If an asteroid has an eccentricity greater than 1, it is classified as a hyperbolic trajectory. This means that the asteroid is on a path that allows it to escape the gravitational influence of the Sun and will not return to its original orbit after passing by Jupiter. Therefore, one of the following statements might be true:
- The asteroid will continue on a path that takes it out of the solar system. This means it will move away after its close encounter with Jupiter and will not be gravitationally bound to the Sun or any other body in the solar system.
Additionally, since the asteroid is slung by Jupiter's gravity, this could also mean:
- The asteroid's velocity increased significantly after its close encounter with Jupiter. The gravitational assist from Jupiter would have imparted enough speed to the asteroid to reach escape velocity from the solar system.
In summary, if the asteroid's eccentricity is greater than 1, it is likely to be on a hyperbolic trajectory, indicating that it will escape the gravitational influence of the Sun and continue on a path that takes it out of the solar system.