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? *
1 point
a. The asteroid slows down as it passes around Jupiter.
b. The asteroid continues out of the solar system, never to return.
c.The asteroid adopts an unusual orbit around the sun, such as an egg shape.
d.The asteroid falls into an regular orbit around Jupiter instead of the sun.
b. The asteroid continues out of the solar system, never to return.
To determine which statement might be true when the eccentricity of an asteroid's new trajectory, as it is slung around Jupiter, is greater than 1, we need to understand what eccentricity represents and how it relates to the shape of orbits.
Eccentricity is a parameter that measures how elliptical or circular an orbit is. It is defined as the ratio of the distance between the foci of the ellipse (which represents the orbital path) to the length of the major axis of the ellipse.
In a standard orbit, with eccentricity between 0 and 1, the orbit is elliptical, and the two foci coincide at the center of mass (e.g., the sun for planets or Jupiter for this asteroid).
If the eccentricity is exactly 1, then the orbit becomes a parabolic trajectory, meaning the asteroid is on a trajectory that will take it away from the sun and it won't return to the solar system.
However, if the eccentricity is greater than 1, the orbit becomes a hyperbolic trajectory. In this case, the asteroid is on a path that will take it away from the sun, never to return to the solar system.
Based on this understanding, the statement that might be true when eccentricity is greater than 1 is:
b. The asteroid continues out of the solar system, never to return.
Option a is incorrect because the asteroid does not slow down as it passes around Jupiter. Option c is incorrect because while the asteroid does adopt an unusual orbit, it is a hyperbolic trajectory rather than an egg-shaped orbit. Option d is incorrect because the asteroid does not fall into a regular orbit around Jupiter or the sun.