Moon Assisted Out of Plane Maneuvers of Earth Spacecraft
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Moon Assisted Out of Plane Maneuvers of Earth Spacecraft C. Circi,' F. Graziani,' and P. Teofflatto" Abstract This paper compares the usual Hohmann and bielliptic geostationary transfer orbits with lunar assisted transfers. It turns out that lunar assisted transfers are more economical for any inclination greater than the Moon orbit inclination. The lunar assisted transfers based on traditional flyby are analyzed: these are characterized by high values of the Keplerian apogee distance X a • Reducing such distance, the spacecraft approaches the Moon with lower energy and the lunar gravitational help can be more effective. In fact it is shown that transfers with smaller X a , called far lunar assisted geostationary transfers, are the most economical.
Introduction The velocity variation needed to transfer a spacecraft from a Low Earth Orbit (LEO) to the Geostationary Orbit depends on the height and inclination of the LEO. The usual Geostationary Transfer Orbit (GTO) is a two impulse Hohmann transfer with plane variation distributed between the two impulses. However it can be easily shown that for inclination greater than 40° any three impulse bielliptic geostationary transfer is convenient with respect to the GTO, regardless of the apogee distance x, of the transfer orbit, and the total variation of velocity d V needed in a bielliptic transfer decreases with X a • For higher apogees, it is appropriate to consider the lunisolar effect and to investigate whether it is possible to take advantage of this effect in order to reduce the d V needed to reach the geostationary orbit. In fact the dV can be reduced if a suitable lunar swing-by is performed [1,2], and such savings can be rather relevant for highly inclined LEO justifying the longer time needed to the transfer as well as the introduction of launch windows. 'Post Graduate Student, Scuola di Ingegneria Aerospaziale, Universita' di Roma "La Sapienza" v. Eudossiana 18,00184 Roma, Italy. 2Full Professor in Astrodynamics, Scuola di Ingegneria Aerospaziale, Universita' di Roma "La Sapienza" v. Eudossiana 18,00184 Roma, Italy. 3Associate Professor in Flight Mechanics, Scuola di Ingegneria Aerospaziale, Universita' di Roma "La Sapienza" v. Eudossiana 18, 00184 Roma, Italy.
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Circi, Graziani, and Teofilatto
It will be shown in this paper that the av needed in a geostationary transfer assisted by lunar swing-by is an increasing function of x a , then it is appropriate to try to reduce X a as much as possible. Namely the lunar swing-by method can be changed into a "far" lunar approach method reducing the height X a of the apogee. In the far lunar approach the trajectory is a low energy transfer, where the spacecraft crosses a region of unstable equilibrium about the intermediate Lagrangian point L 1 in the Earth-Moon system. In such a dynamical state the Moon drives the spacecraft toward the lunar orbit and the geostationary perigee and inclination are achieved after the lunar encounter. It turns out that these far lunar transfers are more economical with respect t
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