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We study a more complex case of Hohmann orbital transfer of a satellite byconsidering non-coplanar and elliptical orbits, instead of planar and circularorbits. We use as parameter the angle between the initial and transferenceplanes 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 eachconfiguration. Some reasonable physical constraints are used: we apply impulsesat perigee or apogee of the orbit, we consider the duration of the impulse tobe short compared to the duration of the trip, we take the nodal line of threeorbits 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 ellipticorbits. In addition, we validate our method through a numerical solutionobtained by using some of the actual orbital elements of Sputnik I and VanguardI satellites. For these orbits, we found that the most fuel-efficient transferis obtained by applying the initial impulse at apocenter and keeping thetransfer orbit aligned with the initial orbit.

On non-coplanar Hohmann Transfer using angles as parameters