Hyperbolic trajectory in the context of "Orbital plane"

An interstellar object is an astronomical object in interstellar space, not gravitationally bound to a star. The term is used for objects including some asteroids, some comets, and rogue planets, but not stars or stellar remnants. The interstellar objects were once bound to a host star and have become unbound since. Different processes can cause planets and smaller objects (planetesimals) to become unbound from their host star.

This term is also applied to an object that is on an interstellar trajectory but is temporarily passing close to a star, such as some asteroids and comets (that is, exoasteroids and exocomets). In this case the object may be called an interstellar interloper. Objects observed within the solar system are identified as interstellar interlopers due to possessing significant hyperbolic excess velocity, indicating they did not originate in the solar system.

This is a list of parabolic and hyperbolic comets in the Solar System. Many of these comets may come from the Oort cloud, or perhaps even have interstellar origin. The Oort Cloud is not gravitationally attracted enough to the Sun to form into a fairly thin disk, like the inner Solar System. Thus, comets originating from the Oort Cloud can come from roughly any orientation (inclination to the ecliptic), and many even have a retrograde orbit. By definition, a hyperbolic orbit means that the comet will only travel through the Solar System once, with the Sun acting as a gravitational slingshot, sending the comet hurtling out of the Solar System entirely unless its eccentricity is otherwise changed. Comets orbiting in this way still originate from the Solar System, however. Typically comets in the Oort Cloud are thought to have roughly circular orbits around the Sun, but their orbital velocity is so slow that they may easily be perturbed by passing stars and the galactic tide. Astronomers have been discovering weakly hyperbolic comets that were perturbed out of the Oort Cloud since the mid-1800s.

Prior to finding a well-determined orbit for comets, the JPL Small-Body Database and the Minor Planet Center list comet orbits as having an assumed eccentricity of 1.0. (This is the eccentricity of a parabolic trajectory; hyperbolics will be those with eccentricity greater than 1.0.) In the list below, a number of comets discovered by the SOHO space telescope have assumed eccentricities of exactly 1.0, because most orbits are based on only an insufficient observation arc of several hours or minutes. The SOHO satellite observes the corona of the Sun and the area around it, and as a result often observes sungrazing comets, including the Kreutz sungrazers.

The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example would be the positions of the centers of a massive body (host) and of an orbiting celestial body at two different times/points of its orbit.

The orbital plane is defined in relation to a reference plane by two parameters: inclination (i) and longitude of the ascending node (Ω).

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity (e) equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a ${\displaystyle C_{3}=0}$ orbit (see Characteristic energy).

Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits.

This is a list of comets (bodies that travel in elliptical, parabolic, and sometimes hyperbolic orbits and display a tail behind them) listed by type. Comets are sorted into four categories: periodic comets (e.g. Halley's Comet), non-periodic comets (e.g. Comet Hale–Bopp), comets with no meaningful orbit (the Great Comet of 1106), and lost comets (5D/Brorsen), displayed as either P (periodic), C (non-periodic), X (no orbit), and D (lost).

Many of the earlier comets observed in history are designated with an X or D due to not having the tools to measure a comet's orbit accurately and eventually losing it. X/1106 C1 (the Great Comet of 1106) is a good example. The orbital elements for the older non-periodic comets in the list assume that the comet has an eccentricity of roughly 1; therefore, the calculations are only approximate.