The Hohmann transfer orbit (1925) is the most fuel-efficient way to move between two circular orbits. It’s the backbone of interplanetary mission design.

How it works

The transfer is an ellipse that is tangent to both the starting orbit and the destination orbit. It requires exactly two burns:

1. Departure burn: At the starting orbit, fire prograde (forward) to raise the apoapsis to the destination orbit’s altitude. You’re now on the transfer ellipse.
2. Arrival burn: Half an orbit later, at apoapsis, fire prograde again to circularise into the destination orbit.

That’s it. Two impulses, one half-ellipse. Minimum energy.

Delta-v: the currency of spaceflight

Delta-v ($\Delta v$) is the total velocity change a spacecraft needs. It’s the fundamental budget of any mission — how much “speed change” your fuel can buy.

For a Hohmann transfer from radius $r_1$ to $r_2$ around a body of mass $M$:

$$\Delta v_1 = \sqrt{\frac{GM}{r_1}} \left( \sqrt{\frac{2r_2}{r_1 + r_2}} - 1 \right)$$

$$\Delta v_2 = \sqrt{\frac{GM}{r_2}} \left( 1 - \sqrt{\frac{2r_1}{r_1 + r_2}} \right)$$

The cost of getting to Mars

Earth orbits at ~1 AU. Mars at ~1.52 AU. A Hohmann transfer takes about 259 days (just over 8.5 months) and requires ~3.6 km/s of delta-v from Earth’s orbit.

But you also need to escape Earth’s gravity (~3.2 km/s) and then slow down into Mars orbit (~1.5 km/s). The total mission delta-v is around 5.7 km/s — explaining why Mars missions are challenging but feasible.

Launch windows

A Hohmann transfer only works when the planets are in the right relative positions. For Earth-Mars, this alignment happens roughly every 26 months — the synodic period. Miss the window and you wait over two years.

This is why Mars missions cluster in time: 2020 saw three missions launch within days of each other (Perseverance, Tianwen-1, Hope) — all catching the same window.

Beyond Hohmann

The Hohmann transfer minimises fuel but not time. Faster transfers (bi-elliptic, low-thrust spirals, gravity assists) trade fuel for speed. For crew missions where radiation exposure matters, faster is better — but more expensive.