The average speed of stars relative to the Sun in the solar neighborhood is about 20 km/s (this is the speed at which we see stars moving toward or away from the Sun - NOT their orbital speed). Suppose you discover a star in a solar neighborhood that is moving at a much higher speed relative to the Sun, say at 200 km/s. What kind of orbit does this star probably have around the Milky Way? In what part of the Galaxy does it spend most of its time? Explain.

Most stars in the vicinity of the sun are going around the center of the Milky Way galaxy with an average speed of about 220 km/s. The 20 km/s typical relative speed of most nearby stars represents a random variation from the average orbital speed.

If some nearby star had a relative velocity of 200 km/s, it would be in a completely different type of orbit, and one that would not be as circular as our sun's (and NOT going around the center in the opposite direction). That means it would spend most of its time much farther away from the sun's position. It could be coming from the "outer halo" of stars that extends far above and below the galactic plane.

When a star in the solar neighborhood has a much higher speed relative to the Sun, like 200 km/s, it is likely to have a different orbit around the Milky Way compared to the average star. Stars in the Milky Way can have different types of orbits, depending on their initial conditions and gravitational interactions.

Since this star's speed is significantly higher than the average, it suggests that the star's orbit is likely to be more eccentric or inclined compared to other stars. An eccentric orbit refers to an elliptical or elongated path around the galaxy, while an inclined orbit refers to a path that is tilted relative to the plane of the galaxy.

If a star in the solar neighborhood is moving at a much higher speed, it is more likely to spend most of its time in the halo of the Milky Way rather than the disc. The halo of the galaxy refers to the region surrounding the disk, which contains older stars and globular clusters. These stars follow more eccentric and inclined orbits, unlike the stars in the disc of the galaxy, which have more circular orbits.

This high-speed star's orbit takes it farther away from the galactic plane and into the halo, where it spends most of its time. It is important to note that this explanation is based on general trends and observations, and individual cases may exhibit variations.

To understand the kind of orbit a star with a high relative speed of 200 km/s around the Milky Way might have and the part of the Galaxy it spends most of its time in, we can consider a few factors.

The first important consideration is that the star's speed is significantly higher than the average speed of stars in the solar neighborhood, which is around 20 km/s. This suggests that the star is likely not in a typical, circular orbit around the Milky Way.

One possibility is that the star is on a highly elliptical orbit. In such an orbit, the star would spend a significant portion of its time at far distances from the center of the Galaxy and then swing back in closer. This would result in a high speed at its closest approach to the Milky Way and a slower speed at the farthest point in its orbit.

Another possibility is that the star is not gravitationally bound to the Milky Way and is instead on a hyperbolic or parabolic trajectory. These types of orbits imply that the star is passing through the Milky Way's gravitational field but not permanently bound by it. The high speed would allow it to move relatively quickly through different regions of the Galaxy.

Considering the high speed of the star, it is more likely that it spends most of its time in the outer regions of the Galaxy rather than the central regions. Stars in the central region of the Milky Way, such as those in the galactic bulge, tend to have lower average speeds compared to stars in the outer regions, which are subject to weaker gravitational forces.

In summary, a star with a high relative speed of 200 km/s is likely to have either a highly elliptical orbit, an unbound hyperbolic or parabolic trajectory, and is more likely to spend most of its time in the outer regions of the Milky Way rather than the central regions.