Bi-Elliptic Transfer

A bi-elliptic transfer is a way of steering a spacecraft from one orbit to another by sending it on a long looping detour far past its destination before settling in. For very large changes in orbit size, this patient route can sip slightly less fuel than the more direct path.

Quick facts

• Type: A three-burn orbital maneuver (a planned change of orbit using engine firings) between two orbits that are usually circular and share the same plane (they lie flat in the same tilt, with no twist between them).
• Compared to: The simpler two-burn Hohmann transfer, which uses a single transfer ellipse.
• When it wins on fuel: Never below a final-to-initial orbit radius ratio of 11.94; sometimes between 11.94 and 15.58; always above about 15.58.
• Worked example (LEO at 6,700 km radius to a circular orbit at 93,800 km, ratio about 14): Hohmann needs 4,133.72 m/s of delta-v; a bi-elliptic path with an intermediate apogee of 268,000 km needs 3,061.04 + 608.825 + 447.662 = 4,117.53 m/s, saving 16.19 m/s (about 0.4%).
• The cost is time: The Hohmann leg above takes roughly 15 h 34 min; pushing the bi-elliptic’s far point to about 75.8 times the starting radius (around 1.3 times the Earth-Moon distance) raises the saving to about 1% but stretches the trip to roughly 17 days.
• Fixed numbers: None. No set altitude, period, inclination, or speed applies — everything depends on the orbits and the chosen far point.

How it works

Delta-v is the total change in velocity an engine must supply, and it stands in for how much propellant a maneuver costs. Apoapsis is the highest, slowest point of an orbit; periapsis is the lowest, fastest point. The bi-elliptic transfer uses three short, sharp engine firings, each treated as an instant push.

Burn 1 fires prograde (in the direction of travel) from the starting orbit, flinging the craft onto a big transfer ellipse whose far point lies well beyond the target. Burn 2 happens out at that distant apoapsis, where the spacecraft is crawling along; a small prograde nudge there cheaply lifts its low point up to the target radius, placing it on a second, inbound ellipse. Burn 3 fires when the craft falls back down to that low point, rounding the path into the final circular orbit.

Two effects make the savings possible. Because of how energy of motion and energy of position trade off, raising the low point of an orbit is extremely cheap when done far out where the craft moves slowly — in the limit of an infinitely distant far point, that middle burn costs nothing. And the Oberth effect means engine burns do the most good where the vehicle is moving fastest, deep in the planet’s gravity. The bi-elliptic plan places its largest, most efficient burn at the high-speed starting point. Together, for big enough orbit ratios, the three-burn total can dip just under the two-burn total.

Why it’s used

It pays off when the destination orbit is enormously larger (or smaller) than the start — radius ratios beyond about 11.94 — where it can shave total delta-v versus a Hohmann transfer. Its bigger practical advantage is for large changes of inclination (the tilt of the orbit’s plane). Tilting an orbit is cheapest where the craft moves slowest, so performing the plane change out at the distant apoapsis, folded together with the orbit-raising, can save far more fuel than tilting in a low, fast orbit. That makes it appealing for combined raise-and-tilt jobs, for reaching very high or lunar-distance orbits, and for studied designs like Mars orbit insertion paired with a plane change.

Notable missions

The bi-elliptic transfer is mainly a textbook and mission-design technique, chosen selectively for combined large-radius and large-tilt cases. It is flown far less often than the standard Hohmann transfer, and most documented uses live in design studies rather than named flagship flights. Examples include:

• Mars orbit insertion designs that fold a plane change into arrival: insertion burn, plane change at apoapsis, then a periapsis raise — a bi-elliptic-style three-burn arrival.
• Studied three-burn bi-elliptic insertion maneuvers for rendezvous with the Martian moons Phobos and Deimos.
• Combined orbit-raising plus large inclination-change maneuvers — for instance moving spacecraft to high orbits or near lunar distance — with the plane change done cheaply at the far apoapsis.

The chief trade-off is time for propellant. Adding a third burn and a long swing far beyond the target makes the trip dramatically longer — the LEO example grows from about 15.5 hours to days or weeks — while the fuel saving is modest, often well under 1 to 2 percent and only above a ratio of about 11.94. The extra burn and long coast add complexity, one more chance for error, and more exposure to disturbances. For that reason it stays reserved for the specific cases where very large orbit or plane changes make the patience worthwhile.