Editing Hohmann transfer orbit (section)

== Worst case, maximum delta-''v'' ==
As the example above demonstrates, the Δ''v'' required to perform a Hohmann transfer between two circular orbits is not the greatest when the destination radius is infinite.  (Escape speed is {{radic|2}} times orbital speed, so the Δv required to escape is {{radic|2}}&nbsp;−&nbsp;1 (41.4%) of the orbital speed.) The Δv required is greatest (53.0% of smaller orbital speed) when the radius of the larger orbit is 15.5817... times that of the smaller orbit.<ref>{{Cite book |last=Vallado |first=David Anthony |title=Fundamentals of Astrodynamics and Applications |page=317 |publisher=Springer |date=2001 |isbn=0-7923-6903-3 |url=https://books.google.com/books?id=PJLlWzMBKjkC}}</ref> This number is the positive root of {{math|1=''x''<sup>3</sup> − 15''x''<sup>2</sup> − 9''x'' − 1 = 0}}, which is <math display="inline">5+4\,\sqrt{7}\cos\left({1\over 3}\arctan{\sqrt{3}\over 37}\right)</math>.  For higher orbit ratios the {{math|Δ''v''}} required for the second burn decreases faster than the first increases.