Based on the physics of gravitational interactions and orbital mechanics, the three correct possible outcomes for the asteroid's trajectory after passing by Jupiter are:
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The asteroid continues out of the solar system.
- If the asteroid gains sufficient speed from the gravitational slingshot effect and is directed outward with enough velocity, it could escape the solar system.
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The asteroid enters an elliptical orbit around the sun.
- The asteroid could be redirected into an elliptical orbit around the sun due to Jupiter's gravitational influence.
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The asteroid adopts an unusual orbit around the sun, such as an egg shape.
- Variations in gravitational forces can result in orbits that are not simple ellipses. The asteroid might end up in a more eccentric (elongated) orbit than a typical ellipse, which could resemble an "egg shape."
The other options, such as the asteroid slowing down as it passes around Jupiter or falling into a perfectly circular orbit, are generally less likely given the dynamics of gravitational interactions. Also, the asteroid spiraling into the sun would not typically occur unless it encountered a force significantly different from a slingshot effect.