The three possible responses regarding the asteroid's interaction with Jupiter are:
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The asteroid enters a stable elliptical orbit around the sun. - After being slung around by Jupiter's gravity, the asteroid could find itself in a new, stable orbital path around the sun.
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The asteroid continues out of the solar system. - Depending on the trajectory after its encounter with Jupiter, the asteroid could gain enough velocity to escape the solar system entirely.
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The asteroid falls into an irregular orbit around Jupiter. - The gravitational interaction with Jupiter may cause the asteroid to be captured into an irregular orbit around the planet.
The other options are less likely based on typical asteroid dynamics and interactions with a large body like Jupiter.