Hohmann transfer orbit

How does a spacecraft orbiting a planet move from one circular orbit to another? It can’t just change lanes like a car going around a racetrack because speed and altitude cannot be changed independently.

The most energy-efficient way to move between circular orbits is the Hohmann transfer orbit [1]. The Hohmann orbit is an idealization, but it approximates maneuvers actually done in practice.

The Hohmann transfer requires applying thrust twice: once to leave the first circular orbit into the elliptical orbit, and once again to leave the elliptical orbit for the new circular orbit.

Suppose we’re in the orbit represented by the inner blue circle above and we want to move to the outer green circle. We apply our first instantaneous burst of thrust, indicated by the inner ×, and that puts us into the orange elliptical orbit.

(We can’t move faster in our current orbit without continually applying trust because velocity determines altitude. The new orbit will pass through the point at which we applied the thrust, and so our new orbit cannot be a circle because distinct concentric circles don’t intersect.)

The point at which we first apply thrust will be the point of the new orbit closest the planet, the point with maximum kinetic energy. The point furthest from the planet, the point with maximum potential energy, will occur 180° later on the opposite side. The first burst of thrust is calculated so that the maximum altitude of the resulting elliptical orbit is the desired altitude of the new circular orbit.

Once the elliptical orbit is at its maximum distance from the planet, marked by the outer ×, we apply the second thrust.  The amount of thrust is whatever it needs to be in order to maintain a circular orbit at the new altitude. The second half of the elliptical orbit, indicated by the dashed orange curve, is not taken; it’s only drawn to show the orbit we would stay on if we didn’t apply the second thrust.

So in summary, we use one burst of thrust to enter an elliptic orbit, and one more burst of thrust to leave that elliptical orbit for the new circular orbit. There are ways to move between circular orbits more quickly, but they require more fuel.

The same principles work in reverse, and so you could also use a Hohmann transfer to descend from a higher orbit to a lower one. You would apply your thrust opposite direction of motion.

There are several idealizations to the Hohmann transfer orbit. The model assume orbits are planar, that the initial orbit and the final orbit are circular, and that the two burns are each instantaneous.

The Hohmann transfer also assumes that the mass of the spacecraft is negligible compared to the planet. This would apply, for example, to a typical communication satellite, but perhaps not to a Death Star.

More orbital mechanics posts

• New math for going to the moon
• Arensdorf’s orbit
• Kepler’s equation

[1] If you’re moving from one orbit to another at 12 times the radius, then the bi-elliptic orbit maneuver would use less fuel. Instead of taking half of an elliptical orbit to make the transfer, it fires thrusters three times, using half each of two different elliptical orbits to reach the desired circular orbit.