Halo orbit

A halo orbit is a three-dimensional periodic trajectory around a collinear Lagrange point in the restricted three-body problem. Its motion combines oscillations above and below the plane of the two primary bodies.

Circular restricted three-body problem: A model of two massive bodies on circular orbits and a third body whose mass is negligible. Halo orbits are periodic solutions of this model’s equations of motion.
Lagrangian point L1: The collinear equilibrium point between two primary bodies in the circular restricted three-body problem. Halo-orbit families around L1 support missions between a planet and its nearer primary.
James Webb Space Telescope: A space observatory designed to study the universe in infrared wavelengths. It operates near the Sun–Earth L2 point on a large halo orbit.
Planar Lyapunov orbit: A periodic orbit confined to the plane of the two primaries near a collinear Lagrange point. Its planar motion contrasts with the above-and-below-plane motion of a halo orbit.
Restricted three-body problem: The gravitational problem of two massive bodies and a third body whose mass is negligible. Halo-orbit theory grew from periodic solutions of this classical celestial-mechanics problem.
Lagrange point: A location in a rotating two-body system where gravitational and centrifugal accelerations balance for a small object. The collinear points provide the centers around which halo orbits are found.
Lagrangian point L2: The collinear equilibrium point beyond the smaller primary, away from the larger one. Many halo orbits used for deep-space observatories encircle L2.
Deep Space Climate Observatory: A spacecraft that continuously observes Earth’s sunlit side and monitors solar conditions. Its Sun–Earth L1 halo orbit enables a persistent view of Earth and incoming solar wind.
Lissajous orbit: A generally nonperiodic trajectory near a Lagrange point that combines oscillations at different frequencies. It resembles a halo orbit locally but does not close into a periodic path.
Victor Szebehely: A Hungarian-American mathematician and celestial mechanician who studied the restricted three-body problem. His work helped establish the mathematical framework used to investigate halo-orbit solutions.

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Frozen orbitCompared with: Halo-orbit stability is organized around libration-point dynamics, not secular element balance.