Box orbit

Type of gravitational orbit seen in triaxial systems

In stellar dynamics, a box orbit refers to a particular type of orbit that can be seen in triaxial systems, i.e. systems that do not possess a symmetry around any of its axes. They contrast with the loop orbits that are observed in spherically symmetric or axisymmetric systems.

In a box orbit, a star oscillates independently^{[citation needed]} along the three different axes as it moves through the system. As a result of this motion, it fills in a (roughly) box-shaped region of space. Unlike loop orbits, the stars on box orbits can come arbitrarily close to the center of the system. As a special case, if the frequencies of oscillation in different directions are commensurate, the orbit will lie on a one- or two-dimensional manifold and can avoid the center.^[1] Such orbits are sometimes called "boxlets".

**Examples of box orbits** (in 2 dimensions)

Beginning of a box orbit	Many cycles of a box orbit	A closed box orbit

References

^ Merritt, D.; Valluri, M. (September 1999), "Resonant Orbits in Triaxial Galaxies", The Astronomical Journal, 118 (3): 1177–1189, arXiv:astro-ph/9903452, Bibcode:1999AJ....118.1177M, doi:10.1086/301012, S2CID 14621588

General	Box Capture Circular Elliptical / Highly elliptical Escape Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic trajectory Parking Prograde / Retrograde Synchronous semi sub Transfer orbit
Geocentric	Geosynchronous Geostationary Geostationary transfer Graveyard High Earth Low Earth Medium Earth Molniya Near-equatorial Orbit of the Moon Polar Sun-synchronous Transatmospheric Tundra Very low Earth
About other points	Mars Areocentric Areosynchronous Areostationary Lagrange points Distant retrograde Halo Lissajous Libration Lunar Sun Heliocentric Earth's orbit Mars cycler Heliosynchronous Other Lunar cycler

Parameters

Shape Size	e Eccentricity a Semi-major axis b Semi-minor axis Q, q Apsides
Orientation	i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis
Position	M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude
Variation	T Orbital period n Mean motion v Orbital speed t₀ Epoch