Lissajous orbit

A Lissajous orbit is a complex path in space. It is a quasi-periodic trajectory used in orbital mechanics. This means an object follows a path that almost repeats but does not perfectly loop. These orbits allow an object to travel around a Lagrangian point. These points are special locations in a three-body system. A three-body system involves three massive objects, like the Sun, Earth, and a spacecraft. Using these orbits is very efficient. They allow a spacecraft to stay near a specific point with minimal propulsion.

The movement of a Lissajous orbit is unique. It contains components in a flat plane. It also includes components perpendicular to that plane. This creates a three-dimensional path that follows a Lissajous curve. This is different from a Lyapunov orbit. A Lyapunov orbit stays entirely within the plane of the two primary bodies. It is also different from a halo orbit. A halo orbit also moves perpendicular to the plane. However, a halo orbit is periodic, meaning it repeats exactly. A Lissajous orbit is usually not periodic.

In space, these orbits are often dynamically unstable. This means that small departures from the equilibrium point grow over time. If a spacecraft drifts slightly, the error gets larger. To fix this, spacecraft must perform orbital station-keeping. Station-keeping is the use of propulsion systems to maintain the desired path. Even though the orbit is not perfectly stable, small efforts keep the craft on track. This allows the spacecraft to stay in the Lissajous orbit for a very long time.

There are conditions where these orbits can be naturally stable. If the ratio of the masses of the two main objects is greater than about 25, they are dynamically stable. In these cases, natural dynamics keep the object near the Lagrangian point. The object stays in the vicinity without needing a propulsion system. However, other massive objects can cause perturbations. A perturbation is a disturbance caused by the gravity of nearby objects. For example, planets in the Solar System can destabilize orbits. Orbits around the Earth-Moon L1 and L2 points might only last a few million years. This is much shorter than the billions of years they might otherwise last.

Jules Antoine Lissajous gave these orbits their name. He was a scientist who studied these mathematical curves. Today, many important space missions rely on this science. Several tools stay at the Sun-Earth L1 point. These include the ACE, SOHO, and DSCOVR missions. The Genesis mission also uses the L1 point to collect solar particles. Other missions use the Sun-Earth L2 point. These include WMAP, Gaia, and the Herschel and Planck observatories. The ESA launched Herschel and Planck on 14 May 2009.

NASA has also used these orbits for complex maneuvers. In 2011, NASA transferred two THEMIS spacecraft. They moved from Earth orbit to Lunar orbit. They did this by traveling through Earth-Moon L1 and L2 Lissajous orbits. In June 2018, the Queqiao satellite entered an orbit around Earth-Moon L2. This satellite acts as a relay for China's Chang'e 4 lunar lander mission. These missions show how Lissajous orbits help us explore the Moon and the Sun.

Lissajous orbits even appear in science fiction stories. In the 2005 novel Sunstorm, authors Arthur C. Clarke and Stephen Baxter describe a huge shield. This shield is placed in a Lissajous orbit at Sun-Earth L1. It is meant to protect Earth from a solar storm. In the 2017 novel Artemis, Andy Weir uses the orbit differently. In his story, a Lissajous orbit serves as a transfer point. It helps with routine travel to and from the Moon. This shows how the concept of these orbits captures the imagination of writers.