The three correct answers regarding the possible outcomes for an asteroid approaching Jupiter are:
- The asteroid continues out of the solar system.
- The asteroid enters a stable elliptical orbit around the sun.
- The asteroid adopts an unusual orbit around the sun, such as an egg shape.
These outcomes are consistent with the gravitational interactions that can occur when an asteroid passes close to a massive body like Jupiter.
The asteroid may gain enough energy to escape the solar system, it could settle into a stable orbit around the sun (which could be elliptical), or its trajectory could become more irregular or unusual due to the gravitational effects from the encounter.
The options involving falling into an irregular orbit around Jupiter or spiraling into the sun are less likely under typical conditions.