A comet is the object that typically has an orbit with an eccentricity greater than one, indicating a hyperbolic pathway around the sun. While some comets can have elliptical orbits (with eccentricities between 0 and 1), other comets, especially those that are in "one-off" trajectories, can have hyperbolic orbits with eccentricities greater than one. Therefore, the correct response is:
A Comet