Bi-elliptic transfer

A spacecraft maneuver that changes between circular orbits using two elliptical transfer arcs and three velocity changes. Its high intermediate apoapsis can reduce total propellant use compared with a Hohmann transfer for sufficiently large radius ratios.

Hohmann transfer: A two-impulse maneuver between coplanar circular orbits using one elliptical transfer orbit. It is the main comparison: bi-elliptic transfers can use less total velocity change when the orbit radii differ greatly.
Kepler orbit: An idealized orbit governed by gravity from a single spherical body, tracing a conic section. Each transfer arc is modeled as a Kepler orbit between impulsive burns.
Orbital transfer: A maneuver or sequence of maneuvers that moves a spacecraft from one orbit to another. Bi-elliptic transfer is a particular strategy within the broader problem of changing orbits.
Gravity-assist maneuver: A trajectory change that uses a celestial body's motion and gravity to alter a spacecraft’s velocity relative to another body. Unlike a bi-elliptic transfer, it can change heliocentric velocity without relying solely on onboard propellant.
Vis-viva equation: An equation relating orbital speed to distance from the focus and the orbit’s semimajor axis. It gives the spacecraft’s speed at each impulse point on the transfer ellipses.
Circular orbit: An orbit with constant distance from its central body and constant orbital speed in the ideal two-body model. The maneuver begins and ends in circular orbits, whose speeds set the endpoint conditions.
Propellant mass fraction: The fraction of a spacecraft’s initial mass consumed as propellant during a maneuver. A lower total delta-v can reduce propellant needs, subject to propulsion-system performance.
Low-thrust trajectory: A spacecraft trajectory shaped by sustained, relatively weak propulsion rather than brief large impulses. It replaces the transfer’s three idealized burns with gradual thrust over time.
Apoapsis: The point in an orbit farthest from the body being orbited. The first transfer arc reaches this point, where the second impulse changes the orbit’s shape.
Orbital energy: The conserved mechanical energy per unit mass of an object in an ideal gravitational orbit. Each impulse changes orbital energy, allowing the next ellipse to reach its required radius.

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