Using exoplanet finding techniques to find additional planets in the solar system

[Spaceception]

So this is really all in the title, but what limitations and challenges are there to using methods like radial velocity to find more planets in the solar system, like planet x, or other major bodies that might be far from the sun? I know radial velocity relies on the Doppler shift of a star's light, so are we too close for it to work? Or do hypothetical Oort cloud planets have too weak of a pull to really be noticeable? Either because of their extremely long orbits or comparatively small masses. What needs to change to make it feasible, and would it be worth our time - or would it make more sense in the end to continue observing as we always have, and simply send up more telescopes to cover the sky?

I was about to post this in questions that don't merit their own thread, but I figured this might.

[Nuke]

i think the transit method would require sending a telescope to the outskirts of the solar system as you need the planets in the foreground. this would need to be far enough out and could only detect planets inside its orbit. its also very unlikely that any new planets are on the ecliptic, otherwise we would have detected them already. so you would probibly need multiple scopes at different phases in the orbit to increase the odds of observing a transit. another issue is time, its going to take a long time if the planet is say at its aphelion as the orbital period is likely to be on the order of centuries to millennia. it would take decades to get the scopes into position. 

there is also the wobble method, but it seems like that wobble would gravitationally couple with the observing orbit and make it harder to detect. this could be measured a lot closer to the sun, and that might actually be advantageous. i think this method has already been used to look for exoplanets extra planets. there are scientists who will claim that every gravity source in the solar system is accounted for. if we find anything its going to be mostly small kbos, and likely a lot of them. anything in the oort cloud probibly doesn't have that much gravitational influence over the sun.

Edited April 23, 2022 by Nuke

[UmbralRaptor]

20 hours ago, Spaceception said:

So this is really all in the title, but what limitations and challenges are there to using methods like radial velocity to find more planets in the solar system, like planet x, or other major bodies that might be far from the sun? I know radial velocity relies on the Doppler shift of a star's light, so are we too close for it to work? Or do hypothetical Oort cloud planets have too weak of a pull to really be noticeable? Either because of their extremely long orbits or comparatively small masses. What needs to change to make it feasible, and would it be worth our time - or would it make more sense in the end to continue observing as we always have, and simply send up more telescopes to cover the sky?

I was about to post this in questions that don't merit their own thread, but I figured this might.

HARPS-N has a solar telescope, and regularly takes RV measurements of the sun. Somewhat infamously, you can see Jupiter in the data by eye, but it has yet to detect eg: Venus. But more generally, my response to trying to use it for distant planets is "lol, lmao". Weirdly enough, the period of a planet in our solar system isn't too important (so you don't need hundreds of years of data), but the sorts of distances would make the semi-amplitude (which scales roughly as mass/sqrt(distance)) negligible. Assuming my math is correct:

Planet	Semi-amplitude (m/s)
Jupiter	12
Saturn	2.8
Uranus	0.30
Neptune (NEID is about here assuming no stellar activity)	0.28
Earth (goal for upcoming RV surveys)	0.09
Venus	0.085
Mars	0.078
10-Earths at 400 au	0.045
Mercury	0.008

Hence KBO/Oort cloud/Planet 9 surveys using direct imaging.