An asteroid approaches jupiter and is slung into a new trajectory around across the solar system. If its eccentricity is greater than 1, which statement might be true?
The asteroid slow 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 a regular orbit around jupiter instead of the sun
The asteroid continues out of the solar system, never to return
If the eccentricity of the asteroid's new trajectory is greater than 1, then the statement "The asteroid continues out of the solar system, never to return" might be true. An eccentricity greater than 1 indicates that the asteroid's orbit is hyperbolic, meaning that it does not form a closed loop and the asteroid will not return to its starting point. Instead, it will continue on its new trajectory, likely leaving the solar system altogether.
To determine which statement might be true if the asteroid's eccentricity is greater than 1, let's first understand what eccentricity means in the context of orbital mechanics.
Eccentricity is a measure of how elliptical or elongated an orbit is. For eccentricity values greater than 1, the orbit is considered hyperbolic rather than elliptical. In hyperbolic orbits, the object's trajectory takes it on a parabolic or hyperbolic path that does not close back on itself.
Now, let's analyze each statement based on this understanding:
1. The asteroid slows down as it passes around Jupiter:
- This statement is unlikely to be true. When an object comes close to a massive body like Jupiter, its gravitational pull increases the object's velocity, rather than slowing it down.
2. The asteroid continues out of the solar system, never to return:
- This statement is possible if the asteroid's trajectory becomes hyperbolic, as indicated by the eccentricity greater than 1. In a hyperbolic orbit, the object does not return to the solar system.
3. The asteroid adopts an unusual orbit around the sun, such as an egg shape:
- This statement is not likely to be true. An eccentricity greater than 1 indicates a hyperbolic orbit, which will not be a closed elliptical orbit. An egg-shaped or highly eccentric elliptical orbit (eccentricity between 0 and 1) is possible, but not when the eccentricity is greater than 1.
4. The asteroid falls into a regular orbit around Jupiter instead of the sun:
- This statement is not likely to be true. When an asteroid passes close to a massive body like Jupiter, it may experience a gravitational slingshot effect that alters its trajectory, but it is unlikely to fall into a regular orbit around Jupiter.
Considering the above analysis, the statement that might be true if the asteroid's eccentricity is greater than 1 is: "The asteroid continues out of the solar system, never to return."