Editing Hohmann transfer orbit (section)

=== Bi-elliptic transfer ===
{{main|Bi-elliptic transfer}}
The bi-elliptic transfer consists of two half-[[elliptic orbit]]s. From the initial orbit, a first burn expends delta-v to boost the spacecraft into the first transfer orbit with an [[apoapsis]] at some point <math>r_b</math> away from the [[central body]]. At this point a second burn sends the spacecraft into the second elliptical orbit with [[periapsis]] at the radius of the final desired orbit, where a third burn is performed, injecting the spacecraft into the desired orbit.<ref name="Curtis">{{Cite book | last = Curtis | first = Howard | title = Orbital Mechanics for Engineering Students | page = 264 | publisher = [[Elsevier]] | year = 2005 | isbn = 0-7506-6169-0 | url = https://books.google.com/books?id=6aO9aGNBAgIC}}</ref>

While they require one more engine burn than a Hohmann transfer and generally require a greater travel time, some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial [[semi-major axis]] is 11.94 or greater, depending on the intermediate semi-major axis chosen.<ref name="Vallado">{{Cite book | last = Vallado | first = David Anthony | title = Fundamentals of Astrodynamics and Applications | page = 318 | publisher = Springer | year = 2001 | isbn = 0-7923-6903-3 | url = https://books.google.com/books?id=PJLlWzMBKjkC}}</ref>

The idea of the bi-elliptical transfer trajectory was first{{citation needed|date=January 2014}}<!-- a primary source of Sternfeld's paper does not establish that he was the "first" --> published by [[Ary Sternfeld]] in 1934.<ref name=sternfeld1934>
{{Citation |last=Sternfeld |first=Ary J. |title=Sur les trajectoires permettant d'approcher d'un corps attractif central à partir d'une orbite keplérienne donnée |language=fr |trans-title=On the allowed trajectories for approaching a central attractive body from a given Keplerian orbit |url=http://gallica.bnf.fr/ark:/12148/bpt6k31506/f711.image.langEN |journal=Comptes rendus de l'Académie des sciences |location=Paris |volume=198 |number=1 |date=1934-02-12 |pages=711–713}}.</ref>