Analysis of Capture Trajectories into Periodic Orbits About Libration Points

Abstract

Spacecraft capture trajectories to Lyapunov/Halo periodic orbits of the L1 and L2 points in the restricted Hill three-body problem are analyzed. The specific focus is on transfer to these orbits from interplanetary trajectories. This application is motivated by future proposals to place "deep space ports" at the Earth and Mars L1 or L2 points. We use stable manifolds for capture trajectories to periodic orbits around the libration points. Numerical results show that the stable and unstable manifolds from periodic orbits around the libration points can intersect the surface of any of the planets of the solar system by changing the size of periodic orbits. Applying this to Earth-Mars transfers, the cost of capture into a periodic orbit is reduced compared with direct capture into a parabolic orbit. Moreover, if a spaceport is built on a periodic orbit in the vicinity of a sun-Mars libration point and propellant can be supplied there to the spacecraft, the required V for entry into a circular orbit about Mars from an interplanetary trajectory can be considerably reduced compared with a direct entry into a circular orbit.

Libration Transfer Design Using Patched Elliptic Three-Body Models and Graphics Processing Units

“…Periodic orbits, quasi-periodic orbits, and their invariant manifolds in three-body systems are well-known dynamical structures and have been employed as tools to design various types of trajectories, such as Sun-Earth libration point missions [2,3], low-energy captures into Mars halo orbit [4,5], and transfers between collinear libration points [68]. However, when a spacecraft moves in the space where all the gravitational inuences of the Sun, Earth, and Moon are too large to be ignored, the complexity of the trajectory design problem increases.…”

Halo Orbits at Sun-Mars L1, L2 in the Photogravitational Restricted Three-Body Problem with Oblateness

“…Applications of liberation point orbits are intensely studied by Farquhar and Kamel [2] on quasi-periodic orbits about translunar liberation points. Mission designs utilizing the halo orbits become more challenging and several works have been done by Farquhar et al [3], Richardson [4] , Huber et al [5] , Gó mez et al [6][7], Rausch [8], Nakamiya et al [9], Koon et al [10], Lu Jing et al [11] and Nath and Ramanan [12]. The subject of periodic solutions of the CRTBP has received enormous attention in the past few decades.…”

Design of optimal impulse transfers from the Sun–Earth libration point to asteroid

“…Meanwhile, the LPOs play a key role in the interplanetary low-energy transfers. The invariant manifold structures associated with the LPOs have been employed as the basic tools to design various types of transfers, such as the transfer trajectories of the Sun-Earth libration point mission (Gó mez et al, 1993;Barden et al, 1997), the low-energy capture trajectories into Mars halo orbit (Nakamiya et al, 2008;Wang et al, 2014), the transfers between the collinear libration points (Howell and Hiday-Johnston, 1994;Gómez and Masdemont, 2000;Davis et al, 2010), and the transfers between lunar orbit/lunar libration and the Sun-Earth collinear libration points in the Sun-Earth-Moon system (Farquhar et al, 2004;Howell and Kakoi, 2006;Canalias and Masdemont, 2008;Ren and Shan, 2014).…”