Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

Abstract

The dynamics of the circular restricted three-body Earth-Moon-particle problem predicts the existence of the retrograde periodic orbits around the Lagrangian equilibrium point L1. Such orbits belong to the so-called family G (Broucke, Periodic orbits in the restricted three-body problem with Earth-Moon masses, JPL Technical Report 32-1168, 1968) and starting from them it is possible to define a set of trajectories that form round trip links between the Earth and the Moon. These links occur even with more complex dynamical systems as the complete Sun-Earth-Moon-particle problem. One of the most remarkable properties of these trajectories, observed for the four-body problem, is a meaningful inclination gain when they penetrate into the lunar sphere of influence and accomplish a swing-by with the Moon. This way, when one of these trajectories returns to the proximities of the Earth, it will be in a different orbital plane from its initial Earth orbit. In this work, we present studies that show the possibility of using this property mainly to accomplish transfer maneuvers between two Earth orbits with different altitudes and inclinations, with low cost, taking into account the dynamics of the four-body problem and of the swing-by as well. The results show that it is possible to design a set of nominal transfer trajectories that require V Total less than conventional methods like Hohmann, bi-elliptic and bi-parabolic transfer with plane change.

Trajectories Derived from Periodic Orbits around the Lagrangian Point L1 and Lunar Swing-Bys: Application in Transfers to Near-Earth Asteroids

“…For example, de Melo et al [4] used the application of small ∆Vs at strategic points at translunar trajectories to perform transfers between LEOs and highinclined LLOs. In [5], an approach to reduce the fuel consumption to change the orbital plane of Earth orbits was presented considering this link and lunar swing-bys maneuvers to provide enough energy for the orbital plane changes. Trajectories derived from the orbits of family G, in combination with swing-by maneuvers with the Moon, were considered as a starting point for a simple analysis of the possibility of planning transfer missions to the NEAs 99942 Apophis, 1994WR12, and 2007 UW1 in [6].…”

Alternative Paths to Reach Asteroids

“…The existence of this type of trajectory enables the search of initial conditions which, starting from a circular orbit around the Earth, promoting a meeting appropriate next to the moon and enough energy gain for the occurrence of escape. As explored in [2] and [3], starting from an initial parking circular orbit around the Earth is possible insert a spacecraft into a trajectory to conduct a close pass of the moon, through an appropriate velocity increment ∆ V 1 . A representation of this scheme is shown in Figure 2 to Earth as a time function.…”

Applications of celestial mechanics in natural objects and spacecrafts

“…The literature is very reach in topics related to this field, starting from basic impulsive maneuvers (Roth 1967;Prussing 1970Prussing , 1969Eckel 1963;Hohmann 1925;Smith 1959;Bender 1962;Jin and Melton 1991;Jezewski and Mittleman 1982;Hoelker and Silber Hoelker and Silber;Shternfeld 1959;Gross and Prussing 1974;Eckel 1982;Prussing and Chiu 1986;Ting 1960;Walton et al 1975). Then, it goes to orbital maneuvers based in low thrust (Casalino and Colasurdo 2002;Casalino et al 1999;Brophy and Noca 1998;Zee 1963;Lion and Handelsman 1968;Prado 2007, 2008;Macau 2000;Macau and Grebogi 2006), swing-by techniques (Flandro 1966;Marsh 1988;Farquhard and Dunham 1981;Prado and Broucke 1995;Prado 2007;Gomes et al 2013;DeMelo et al 2009), and even gravitational capture (Belbruno and Miller 1993;Pierson and Kluever 1994;Neto and Prado 1998). It covers also some more applied concepts, like searches for specific orbits (Chiaradia et al 2003;Carvalho et al 2010;Araujo et al 2012;Domingos et al 2008;D'Amario et al 1982;Farquhar et al 1985;…”