МЕТОДЫ РАСЧЕТА ОГРАНИЧЕННЫХ ОРБИТ ВОКРУГ ТОЧЕК ЛИБРАЦИИ
For a viable program of exploration beyond the Moon, we believe that international collaboration, like for the ISS, and reusable spacecraft will be needed. We use high-energy Earth orbits that can be drastically modified with lunar swingbys and small propulsive maneuvers, especially near the collinear Sun-Earth and Earth-Moon libration points. The work builds on ideas developed by the International Academy of Astronautics' exploration study group presented at the 2008 International Astronautical Congress in Glasgow. The first human missions beyond low-Earth orbit will probably go to the vicinity of the translunar Earth-Moon libration point; these are discussed in separate papers. This paper will concentrate on the next possible step, which might be for servicing large space telescopes in Sun-Earth libration-point orbits. Next, flyby and rendezvous missions to Near-Earth Objects (NEO's) will be presented, with some emphasis on options for defense against potentially hazardous objects. Finally, trajectories to reach Mars, first to Phobos and/or Deimos, will be outlined. The study will use highly-elliptical Earth orbits (HEOs) whose line of apsides can be rotated using lunar swingbys. The HEO also provides a convenient and relatively fast location for rendezvous with crew, or to add propulsion or cargo modules, a technique that we call "Phasing Orbit Rendezvous". From a HEO, a propulsive maneuver, considerably smaller than that needed from a circular low-Earth orbit, can be applied at the right perigee to send the spacecraft on the right departure asymptote to a desired destination. A propulsive maneuver at perigee can be used to re-capture the spacecraft into a loosely-bound orbit at the return, perhaps helped with a lunar swingby. But the astronauts onboard could separate in an Apollo-style capsule for a direct Earth return. Earth-Moon (and possibly Sun-Earth) libration point orbits and double-lunar swingby orbits, like those flown first by the third International Sun-Earth Explorer, will be used, along with time to change the orbital orientation between missions. There might be waits of several months between missions, when the interplanetary spacecraft could be "parked" in a small-amplitude Lissajous orbit about a libration point, similar to that flown by the WMAP mission. During that time, if there wasn't an L2 space telescope needing servicing, the spacecraft could be unmanned and controlled remotely from the Earth. Sequential missions to fly by and then rendezvous with NEO's will be described, followed by a mission to the Martian moons.
A procedure has been proposed for calculating limited orbits around the L2 libration points of the Sun–Earth system. The motion of a spacecraft in the vicinity of the libration point has been considered a superposition of three components, i.e., decreasing (stable), increasing (unstable), and limited. The proposed procedure makes it possible to correct the state vector of the spacecraft so as to neutralize the unstable component of the motion. Using this procedure, the calculation of orbits around various types of libration points has been carried out and the dependence on the orbit type on the initial conditions has been studied.
Halo orbits of Sun-Earth system are utilized in space missions as they allow to maintain the spacecraft in an area that is stationary relative to Sun and Earth. The advantage of halo orbits is their periodicity and their form allowing the spacecraft to avoid the zones of solar interference and the Earth shadow. The transfer between a low-Earth orbit and a halo orbit around a libration point can be realized by a single-burn maneuver, which transfers the spacecraft to an orbit of stable manifold resulting in a halo orbit. An amplitude of halo orbit depends on the altitude of the parking low-Earth orbit at which the transfer maneuver is performed. This work is aimed to explore and systemize the single burn transfer options utilizing single and multiple Earth passing trajectories in the framework of the circular restricted three body problem. The algorithms providing transfer options for the desired halo orbit and the parking orbit altitude are developed. The transfer trajectories for the Sun-Earth L1 and L2 halo orbits in a wide range of out-of-plane amplitudes were constructed and studied. The constructed trajectories were clustered based on the transfer time and the halo orbit amplitude.