Interstellar Interlopers, Coming in from the great beyond Options

[Holder of the Tw...]

They finally found a chunk of something coming into the Solar System. Something much bigger than cosmic rays or dust particles.

Asteroid/comet in hyperbolic trajectory

[Xcalibrator]

In all seriousness, this comic provides a helpful illustration of the gravitational potentials involved: xkcd681 Gravity Wells

[JRehling]

It would be nice to have a simple formula for the results of gravity assists, but there's nothing simple about them. However, to clear up one misconception implicit above, they are a dynamic that occurs with a pair of large bodies accelerating a third, and they are not in any way a dynamic that can exist with just one large body and one small one. That will give you Keplerian motion. A body from the outer solar system cannot get a gravity assist from the Sun and be accelerated beyond the Sun's escape velocity; it can only orbit the Sun. The Sun is not a body that can deliver gravity assists.

Oumuamua approached the Sun already far above escape velocity. This is probably a consequence, as others have noted, of Oumuamua escaping some other system at a more pedestrian velocity, but that system and ours having a high difference in relative velocity.

Both Voyager spacecraft were launched into elliptical orbits that could not have left the solar system. For each, the gravity assist at Jupiter was sufficient to allow them to escape the solar system, but Voyager 1 now has only about half the velocity with respect to the Sun that Oumuamua had at a comparable distance. However, if Voyager randomly wandered into some other sunlike star's planetary system, its velocity with respect to that star would in many cases be dominated by the proper motion of the star (= relative velocity of that star and the Sun with respect to one another). It's like someone in a car throwing something out their window and into the window of another passing car. How fast the object is tossed will be almost irrelevant to how fast the object is going with respect to the second car. There's no reason to suppose that the velocity of Oumuamua was exceptionally fast with regard to its star of origin.