On trajectories of Earth-Moon flight of a particle with its temporary capture by the Moon

Low energy trajectories for the Moon-to-Earth space flight

“…, from the perilune of an initial elliptic orbit with the perilune altitude H π0 = 100 km and semimajor axis a 0 = 38,455 km. This orbit is close to the final orbit of the Earth-to-Moon space flight (Ivashkin 2002(Ivashkin , 2004a. All the following motions of the particle are passive (without taking into account possible corrections).…”

“…As a result of the analysis and taking into account the experience of the Earth-to-Moon trajectories studies (Ivashkin 2002(Ivashkin , 2004a, a numerical algorithm has been developed that has allowed us to find a family of detour trajectories for space flights to the Earth from elliptic orbits of the lunar satellite. These trajectories correspond to the spacecraft starting from both the Moon's surface and the low orbit of the lunar satellite for several positions of the Moon on its orbit.…”

“…First, we estimate an increase ∆E s = −E s0 of selenocentric energy (1) from the negative value E s0 for the initial elliptic orbit to the zero energy which can be caused by the Earth gravity during the particle selenocentric motion on the arc D Es from the initial state D to the escape point Es. On the basis of the orbit evolution theory (Lidov 1961(Lidov , 1962) and assuming that the particle's selenocentric orbit eccentricity is e s ≈ 1, the mean energy is E s ≈ −∆E s /2, and taking into account the change in the Moon-Earth direction, we obtain (Ivashkin 2002(Ivashkin , 2004a:…”

“…P 1 Es P 2 P 3 from the energy E s < 0). This acceleration is qualitatively described by an approximate model of the one-dimensional rectilinear particle's motion with the Earth, placed on the same line at a distance r M beyond the Moon (Ivashkin 2002(Ivashkin , 2004a, see figure 6. In this case dρ/dt > 0, i.e., the particle moves away from the Moon.…”

“…These trajectories are characterized by a small (several days) flight time and by the fact that the departure of the particle from the Moon occurs along a hyperbola. Recently (see, e.g., Belbruno and Miller 1993;Hiroshi Yamakawa et al 1993;Belló Mora et al 2000;Biesbroek and Janin 2000;Koon et al 2001;Ivashkin 2002Ivashkin , 2004a, a new class of trajectories with the Earth-to-Moon indirect detour space flight was discovered within the framework of the four-body system (Earth-Moon-Sun-particle). These trajectories use first the space flights towards the Sun (or away from the Sun) beyond the Earth's sphere of influence, and only afterwards, space flights towards the Moon.…”