An asteroid approaches Jupiter and is slung into a new trajectory around across the solar system. if it's eccentricity is greater than 1, which statement might be true?

Question

the asteroid slows down as it passes around Jupiter
the asteroid continues out of the solar system, never to return
the asteroid adopts an unusual orbit around the sun, such as an egg shape
the asteroid falls into an regular orbit around Jupiter instead of the sun

Answer 1

The statement "the asteroid continues out of the solar system, never to return" might be true.