In stellar dynamics a box orbit refers to a particular type of orbit which can be seen in triaxial systems, that is, systems which do not possess a symmetry around any of its axes. They contrast with the loop orbits which are observed in spherically symmetric or axisymmetric systems. Stellar dynamics is the branch of astrophysics which describes in a statistical way the collective motions of stars subject to their mutual gravity. ... m. ... Sphere symmetry group o. ... A coordinate axis is one of a set of vectors that defines a coordinate system. ...

In a box orbit, the star oscillates independently 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 oscillations in different axes are exact multiples of each other, the orbit will be closed.

Examples of box orbits (in 2 dimensions)

Beginning of a box orbit

Many cycles of a box orbit

A closed box orbit

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A Keplerian orbit is a closed ellipse, where the pericenter and apocenter distances are determined by the energy and angular momentum of the orbit.

However, the orbits of stars in a galaxy are not Keplerian, because the mass distribution is not concentrated in a point mass.

Orbits form a rosette, in which a star will eventually pass through every point on an annulus whose inner and outer radii are the pericenter and apocenter distances determined by the energy and angular momentum of the orbit.

First, he found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed, and that the sun is not located at the center of the orbits, but rather at one focus.

In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less.

The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it.

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