Halo orbit

A halo orbit is a specific type of periodic, non-planar path in space.

This orbit is associated with one of the three Lagrange points in a three-body system. A three-body system involves the gravitational interaction between two large bodies, such as the Sun and the Earth, or the Earth and the Moon. While a Lagrange point is technically just a spot in empty space, it has unique characteristics. A spacecraft near these points can follow a Lissajous orbit or a halo orbit. Halo orbits are particularly useful because they are non-planar, meaning they do not follow a flat, single plane. This allows satellites to maintain specific views of celestial bodies.

To understand how this movement works, we must look at several competing forces. The orbit results from the interaction between the gravitational pull of two massive planetary bodies. At the same time, the spacecraft is affected by centrifugal force and Coriolis force. These forces work together to create a looping path. Unlike a simple circle, a halo orbit moves up and down as it travels. This creates a three-dimensional shape rather than a flat ring. Because these orbits tend to be unstable, they require constant attention. Satellites often use small thrusters for station-keeping to stay on their intended path.

There are different types and variations of these paths in space. Halo orbits exist in any three-body system, such as the Sun-Earth system or the Earth-Moon system. Within these systems, continuous "families" of orbits exist. These families include both northern and southern halo orbits at each Lagrange point. Scientists also study Lissajous orbits, which are related but non-periodic variations. While a halo orbit repeats its path exactly, a Lissajous orbit does not. Many modern missions, such as the Gaia astrometric space observatory, use these Lissajous-type orbits instead of true halo orbits.

The history of these orbits began with the work of Robert W. Farquhar. He first used the name "halo" in 1966 to describe orbits around the L2 point. Farquhar suggested using these orbits for the Apollo missions to the Moon. He proposed a communications relay station located in a halo orbit. Such a satellite would have a continuous view of both the Earth and the far side of the Moon. This would differ from a Lissajous orbit, which might cause the spacecraft to go behind the Moon. Although the idea was brilliant, no such relay was launched for Apollo because landings occurred on the near side.

Research continued to refine our understanding of these complex paths. In 1973, Farquhar and Ahmed Kamel discovered a mathematical connection. They found that if the in-plane amplitude of a Lissajous orbit was large enough, it created a corresponding out-of-plane amplitude. This resulted in an orbit with the same period, effectively turning it into an approximate ellipse. In 1984, Kathleen Howell improved this work by showing how to compute more precise trajectories numerically. She also discovered that stable orbits exist for most mass ratios between two bodies, like the Earth and the Moon.

Many significant space missions have successfully utilized halo orbits for science. The first mission to use one was ISEE-3, a joint ESA and NASA spacecraft launched in 1978. It traveled to a Sun-Earth point and stayed there for several years. In 1996, the Solar and Heliospheric Observatory (SOHO) arrived at a Sun-Earth point using a similar orbit. More recently, the James Webb Space Telescope entered a Sun-Earth halo orbit on 24 January 2022. The Euclid mission also entered a similar orbit in August 2023 to study the universe.

Recent achievements show how these orbits help us explore the Moon and the Sun. In May 2018, China realized Farquhar's original vision by placing the Queqiao satellite into a halo orbit. This satellite acted as a relay for the Chang'e 4 spacecraft, which landed in the Von Kármán crater on 3 January 2019. This allowed communication with the far side of the Moon. Additionally, India's Aditya-L1 mission reached its goal on 6 January 2024. It entered a halo orbit around the Sun-Earth L1 point to study the Sun. This orbit has a period of approximately 178 days and sits about 1.5 million kilometers from Earth.

These orbits are vital components of modern orbital mechanics and space exploration. By understanding the Restricted Three-Body Problem, scientists can place tools in perfect positions. While it was once difficult to compute translunar halo orbits, new models like the Quasi-Bicircular Problem (QBCP) made it possible. These mathematical models allow us to navigate the complex gravity of the Earth-Moon-Sun system. Today, halo orbits remain a primary method for placing space telescopes and communication relays where they are most effective.