  We study a more complex case of Hohmann orbital transfer of a satellite by
considering non-coplanar and elliptical orbits, instead of planar and circular
orbits. We use as parameter the angle between the initial and transference
planes that minimizes the energy, and therefore the fuel of a satellite,
through the application of two non-tangential impulses for all possible cases.
We found an analytical expression that minimizes the energy for each
configuration. Some reasonable physical constraints are used: we apply impulses
at perigee or apogee of the orbit, we consider the duration of the impulse to
be short compared to the duration of the trip, we take the nodal line of three
orbits to be coincident and the three semimajor axes to lie in the same plane.
We study the only four possible cases but assuming non-coplanar elliptic
orbits. In addition, we validate our method through a numerical solution
obtained by using some of the actual orbital elements of Sputnik I and Vanguard
I satellites. For these orbits, we found that the most fuel-efficient transfer
is obtained by applying the initial impulse at apocenter and keeping the
transfer orbit aligned with the initial orbit.
