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Lissajous orbit around L₂

In orbital mechanics, a Lissajous orbit is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system without requiring any propulsion. Lyapunov orbits around a libration point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve. Halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.^[1]

In practice, any orbit around a Lagrangian point is dynamically unstable, meaning small departures from equilibrium grow exponentially over time.^[2] As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital station-keeping.

Several missions have used Lissajous trajectories. ACE at Sun-Earth L₁ and WMAP at Sun-Earth L₂. On May 14, 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which use Lissajous orbits at Sun-Earth L₂.^[3] ESA's future Gaia mission will also use a Lissajous orbit at Sun-Earth L₂.^[4]