On the influence of the planet's gravitational field on the characteristic velocity of an interorbital transfer

G. P. Maliavkin

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2015), pp. 88-99

Résumé

The neighborhoods of the collinear libration points of the Sun–Earth system are currently quite attractive for space exploration. Today, various projects on placement of spacecrafts in the $L_1$ libration point to observe the Sun and telescopes in $L_2$ have been implemented. Many of such projects are under development. At present, different ways of using libration points connected with the idea of transporting small celestial bodies to the near-earth space are being investigated. This idea arouses growing interest in the impulse transfer theory that was developed to approximately describe transfers of celestial bodies from one orbit to another. In this paper a model example of a two-impulse transfer of a celestial body from its circular heliocentric orbit to the collinear libration point $L_1$ of the Earth–Sun system is examined. The boundary conditions for the endpoint of the transfer trajectory are somewhat loosened. The loosening of the boundary conditions is based on the idea that the body is not required to be placed exactly in $L_1$, but only to stay close to the libration point for an extended period of time. As a characteristic of a residence time of a body in the neighbourhood of a libration point a special function of phase variables, “the hazard function”, is used. It is shown, that in this case the energy consumption, expressed by the characteristic velocity of the transfer, could be reduced by several percent. Collinear libration points are unstable. This fact entails the problem of stabilization of the celestial body's motion after its transportation. It is shown that control, constructed with the use of the hazard function, provides the stabilization of the orbital motion in the neighbourhood of the libration point. Refs 8. Figs 9. Table 1.

Détail

Keywords: restricted three-body problem, collinear libration point, impulse transfer, stabilization of the motion.