STUDY OF THE TRANSFER FROM THE EARTH TO A HALO ORBIT AROUND THE EQUILIBRIUM POINT L1 GtMEZ Departament de Matemg~tica Aplicada i Anfdisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain A. JORBA and J. MASDEMONT Departament de MatemgaicaAplicada I,, UniversitatPolitScnica de Catalunya, E.T.S.E.LB., Diagonal 647, 08028 Barcelona, Spain and c. SIM6 Departament de MatemglticaAplicada i Angdisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (Received 3 March 1992; accepted 9 November, 1992) Abstract. The purpose of this paper is to study a transfer strategy from the vicinity of the Earth to a halo orbit around the equilibrium point L1 of the Earth-Sun system. The study is done in the real solar system (we use the DE-118 JPL ephemeris in the simulations of motion) although some simplified models, such as the restricted three body problem (RTBP) and the bicircular problem, have been also used in order to clarify the geometrical aspects of the problem. The approach used in the paper makes use of the hyperbolic character of the halo orbits under consideration. The invariant stable manifold of these orbits enables the transfer to be achieved with, theoretically, only one manoeuvre: the one of insertion into the stable manifold. For the total Av required, the figures obtained are similar to the ones given by the standard procedures of optimization. Key words: Halo orbits, quasi-periodic orbits, invariant manifolds, transfer orbits, gravity assist orbits. 1. Introduction In this paper we shall consider halo orbits around the equilibrium point L1 of the Earth-Sun system. This point is between the Earth and the Sun at approximately 1500000 km (0.01 AU) from the Earth. The halo orbits that will be studied are close to the one that was followed by the ISEE-3 spacecraft in 1978, or the one that shall be used for the SOHO mission in the near future. Both orbits, as seen from the Earth, have approximately a vertical amplitude, with respect to the ecliptic, of 120000 km and a horizontal one of 666000 km. The usual way to obtain transfer trajectories from the Earth to a halo orbit is by means of an optimization procedure. The method looks for an orbit between the Earth and the halo maintaining some boundary conditions, subject to some technical constraints, which minimizes the total fuel to be spent in manoeuvres during the transfer (see [6]). The approach we propose in this paper is a geometrical one that avoids the main procedure of optimization, which gives no information about the Celestial Mechanics and Dynamical Astronomy 56" 541-562,1993. © 1993 Kluwer Academic Publishers. Printed in the Netherlands.