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?
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
The statement "the asteroid continues out of the solar system, never to return" might be true.
If the eccentricity of the asteroid's new trajectory is greater than 1, the statement that might be true is: "The asteroid continues out of the solar system, never to return."
If the eccentricity of the asteroid's new trajectory is greater than 1, it means that the orbit of the asteroid is not closed and it is a hyperbolic or parabolic orbit. In this case, the asteroid will not be trapped in a regular orbit around any celestial body like Jupiter or the Sun. Therefore, the statement "the asteroid falls into a regular orbit around Jupiter instead of the sun" is not true.
Now, let's analyze the other options:
1. "The asteroid slows down as it passes around Jupiter": This statement is generally not true. As the asteroid approaches Jupiter, it will experience the gravitational pull of the planet, which will accelerate it. Hence, it will generally speed up rather than slow down.
2. "The asteroid continues out of the solar system, never to return": This statement is a possibility. If the eccentricity of the asteroid's orbit is significantly greater than 1, it implies that the asteroid's velocity is high enough to overcome the gravitational pull of the Sun. As a result, the asteroid will escape the Solar System and not return.
3. "The asteroid adopts an unusual orbit around the Sun, such as an egg shape": This statement is also not true. When the eccentricity of an orbit is greater than 1, it means that the shape of the orbit is either hyperbolic or parabolic. Both shapes do not resemble an egg shape. Instead, they have a more elongated and open form.
Therefore, the statement "the asteroid continues out of the solar system, never to return" is the most likely to be true if the eccentricity of the asteroid's new trajectory around Jupiter is greater than 1.