Orbit - Lissajous Orbit

Lissajous orbit

Lissajous orbit around L₂

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 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 Lagrangian points L₁, L₂, or L₃ 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. 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.^[3] These orbits can however be destabilized by other heavy nearby objects. It has been found for example that the L₄ and L₅ points in the Earth–Moon system would be stable for billions of 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.^[4]
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.^{[citation needed]} 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.^[5] ESA's current Gaia mission also uses a Lissajous orbit at Sun–Earth L₂.^[6] 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.^[7] China's lunar orbiter Chang'e 2 left lunar orbit on June 8, 2011 and flew to L₂.^{[8][full citation needed]}
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 storm. The shield is described to have been in a Lissajous orbit at L₁. Similarly a group of wealthy and powerful people sheltered opposite the shield at L₂ so as to be protected from the solar storm by the shield, Earth and Moon.