The three possible responses regarding the asteroid's trajectory as it approaches and interacts with Jupiter are:
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The asteroid falls into an irregular orbit around Jupiter. - Depending on the gravitational forces at play, it's possible for the asteroid to get captured into a chaotic or irregular orbit.
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The asteroid continues out of the solar system. - Depending on the asteroid's speed and trajectory relative to Jupiter, it could gain enough velocity from the gravitational interaction to escape the solar system entirely.
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The asteroid enters a stable elliptical orbit around the sun. - If the asteroid is influenced by Jupiter's gravity correctly, it could be slung into a stable elliptical orbit around the sun.
The other options either contradict typical orbital mechanics or are less likely outcomes in this scenario.