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I've read about the possible 5th gas giant in the Solar System, and about its ejection about ~100 million years after the formation of the Solar System. However, I have not seen anything about its potential whereabouts. Assume this gas giant (let's call it G5) was completely ejected from the solar system. Would G5 still remain in the vicinity (100 ly or less) or would it be very far away from the Sun right now?

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    $\begingroup$ Do you have a rough time for when G5 started on its escape trajectory? If it left 4 billion years ago, it would be over 220 lightyears away by now, using the simple radial parabolic trajectory equation. Of course, that answer is for a simple 2 body trajectory, and totally ignores the galaxy's gravitational field, but I guess it's a reasonable 1st approximation. $\endgroup$
    – PM 2Ring
    Feb 1 at 6:32
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    $\begingroup$ @PM2Ring: Your comment is actually an answer, if not the answer, isn't it? $\endgroup$
    – B--rian
    Feb 13 at 9:06
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    $\begingroup$ @B--rian I didn't post it as an answer mostly because I couldn't find a time for when G5 was supposedly kicked out of the Solar System. I'm still hoping for the OP to give us that info... $\endgroup$
    – PM 2Ring
    Feb 13 at 10:26
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    $\begingroup$ @fasterthanlight Did I guess your source correctly? $\endgroup$
    – B--rian
    Feb 13 at 10:41
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    $\begingroup$ @B--rian Generally, New Scientist isn't considered to be a great reference. (Neither is Wikipedia, but at least WP articles have citations to proper references). Fortunately, that NS article has this link to the preprint of the article by David Nesvorny, Young Solar System's Fifth Giant Planet?, Sep 2011. The abstract doesn't say when G5 was ejected, but I've had a quick look at that article, and on p.3 it says "it is often assumed that the instability occurred at the time of the Late Heavy Bombardment (LHB) of the Moon some 3.9 Gy ago". $\endgroup$
    – PM 2Ring
    Feb 13 at 12:39
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It could be anywhere in the Galaxy or even (unlikely) have left the Galaxy.

The kinematics of freely orbiting objects in the Galaxy are heated - that is, the velocity dispersion of objects increases with time.

For objects of age of 4 billion years we might expect a dispersion of about 10 -15 km/s in each velocity coordinate. That's about 10-15 pc/Myr. So in 4000 Myr, an object could have scattered to most parts of the Galaxy, or at least to a reasonably wide and thick annulus around the Galactic centre.

It is for similar reasons that, even though the Sun was probably born in a cluster of $\sim 10^4$ stars, none of those siblings have been firmly identified.

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