To provide the most accurate responses, I would need to know the specific options you are considering regarding the asteroid's new trajectory after passing Jupiter. However, I can outline some possible scenarios for an asteroid that is slung around by Jupiter's gravity:
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Ejection from the Solar System: The asteroid could gain enough speed from the gravitational assist and be catapulted out of the solar system entirely.
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New Orbit Around the Sun: The asteroid could enter a new orbit around the Sun, potentially becoming a part of the main asteroid belt or even taking a more distant or eccentric orbit.
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Collision Course with Other Celestial Bodies: Depending on its new trajectory, the asteroid might have a chance of encountering other planets or moons, increasing the risk of collision.
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Capture by a Planetary Body: In some scenarios, the asteroid might be captured by the gravity of another planet, potentially becoming a moon if it is small enough and passes close enough to a planet.
If you can provide the specific options you have in mind, I'd be happy to help you select the correct ones!