Astronomical object not orbiting the Sun
A hyperbolic asteroid is any sort of asteroid or non-cometary astronomical object observed to have an orbit not bound to the Sun and will have an orbital eccentricity greater than 1 when near perihelion. Unlike hyperbolic comets, they have not been seen out-gassing light elements, and therefore have no cometary coma. Most of these objects will only be weakly hyperbolic and will not be of interstellar origin.
Orbit explanation.
The planets and most satellites of the solar system revolve in an almost circular motion – called an elliptical orbit – around the Sun or their parent planet, so their orbital eccentricity is generally much closer to 0 than to 1. In mathematics, by definition, an eccentricity ("e") of 1 characterizes a parabola, and "e" ; 1, a hyperbola. Some comets are on parabolic and hyperbolic orbits. This means that these hyperbolic asteroids all have an orbital eccentricity greater than 1.
Known hyperbolic asteroids.
So far most hyperbolic asteroids discovered have later displayed cometary behavior by either outgassing or demonstrating motion based on solar radiation pressure. Hyperbolic asteroids are orbital objects with an orbit not bound to the Sun while near perihelion. ʻOumuamua had the motion of a comet but was never seen outgassing and thus it is listed as a hyperbolic asteroid by the JPL Small-Body Database.
Perturbation.
Asteroids can become ejected or in a highly eccentric orbit around the Sun by being ejected by planets like Jupiter. Just because an orbit solution looks unbound at an epoch when the object is near perihelion (closest approach to the Sun) does not mean the orbit will be unbound when beyond the planets.
References.
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