Libration Point Orbits and the Three‐Body Problem

Abstract

Libration point orbits in the three‐body problem play an important role in mission design. Their size, shape, location, and dynamical features are attractive for many different science and exploration missions, with objectives ranging from the collection of solar observations and measurements, to a search for the first massive black holes, to the direct imaging of planets within the habitable zone of stars beyond our solar system. The gravitational forces of two massive bodies govern the dynamics in the vicinity of the libration points and the motion in this regime is vastly different from traditional Keplerian motion. This chapter presents a historical overview of the three‐body problem, its formulation and assumptions, and the corresponding equations of motion. Methods of analytically and numerically computing libration point orbits are presented, along with a discussion on orbit stability. Invariant manifolds, trajectories that asymptotically approach or depart a nominal orbit, are described, as is their application for constructing transfers between orbits. Additionally, a brief survey of past, future, and proposed libration point orbit missions is presented.