Understanding there's orders of magnitude of possible scale, what's the likelihood that one of these passing through the solar system would destabilize it enough to affect Earth? What happens if it hits the sun?
A passing star is more likely to do this though and we believe that they indeed have caused disturbances in our oort cloud in the past. They might be potentially less numerous than rogue planets as our universe ages but they have a far larger potential hill sphere than even a very large planet so interactions with neighboring stars' hill spheres are more likely and frequent.
The Oort cloud (/ɔːrt, ʊərt/),[1] sometimes called the Öpik–Oort cloud,[2] first described in 1950 by Dutch astronomer Jan Oort,[3] is a theoretical[4] concept of a cloud of predominantly icy planetesimals proposed to surround the Sun at distances ranging from 2,000 to 200,000 au (0.03 to 3.2 light-years).[note 1][5] It is divided into two regions: a disc-shaped inner Oort cloud (or Hills cloud) and a spherical outer Oort cloud. Both regions lie beyond the heliosphere and in interstellar space.[5][6] The Kuiper belt and the scattered disc, the other two reservoirs of trans-Neptunian objects, are less than one thousandth as far from the Sun as the Oort cloud.
The scale of the universe never ceases to elicit feelings of existential dread.
As for the scale of the Universe: https://htwins.net/scale2/
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[0]: https://en.wikipedia.org/wiki/Oort_cloud#/media/File:PIA1704...
[1]: https://imagine.gsfc.nasa.gov/features/cosmic/nearest_star_i...
[2]: https://solarsystem.nasa.gov/solar-system/oort-cloud/overvie...
Either way, whenever I try to think about these things, I feel mild anxiety. Why am I here? What's the point of all this? I'M SO TINY! Aaaahhhhhhhhh! I probably need to lay off the sci-fi novels for a while.
Interestingly, the paper I linked talks about Mercury having a 1% chance of becoming unstable before the Sun enters its red giant phase:
> The mechanism forthe onset of Mercury’s instability is well understood: by virtue of locking into a linear secular resonance with theg5mode of the solar system’s secular solution, Mercury’s eccentricity can attain near-unity values, resulting in a collision with the Sun, or even Venus. Intriguingly, General Relativistic effects factor into this estimate, with ancillary apsidal precession providing a stabilizing influence on Mercury’s orbit.
If Mercury collides with the Sun, not much interesting will happen. Mercury doesn't have enough mass to disrupt the center of gravity of the Solar System when it falls into the Sun, so, all that will happen is that the planet will get vaporized, and the Sun will become infinitesimally more enriched in metals. If you were around to witness the event, it might be visually spectacular, but not particularly significant with respect to the fate of the system itself.
They go on to say:
> Within the context of this narrative, however, the remaining planets appear unaffected and are currently expected to remain stable for a lower limit of 10^18 years, when diffusion arising from the overlapping mean motion resonance of Jupiter and Saturn are expected to decouple Uranus.
This analysis, however, is reflective of older studies, which don't take into account certain factors that this paper does.
Yeah...but if it hits Venus......