Halo orbit

A halo orbit is a repeating, three-dimensional path that loops around one of the Lagrange points—L1, L2, or L3—in a three-body gravitational system. While a Lagrange point is merely a location in space, it can be encircled by either a Lissajous orbit or a halo orbit. These curved trajectories arise from the combined effects of the gravity of two large bodies and the Coriolis and centrifugal forces acting on a spacecraft. Such orbits appear in any three-body setup, like a Sun–Earth–satellite system or an Earth–Moon–satellite system. At each Lagrange point, there are continuous families of both northern and southern halo orbits. Because these orbits are generally unstable, satellites often need to use thrusters for station-keeping to stay on course. Most spacecraft in halo orbits are used for scientific missions, such as space telescopes.

The term "halo" was first used by Robert W. Farquhar in 1966 to describe orbits around L2 that were made periodic with thrusters. Farquhar proposed using a spacecraft in such an orbit beyond the Moon—at Earth–Moon L2—as a communications relay for an Apollo mission to the Moon's far side. A spacecraft there would always see both Earth and the far side of the Moon, unlike a Lissajous orbit, which would occasionally hide the spacecraft behind the Moon. No relay satellite was launched for Apollo, as all landings occurred on the near side. In 1973, Farquhar and Ahmed Kamel discovered that when a Lissajous orbit's in-plane amplitude grew large enough, its out-of-plane amplitude matched its period, turning the orbit from a Lissajous into something close to an ellipse. They used analytical formulas to describe these halo orbits; in 1984, Kathleen Howell showed that more precise paths could be computed numerically. She also found that for most mass ratios between two bodies—like Earth and the Moon—a range of stable orbits existed.

The first mission to use a halo orbit was ISEE-3, a joint ESA/NASA spacecraft launched in 1978. It traveled to the Sun–Earth L1 point and stayed there for several years. The next was the Solar and Heliospheric Observatory (SOHO), another ESA/NASA mission to study the Sun, which arrived at Sun–Earth L1 in 1996 on a similar orbit. While many later missions have visited Lagrange points, they—like the Gaia astrometric observatory—have typically used the related non-periodic Lissajous orbits instead of true halo orbits. Although halo orbits were well understood in the restricted three-body problem, computing them for the real Earth–Moon system proved difficult. Translunar halo orbits were first calculated in 1998 by M.A. Andreu, who introduced a new model called the Quasi-Bicircular Problem (QBCP) for spacecraft motion in the Earth–Moon–Sun system.

In May 2018, Farquhar's original idea was finally realized when China placed the first communications relay satellite, Queqiao, into a halo orbit around Earth–Moon L2. On 3 January 2019, the Chang'e 4 spacecraft landed in the Von Kármán crater on the Moon's far side, using Queqiao to communicate with Earth. The James Webb Space Telescope entered a halo orbit around Sun–Earth L2 on 24 January 2022. Euclid entered a similar orbit around that point in August 2023. India's space agency ISRO launched Aditya-L1 to study the Sun from a halo orbit around Sun–Earth L1. On 6 January 2024, the spacecraft—India's first solar mission—successfully entered a halo orbit with a period of about 178 days, at a distance of roughly 1.5 million kilometers from Earth.