If the fifth gas giant in the early Solar System was completely ejected, where would it be now? 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?
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.