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:

1. It's optimal for the most common class of orbital maneuvers.
2. It's simple — two burns, one ellipse, no exotic physics.
3. It scales — works the same for a CubeSat as for a flagship mission.
4. 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.

What Hohmann transfers don't tell you

A pure Hohmann transfer assumes co-planar circular orbits and impulsive burns. Real missions relax almost every assumption. Inclined target orbits require combining the perigee burn with a plane change, which costs much more delta-v than the pure Hohmann. Non-circular target orbits (operational orbits with slight eccentricity) require a third burn to circularize at apogee, called the apogee kick motor for GEO missions or the orbit circularization burn for lunar orbiters. Low-thrust propulsion (electric or ion) replaces the impulsive burns with extended arcs of thrust, which compresses the delta-v budget by exploiting the Oberth effect.

The Hohmann is the first-order answer for many missions, but real mission designers almost never fly a textbook Hohmann. They compose multiple Hohmann-like segments with plane changes, gravity assists, low-thrust spirals, and parking orbits. The Apollo free-return trajectory — what got the crew home safely when the service module oxygen tank exploded on Apollo 13 — was a Hohmann-cousin combined with a lunar gravity assist.

Hohmann transfer to Mars: a worked example

Take an Earth-Mars Hohmann transfer launched from a 300 km circular parking orbit. The relevant delta-v budget:

• LEO to LEO-perigee: 0 (already in parking orbit)
• Trans-Mars injection (LEO perigee burn): roughly 3.6 km/s
• Mars orbit insertion (Mars arrival burn): roughly 0.9-1.4 km/s, depending on the target orbit

That 3.6 km/s for trans-Mars injection is larger than a Falcon 9 second stage can produce — which is why Mars missions launch on a heavy-lift vehicle (Atlas V, Falcon Heavy, SLS, Starship) that can deliver a fully-loaded upper stage and payload directly to a high-energy departure orbit. Pure Hohmann from low Earth orbit is impractical for Mars; the parking orbit is more typically near-geosynchronous (GTO, then escape from apogee) or higher.

For Earth-return Hohmann transfers, the budget is similar: roughly 0.9-1.2 km/s at Mars departure, then Earth re-entry absorbs the rest of the kinetic energy in the atmosphere (which is why re-entry is hot).

FAQ

Why does the Hohmann transfer take 9 months to Mars when the planets are close?

Because the Hohmann transfer matches the orbital geometry of two circular orbits, and the planets travel on those orbits. The transfer ellipse is shaped by the relative position of Earth at departure and Mars at arrival; the geometry constrains the transit time to roughly 8.5 months (closing geometry) or roughly 9-10 months (opposition-class transfers).

Is the Hohmann transfer ever used for satellites in different orbital planes?

Yes, but the cost goes up. A combined plane change + Hohmann requires burning at the node where the orbit crosses the target plane, which can be far from the optimal Hohmann apogee/perigee. Many operators instead launch directly into the target plane and avoid the problem — which is why launch sites near the equator (Kourou, Wenchang) are preferred for inclined orbits.

What if my spacecraft has only one engine?

A single-engine spacecraft can still execute a Hohmann transfer — the two burns just happen sequentially rather than in parallel. Many small satellites and most deep-space probes fire the same main engine twice. The catch is that the orbit is fixed between burns; you cannot abort the second burn unless you have backup propulsion or careful navigation software.

Do Hohmann transfers work for the Moon?

Yes — and most lunar missions use one. The Apollo free-return trajectory is essentially a Hohmann with a lunar gravity assist that bends the path through the Moon's sphere of influence. Modern NASA missions to the Moon use the trans-lunar injection burn to drop into a Hohmann-like transfer with a free-return backup mode — the same Apollo playbook, modernized.

What's the fastest orbital transfer that's lower fuel than Hohmann?

There isn't one. Hohmann is provably optimal for co-planar circular-to-circular transfers when impulsive burns are available. The alternatives (bi-elliptic, low-thrust spiral, plane-change strategies) either trade time for fuel or relax one of those assumptions. The Hohmann is the optimal when all four constraints are fixed.

How does Starship's orbital refueling change the calculus?

It doesn't change Hohmann math. It changes the delta-v budget available to a mission. A Starship with on-orbit refueling can take a payload to the Moon or Mars with a much higher departure delta-v than a single-launch vehicle. That translates to a faster Hohmann transfer (shorter transfer ellipse, more aggressive trajectory) or a higher-energy non-Hohmann trajectory. Refueling doesn't break Hohmann optimality; it just lets you spend more fuel on maneuvers that violate Hohmann assumptions.