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Orbit Transfer



I am having trouble explaining conceptually why the following is true. If one
wants to transfer between 2 circular orbits a Hohmann transfer is the most
efficient way if there is no plane change. If the energy required for the
Hohmann transfer is compared to the difference in the total energy (-GMm/2a) of
the 2 circular orbits, it is always greater. Where was this energy "lost"? If
it were possible to lift the satellite directly up to the higher orbit then it
would have to be slowed down to stay in the higher orbit. In a Hohmann transfer
there is no slowing down (transferring to a higher orbit). How can this be
explained to students who are sharp enough to discover this discrepancy?

Dan Burns
Los Gatos High School