A Hohmann transfer orbit is a fuel-efficient way to move a spacecraft between two circular orbits around the same central body. Instead of firing the engine continuously, the spacecraft uses two carefully timed engine burns. The first burn places the spacecraft on an elliptical transfer orbit, and the second burn circularizes the path at the new altitude.
This method matters because fuel is one of the most limited resources in spaceflight.
For a transfer from a lower circular orbit to a higher circular orbit, the spacecraft speeds up at the lower orbit to raise the far side of its path. It then coasts along the ellipse until it reaches the higher orbit, where it speeds up again to match the circular orbital speed there. For a transfer to a lower orbit, the same idea works in reverse, with engine burns that reduce speed.
The Hohmann transfer is not always the fastest route, but for many basic orbit changes it uses less fuel than most simple alternatives.
Key Facts
- A Hohmann transfer uses two engine burns: one to enter the elliptical transfer orbit and one to circularize at the destination orbit.
- The transfer ellipse has periapsis at the lower orbit radius and apoapsis at the higher orbit radius.
- Circular orbital speed is v = sqrt(mu / r), where mu = GM and r is orbital radius.
- The semi-major axis of the transfer ellipse is a = (r1 + r2) / 2.
- Transfer orbit speed at radius r is v = sqrt(mu(2 / r - 1 / a)).
- The total fuel cost is measured by delta-v: Delta v total = |Delta v1| + |Delta v2|.
Vocabulary
- Hohmann transfer
- A two-burn orbital maneuver that moves a spacecraft between two circular orbits using an elliptical transfer orbit.
- Delta-v
- The change in velocity a spacecraft must produce with its engines to complete a maneuver.
- Periapsis
- The point in an orbit where the spacecraft is closest to the body it is orbiting.
- Apoapsis
- The point in an orbit where the spacecraft is farthest from the body it is orbiting.
- Circularization burn
- An engine burn that changes an elliptical orbit into a circular orbit at the current altitude.
Common Mistakes to Avoid
- Treating altitude as orbital radius is wrong because orbital radius is measured from Earth's center, not from Earth's surface. Add Earth's radius to the altitude before using orbital equations.
- Assuming the spacecraft points straight upward during the first burn is wrong because the burn is mostly along the direction of motion. A tangential speed change reshapes the orbit efficiently.
- Forgetting the second burn is wrong because reaching the higher altitude does not mean the spacecraft is in the higher circular orbit. It must change speed again to match the circular orbit at that radius.
- Thinking the Hohmann transfer is the fastest path is wrong because it is designed for fuel efficiency, not minimum travel time. Faster transfers often require larger delta-v.
Practice Questions
- 1 A spacecraft is in a circular orbit with radius r1 = 7000 km around Earth and transfers to a circular orbit with radius r2 = 14000 km. Using mu = 398600 km^3/s^2, find the semi-major axis of the transfer ellipse.
- 2 Using v = sqrt(mu / r), calculate the circular orbital speed at r = 8000 km around Earth. Use mu = 398600 km^3/s^2 and give your answer in km/s.
- 3 A spacecraft moving from a lower circular orbit to a higher circular orbit uses a Hohmann transfer. Explain why the first burn raises the apoapsis and why a second burn is needed at apoapsis.