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halo orbit

(type of orbit around an instable Lagrangian point)

A halo orbit is a type of orbit around an L1, L2, or L3 Lagrangian point. It is periodic, in that it follows same path each cycle other than the slow degradation due to the point's instability (which can be handled by stationkeeping). Such orbits can allow a line of sight to the further body; for example an object can be in a halo orbit on the other side of the Moon such that it has a line of sight to Earth. They also help allow multiple spacecraft to operate "at" (in the vicinity of) the same point, such as all the spacecraft currently at Earth-Sun L1 and L2.

Two other kinds of orbits are possible for use at the L1-L3 points: a Lissajous orbit, which is not periodic in the same sense. With each cycle, the path is different, but I believe they remain in a cylinder-like thin curved volume. Lissajous orbits are now more commonly used than halo orbits. A Lyapunov orbit is also aperiodic, but remains in a plane. I suspect halo orbits and Lyapunov orbits can be taken as special cases of Lissajous orbits, but I haven't seen this stated.

Lissajous orbit aperiodic not within a plane
Halo orbit periodic not within a plane
Lyapunov orbit aperiodic within a plane

I also suspect some or all of these can be used with L4 and L5, which haven't been as popular for use by spacecraft, and less is written about their possible orbits.

Further reading:

Referenced by pages:
Advanced Composition Explorer (ACE)
Lagrangian point