Lissajous Orbit

In orbital mechanics, a Lissajous orbit, 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 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.

In practice, any orbit around Lagrangian points L₁, L₂, or L₃ is dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital station-keeping. Orbits about Lagrangian points L₄ and L₅ are dynamically stable in theory so long as the ratio of the masses of the two main objects is greater than about 25, meaning the natural dynamics (without the use of a spacecraft's propulsion system) keep the spacecraft in the vicinity of the Lagrangian point even when slightly perturbed from equilibrium. These orbits can however be destabilized by other heavenly objects. It has been found for example that the L₄ and L₅ points in the Earth–Moon system would be stable for 1000 million years, even with perturbations from the sun, but because of smaller perturbations by the planets, orbits around these points can only last a few million years.

Several missions have used Lissajous trajectories: ACE at Sun–Earth L₁ and WMAP at Sun–Earth L₂ and also the Genesis mission collecting solar particles at L₁. On 14 May 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which use Lissajous orbits at Sun–Earth L₂. ESA's future Gaia mission will also use a Lissajous orbit at Sun–Earth L₂. In 2011, NASA transferred two of its THEMIS spacecraft from Earth orbit to Lunar orbit by way of Earth-Moon L₁ and L₂ Lissajous orbits. China's lunar orbiter Chang'e 2 will leave lunar orbit on June 16, 2011 and fly to L₂.

In the science fiction novel Sunstorm by Arthur C. Clarke and Stephen Baxter, a huge shield is constructed in space to protect the Earth from a deadly solar superstorm which would have been in a Lissajous orbit as would a group of other wealthy and powerful people who sheltered opposite it at L₂ – in line with both Earth and Moon as well as the L₁ shield with a Lunar eclipse taking place at the time.