to get somewhere fast, a faster (less fuel-efficient) trajectory is worth it. Apollo used a hybrid free-return trajectory; Artemis is more flexible.
- Very large orbit changes. For changes where the ratio of final to initial altitude is more than ~11.5:1, a bi-elliptic transfer can save delta-v. This is rare in practice but worth knowing.
Why it has lasted 100 years
The Hohmann transfer survives because:
- It's optimal for the most common class of orbital maneuvers.
- It's simple — two burns, one ellipse, no exotic physics.
- It scales — works the same for a CubeSat as for a flagship mission.
- It composes — you can chain multiple Hohmann transfers for complex multi-moon or multi-body missions.
The basic idea is now 100 years old, and the physics hasn't changed. The rockets have just gotten cheaper.