Lissajous orbit In orbital mechanics, a Lissajous orbit (pronounced [li.sa.ʒu]), named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system with minimal propulsion, tracing a Lissajous curve. Lyapunov orbits around a Lagrangian point are plane curves that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits are space curves and include components in this plane and perpendicular to it. Halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are usually not. In practice, any orbits around Lagrangian points L 1, L 2, or L 3 are dynamically unstable, meaning small departures from equilibrium grow over time. [1] As a result, spacecraft in these Lagrangian point orbits must use their propulsion systems to perform orbital station-keeping. Although they are not perfectly stable, a modest effort of station keeping keeps a spacecraft in a desired Lissajous orbit for a long time. In the absence of other influences, orbits about Lagrangian points L 4 and L 5 are dynamically stable so long as the ratio of the masses of