A note on libration point orbits, temporary capture and low-energy transfers

Optimal low-thrust transfers between libration point orbits

“…We applied this technique to compute low-thrust solutions for five connections from SB L 1 to EM L 1 . Table 2 reports the values of the Jacobi constants (J SB and J EM , respectively) of the two planar Lyapunov orbits, the x-coordinate x P of the Poincaré section in the SB synodical barycentric reference frame, the time of flight on each of the two segments ( T EM and T SB , respectively), the total time of flight (TOF) and the estimated magnitude ( V ) of the impulsive maneuver to be applied at the Poincaré section according to Fantino et al (2010). An additional column provides an estimate of the final spacecraft mass m f as obtained by assuming that the initial value is of 500 kg and the specific impulse of the chemical engine is of 300 s. The low-thrust solutions for the same cases are presented in Table 3 where the total flight time T O F (fifth column) is divided into three parts (columns 2-4), i.e., the travel time on the EM manifold trajectory ( t EM ), the propelled phase ( t SB p ) and the overall ballistic phase in the SB CR3BP ( t SB ).…”

“…The strategy of flying a spacecraft to the Moon via this technique can reduce considerably (∼1 km s −1 ) the propellant budget relative to traditional techniques like the Hohmann transfer, although the time of flight is much longer (i.e., months vs. a few days) (Parker and Lo 2005). In a recent work by Fantino et al (2010), low energy transfers between libration point regions in the Sun-Earth and Earth-Moon systems are analyzed systematically by searching for connections between any two libration points L 1 and L 2 in the Sun-Earth and Earth-Moon coupled CR3BPs. The coupling between the two systems is parameterized by the relative orbital phase of the two rotating reference frames in inertial space; the Jacobi constants J SE and J EM of the LPOs to be connected is varied over a range which defines a family of Lyapunov orbits in each system; finally, the point of application of the impulsive maneuver varies over a certain domain.…”

Sun–Earth $$L_{1}$$ L 1 and $$L_{2}$$ L 2 to Moon transfers exploiting natural dynamics

“…For instance, the methodology has been employed in the study of multi-moon tours Lantoine et al 2011;Campagnola and Russell 2011) and in the context of the CR3BP Gómez et al 2001;Marsden and Ross 2006;Canalias and Masdemont 2008;Fantino et al 2010). e defnition and equations of motion of the CR3BP (seion 2.1), its equilibrium points (seion 2.2), the fow near these equilibrium points (seion 2.3), and the method of conneing two CR3BPs (seion 2.4) provide the background theory from existing literature on which the subsequent seions (use of the survival maps and the design of the transfers) rely.…”

“…Figure 7 shows that the arcs fowing towards the lunar arrival states bear quite some similarity to the manifold struure fowing towards its associated libration point orbit. Moon systems is necessary (Fantino et al 2010). e concept is illustrated in Figure 8a, where a segment of arcs in the Earth-Moon system (shown in blue) has been converted into the SunEarth barycentric synodical reference frame.…”

“…is methodology has been used in the past to study trajeories between the Sun-Earth libration points and the vicinity of the Earth and Moon, where a conneion is made using the unstable manifold fowing from the Sun-Earth libration point (within the Sun-Earth CR3BP) and the stable manifold fowing towards the Moon L2 point (within the Earth-Moon CR3BP) at low ∆v cost. Examples include the work done by ; Gómez et al (2001); Canalias and Masdemont (2008);and Fantino et al (2010).…”