9. An asteroid approaches Jupiter and is slung around by gravity into a new trajectory across the solar system. It's eccentricity is now greater than 1. Which of the following is possible?
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1 point
The asteroid slows down as it passes around Jupiter.
The asteroid continues out of the solar system.
The asteroid adopts an unusual orbit around the sun, such as an egg shape.
The asteroid falls into an irregular orbit around Jupiter.
The correct option is:
The asteroid continues out of the solar system.
When the eccentricity of an object's orbit is greater than 1, it means that the object's orbit is not closed and it will eventually escape the gravitational influence of whatever body it is orbiting. In this case, since the asteroid's eccentricity has increased after being slung around by Jupiter's gravity, it is now possible for the asteroid to continue out of the solar system.
The correct answer is: The asteroid continues out of the solar system.
To determine which of the given options is possible when the eccentricity of an asteroid's trajectory becomes greater than 1 after being slung around by Jupiter's gravity, we need to understand the concept of eccentricity and its implications on the object's orbit.
Eccentricity is a measure of how elongated or stretched out an object's orbit is. In elliptical orbits (eccentricity between 0 and 1), the object moves in an oval-shaped path around the central body. A circular orbit has an eccentricity of 0, and an eccentricity close to 1 implies a significantly elongated elliptical orbit. However, when the eccentricity exceeds 1, the object does not follow an elliptical path but rather follows a hyperbolic or parabolic trajectory.
Based on this understanding, we can assess the given options:
1. The asteroid slows down as it passes around Jupiter: This option is not possible because passing around Jupiter, or any massive object, with a high eccentricity would not cause the asteroid to slow down. In fact, the asteroid would experience a gravitational slingshot effect, increasing its velocity.
2. The asteroid continues out of the solar system: This option is possible. When an asteroid gets slung around by Jupiter's gravity and its eccentricity becomes greater than 1, it is on a hyperbolic or parabolic trajectory. This means that the asteroid's velocity is greater than the escape velocity of the solar system, allowing it to continue its journey away from the Sun and eventually leaving the solar system.
3. The asteroid adopts an unusual orbit around the sun, such as an egg shape: This option is not possible. With an eccentricity greater than 1, the asteroid's trajectory is no longer closed and does not form an elliptical orbit. Thus, it cannot have an unusual egg-shaped orbit around the Sun.
4. The asteroid falls into an irregular orbit around Jupiter: This option is not possible. With an eccentricity greater than 1, the asteroid is no longer gravitationally bound to Jupiter. It would follow a hyperbolic or parabolic trajectory, taking it away from Jupiter and into a path that may lead it out of the solar system.
So, the possible option is: The asteroid continues out of the solar system.