Science & Technology

What Is the Hohmann Transfer? Calculating the Hohmann Transfer for Orbits

Written by MasterClass

Jun 20, 2019 • 3 min read

Spaceships and satellites are often used to orbit celestial bodies, whether that’s the moon, a distant planet, or the Earth itself. But not all orbits are the same. Orbits at low altitudes require different speeds and expenditures of energy than orbits at high altitudes. Once an object is orbiting at a specific altitude, the laws of inertia make it very easy to maintain that orbit. But changing the altitude of orbit is quite complicated. Fortunately, modern physicists have a method to make such a thing possible: the Hohmann transfer.

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What Is the Hohmann Transfer?

The Hohmann transfer is a system of firing rockets that physicists use to move a spacecraft into a different altitude of orbit. To understand how the Hohmann transfer works, it’s important to understand the broader principle of orbital mechanics.

“Orbital mechanics” is a term for the mathematics by which a spaceship changes orbit. For objects that are in orbit, the closer they are to the object they are orbiting, the faster they will travel around it. This applies to any object orbiting another:

  • Earth orbiting the sun
  • The moon orbiting Earth
  • A spaceship orbiting a planet

In orbital mechanics, the concepts of speeding up and slowing down are complex and counterintuitive. In orbit, firing your engines frontwards moves you forward into a higher orbit, which actually means you slow down, because objects in a higher orbit move more slowly. In order to go faster you need to decelerate and fall into a lower orbit.

The farther away you are from Earth, the less magnified this effect is. When you get far enough away from Earth, the relative effects of orbital mechanics are so low that you can navigate as if you are operating your spaceship in deep space.

How Does the Hohmann Transfer Work?

The Hohmann transfer is the most commonly used method to move a spaceship from a lower orbit to a higher one.

In the 1920s, German engineer Walter Hohmann, inspired by science fiction, calculated the most efficient way to move to a higher orbit.

  • The Hohmann transfer works by firing the rocket engines once at a certain point in the lower orbit. This firing adds energy to the orbit and propels the spaceship farther from Earth, changing its orbit from a circular orbit to an oval-shaped orbit.
  • At the point in that new oval orbit at which the spaceship is farthest from Earth, the crew fires the rocket’s engines again, and the oval orbit turns back into a circle—this one farther from Earth than the last.

The Hohmann transfer is the industry standard for the most energy efficient orbital transfer, and it applies no matter how far into space you are traveling. If a spaceship in orbit fires its engine long enough, it will eventually go fast enough to fly away into deep space, escaping the planet’s gravity. That speed, called escape velocity, is simply the square root of 2, or 41% faster than orbital speed.

How Does the Hohmann Transfer Apply to the International Space Station?

The Hohmann transfer is used by the crew of the International Space Station (ISS). Because of small bits of air around the ISS, the station gets pulled back toward Earth ever so slightly as it orbits. In order to avoid a continued spiral inward to Earth, the crew on board the ISS or Mission Control has to fire its engines every so often to move it into a higher orbit.

How Is the Hohmann Transfer Applied to Interplanetary Travel?

Let’s say you are trying to send a spacecraft from Earth to Mars, and you want to do so as efficiently as possible. To accomplish this, scientists take advantage of the fact that the spacecraft is already in orbit before it launches. How is this true? The reason is that the spacecraft sits on Earth, and Earth orbits the sun.

Mars also orbits the sun, but at a much greater distance (or altitude above the sun). Scientists use the Earthly and Martian orbits to establish what’s known as a perihelion and an aphelion.

  • The perihelion (closest approach to the sun) will be at the distance of Earth’s orbit
  • The aphelion (farthest distance from the sun) will be at the distance of Mars’ orbit

Scientists design an orbit for the rocket that will include both the perihelion and the aphelion. In other words, the rocket, in a single orbit of the sun, will coincide with Earth’s orbit at the start of its journey and will coincide with Mars’ orbit at the end of its journey. This is known as a Hohmann Transfer orbit. The specific portion of the rocket’s solar orbit that takes it from Earth to Mars is called its trajectory.

Learn more about space exploration in former astronaut Chris Hadfield’s MasterClass.