Minimum-Fuel Transfer between Coplanar Elliptic Orbits - Global Results Using Green’s Theorem

The use of Green’s theorem to determine the minimum-fuel transfer between coplanar elliptic orbits in the time-free, orientation-free case is reviewed and extended to the consideration of aeroassisted transfers. In addition to the two-impulse Hohmann transfer, there are many other transfers between a given pair of elliptic orbits that satisfy the local optimality conditions. Green’s theorem offers a straightforward and effective means of proving that most of these transfers cannot be globally optimal. Using Green’s theorem, it is shown that the minimum-fuel aeroassisted transfer belongs to one of two one-parameter families of transfers. Direct numerical comparison of the fuel consumption is used to determine the optimal value of the parameter for each family. There remains a best aeroelliptic transfer and a best aero-parabolic transfer which must be compared with the Hohmann and bi-parabolic all-propulsive transfers to determine the minimum-fuel transfer for each pair of initial and final elliptic orbits.

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