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Considering their distance from their parent stars, might Oort cloud object such as comets be exchanged between passing stars (assuming that other stars have similar Oort clouds)?

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Similar: physics.stackexchange.com/questions/41059/… –  Everyone Nov 14 '13 at 3:01

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up vote 4 down vote accepted

You can exclude the 'considering the distance' piece - of course Oort Cloud objects could transfer between different gravitational fields.

However what is it you think will make this transfer? Without some sort of gravitational impetus why would one of these objects leave the solar system? And if you do manage to slingshot one out of the solar system at a high enough speed to exit the Sun's gravity, remember that most directions end up very far away from any other solar systems.

Tl;Dr sure, but not very likely

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Methinks the question **may** have been prompted by Nevski's transit through the Solar System on a hyperbolic trajectory out of the Oort cloud ... –  Everyone Nov 14 '13 at 3:06
    
My line of thinking is that as stars pass one another on their way around the galaxy, they could 'brush' Oort clouds and thus exchange comets. The same mechanism may also perturb the comets to rain down on their own suns/stars. –  dotancohen Nov 14 '13 at 5:45
    
Everyone - sure. There is no reason why that can't happen, but the distances involved are huge, so I would expect most of the casualties of that kind of pass to not be captured. –  Rory Alsop Nov 14 '13 at 7:38
    
Dotancohen - distances! Oort clouds are pretty distant, but not a patch on the distance to another star. And generally there isn't much passing going on :-) –  Rory Alsop Nov 14 '13 at 7:39
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Note that this answer supports the assertion that passing stars can influence Oort cloud objects. –  dotancohen Oct 19 at 12:27

TL;DR In response to your comment that "note that [link to answer] supports the assertion that passing stars can influence Oort cloud object" I will talk about whether this could happen to comets in the Oort cloud that surrounds the solar system.

It can happen but the stars that exist today don't pass by close enough to yank away a comet at once. However many star passages could eventually do it. In this answer I attempt to present a way to think about this problem. Skip to the last paragraph to get the directly to my answer to your question without the extra.

In my answer here I clearly state that many stars have their own Oort cloud and that if they pass by each other close enough the stars will exchange comets. This is a direct answer to your question. It is believed to happen a lot in young star clusters, but you have to realize that older stars are often separated from other stars by a great distance which prohibits this type of exchange.


Now I will discuss influence by stars on the comets in the Oort cloud (the usual one, that surrounds the solar system). This is the topic of chapter of 5.2, Stellar Perturbations, in Julio Angel Fernández's book Comets. It is possible to approximate the influence of a passing star with some reasonable simplifications. I will try to retell Fernández argument here below.

Let's say that a comet is located at a heliocentric distance $r$. Since Oort cloud comets travel very slowly compared to stars, $0.1\rm{km\cdot s^{-1}}$ versus $30 \rm{km\cdot s^{-1}}$, we can assume that the comet is at rest in the heliocentric frame. If we neglect any influence of the star when it is further away than $10^5 \rm{AU}$ from the closest approach to the Sun we only have to be concerned about the time it takes for a star to travel $2\times 10^5\rm{AU}$ (imagine the star moving through the Sun), and during this time the comet has only travelled approximately $10^3\rm{AU}$. The star can be taken to travel in a straight line since it is only slightly perturbed by the Sun. This leads, and as with everything else this comes from Fernández text, to the integral

$$ \Delta v=\int_{-\infty}^\infty F\times \rm{dt}=-\frac{2GM}{VD} $$

where $\Delta v$ is the change of velocity of the comet, $G$ is the universal gravitational constant, $M$ is the mass of the star, $V$ is the velocity of the star and $D$ is the distance of closest approach between the star to the comet. However, we can't forget either that the Sun is also influencing the comet. If the comet is much closer to the Sun than the star the influence of the star can be neglected and vice versa. Since in this question we are dealing with the case "is it possible" I will assume that the comet is far out in the Oort cloud. Under these conditions we get another expression (after taking the Sun into account), i.e.

$$ | \Delta v | \approx \frac{2GMr\rm{cos}(\beta)}{VD_\odot^2} $$

where $\beta$ is the angle between the vector between the sun and the closest point of approach to the sun of the star and the vector from the sun to the comet. $D_\odot$ is the distance between the sun and the star at the closest point of approach.

All this math is somewhat superfluous in the current context. I wanted to show you that it is possible to reason analytically about these things. Your question is whether a comet can be yanked away from its orbit in the Oort cloud and be captured by a passing star. The last formula presented here shows that for stars that actually exist now (not to say that stars or other small bodies have never passed by close to the solar system or even gone through it) the change of velocity imparted on the comet by the star is far to small for this to happen. However the change of velocity will accumulate over many star passages, and over a long time it will change the orbit of the comet in a meaningful way. Long periodic comets (LP comets) are comets that travel into the solar system in an orbit that is a very narrow ellipsis so that its perihelion (closest approach to the sun) is small but the aphelion (furthest point away from the sun) can be a great distance outside Oort cloud. Long periodic comets meet their end in different ways. Some passes to close to the sun and melt, others collide with planets, especially the big gas planets, and some get catapulted out of the solar system by a close approach to for example Jupiter. It is possible however, because long periodic comets can have orbits that extend beyond the Oort cloud where they are less influenced by the sun and more influenced by passing stars, that they might be yanked away and join another star eventually, although I still don't think it is likely. It would be possible I think to use the same kind of math to approximate the change of velocity that stars incur on LP comets to see if it is feasible, but I haven't done it.

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Thank you for this terrific analysis. –  dotancohen 2 days ago

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