Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem

Abstract

Of the three collinear libration points of the Sun-Earth Circular Restricted Three-Body Problem (CR3BP), L 3 is that located opposite to the Earth with respect to the Sun and approximately at the same heliocentric distance. Whereas several space missions have been launched to the other two collinear equilibrium points, i.e. L 1 and L 2 , taking advantage of their dynamical and geometrical characteristics, the region around L 3 is so far unexploited. This is essentially due to the severe communication limitations caused by the distant and permanent opposition to the Earth, and by the gravitational perturbations mainly induced by Jupiter and the close passages of Venus, whose effects are more important than those due to the Earth. However, the adoption of a suitable periodic orbit around L 3 to ensure the necessary communication links with the Earth, or the connection with one or more relay satellites located at L 4 or L 5 , and the simultaneous design of an appropriate station keeping-strategy, would make it possible to perform valuable fundamental physics and astrophysics investigations from this location. Such an opportunity leads to the need of studying the ways to transfer a spacecraft (s/c) from the Earth's vicinity to L 3 . In this contribution, we investigate several trajectory design methods to accomplish such a transfer, i.e., various types of two-burn impulsive trajectories in a Sun-s/c two-body model, a patched conics strategy exploiting the gravity assist of the nearby planets, an approach based on traveling on invariant manifolds of periodic orbits in the Sun-Earth CR3BP, and finally a low-thrust transfer. We examine advantages and drawbacks, and we estimate the propellant budget and time of flight (TOF) requirements of each.

Transfers from Earth to Earth–Moon L3 halo orbits using accelerated manifolds

“…Bi-elliptic transfers, transfers using patched conics with gravity assists, and transfers utilizing low-thrust were modeled using the two-body problem. Following the work done by Hou et al, transfers using invariant manifolds associated with Lyapunov orbits about L 1 and L 2 were also explored (Tantardini et al, 2010).…”

Short-period effects of the planetary perturbations on the Sun–Earth Lagrangian point L3

“…ISEE-3, SOHO, WMAP, Genesis, Herschel and Planck are just few examples of missions in which the spacecraft reached the vicinity of the L 1 and L 2 Lagrangian points of the Sun-Earth system during its journey. While L 3 is also potentially useful for astrodynamics Gómez & Mondelo 2001;Barrabés & Ollè 2006;Terra et al 2014;Pàez & Efthymiopoulos 2015;Jorba & Nicolás 2020), no significant attention has been paid to the Sun-Earth L 3 point even if its Lyapunov orbits have been proposed as an ideal place for spacecraft because of the possibility to obtain data for the Sun, the inner planets, and the main belt from a new perspective (Hou et al 2007;Tantardini et al 2010). The aim of this study is to find orbits close to the Sun-Earth L 3 point that are useful for applications of astrodynamics.…”

Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem

“…There is much literature on invariant manifolds and connecting orbits in the CR3BP; see for example Gómez et al (2004); Koon et al (2008); Lo and Ross (1997); Davis et al (2010Davis et al ( , 2011; Tantardini et al (2010). In particular, connecting orbits in the planar CR3BP are well understood.…”