Considering our methods of exploration, how likely is it that there are unfound planets (not dwarf planets) in our solar system?
I think it's probably unlikely that there are more planets between Mercury and Mars, but out from Jupiter, there's lots of empty space between the planets. Could there be some small planet hidden out there?
FYI when the first speculation about a large planet hiding in the Oort cloud came out, I took the worst case numbers given then to do some estimating about how hard it would be to find. The potential orbit's been refined since then, but the baseline conclusion of "too faint to be found in an prior all sky survey, but detectable via a targeted search if where expected" is still valid; and such a search is ongoing now. https://astronomy.stackexchange.com/questions/13270/9th-planet-location/13279#13279
There are no undiscovered planets between the sun and Neptune.
Objects closer (to Sun) than Neptune that are large enough to be considered planets (and not dwarf planets) can't remain 'hidden'. If it's there, the light from the sun will bounce off it and we will see it. As it moves in its orbit, we will notice the position in the sky change, so we will know it isn't a star.
I would like to give a more broad answer to this question though:
What is the maximum size of an undiscovered solar system object and how does it change as you get further from the sun?
The further out a solar system object is, the harder it is to detect. The rate at which it gets harder is severe; the light we receive from an object scales roughly as $1/r^4 $.
($1/r^2$ for the light travelling from the Sun to the object, and again, $1/r^2$ for the light travelling from the object to us on earth).
We are able to detect some very small earth-crossing asteroids. Some as small as ~50 metres across. At a guess (and this is just based on my intuition, not any calculations), there are probably no undiscovered objects larger than 1 km close to earth.
As you travel to the outer solar system (Jupiter to Neptune), the number of bodies increases dramatically. There are currently ~700,000 known solar system bodies and most of them occur in this area. It is believed that all asteroids larger than 10 km have been found.
In the area immediately beyond Neptune (30 AU to 100 AU), we have been finding many pluto-like objects in the past two decades, objects with diameters of 500 km or more. For reference, Pluto is about 2200 km across. It is entirely plausible that there are some, if not many, similar objects at this distance range that have not yet been found. Some of these would classify as dwarf planets, in that they are round, orbit the sun, but have not cleared 95% of their orbit of other matter.
And finally - and this is where it gets exciting - where it gets really far out, there may be an undiscovered large planet, out at ~700 AU. Referred to as Planet Nine, this is a hypothetical object that some (noteworthy) astronomers believe exist because of patterns they see in the orbits of other distant dwarf planets. From calculations, they estimate that it would be as heavy as 10 earths and travel between 200 and 1200 AU. However, these distances are so large and the sunlight out there is so dim, that even with the best telescopes and two years of looking, they haven't found it.
Finally, I'd like to share two graphs. The first one is of distance (of closest approach, or perihelion) vs diameter of various outer solar system bodies. In the bottom right corner there is a noticeable lack of dots, indicating roughly where we don't yet have the capability of seeing objects that small and distant.
+1 for a detailed but simply-explained answer that adds value to not just the question but our site as a whole!
And even if the planet was somehow invisible, we would still detect its impact on the orbits of other planets as long as it's close enough - after all, that's how we found e.g. Neptune.
About that possible 9th planet, would that still be considered inside of the bounds of our solar system? I mean, 700 AU is what, over 15x the distance between Pluto and the sun?
@Mast by definition, as long it is orbiting the sun, it's part of the solar system...
`If it's there, the light from the sun will bounce off it and we will see it.` Just as an extreme example, if there were a "second Earth", exactly 50% further along Earth's orbit; would we have observed it? (I know that Earth's orbit isn't perfectly circular and the other planet would occasionally peek out, but would we really see it if it was only visible when looking into direct sunlight?) Have we ever looked at the solar system from a vantage point not near Earth?
@Flater - There is really no possibility of there being such a "counter-Earth". Unless it is in a *perfectly* matched orbit, it will slowly overtake Earth, or Earth will overtake it. And it cannot be in a perfectly matched orbit because the other planets will perturb its orbit and Earth's orbit differently, since Earth and counter-Earth would be in different places. There really is no place for a planet inside the orbit of Neptune to hide. Careful surveys have been made of the entire sky, and space is so empty that there is nothing to get in the way.
Quoting intriguing question from @Flater “Have we ever looked at the solar system from a vantage point not near Earth?”
And to the best of my ability to track it down, the source for the first image is Johnston's trans-Neptunian objects page.
@Edoardo There's the Family Portrait) from Voyager 1 that was taken a small distance from Earth (about 40.11 AU and about 32° above the ecliptic), though it's not quite a complete survey of the solar system.
You seem to know your stuff - so is there any chance that a rocky planet 9 could have a very low albedo?
@RobJeffries it would have to have a very low albedo to not be readily visible. The main method now of finding new planet(oid)s is to calculate their estimated position and size based on perturbations in the orbits of other objects caused by their mass (gravity...) and then look with the best instruments we have in the predicted area of the sky.
@jwenting There are perturbations of KBOs. Planet 9 has not been found. Planet 9 is not readily visible. Hence my question. What is the distribution of albedos of KBOs? And I guess we may never know about the really dark ones.
xkcd also has an "explain" page that unpacks the information in each comic. The xkcd explanation for this comic is well worth reading, as it provides an excellent *scientific* background.
@Edoardo If memory serves there is or was a Solar observatory probe stationed near either Lagrange 4 or Lagrange 5. That might still be counted as near-Earth. The Voyager probes and probably some of the stuff send to Jupiter and Saturn (Cassinni ?) also took images looking back towards Earth/Sun.
@Tonny this should be made a question on its own, if there isn’t already: it appears is not of any general interest though if the only attempt with the family picture was made in 1990
The "planet" in the chart appears to be Neptune at 30 AU and 4000 dia. What is the cubewano to the right at 39 AU and bigger? (Pluto/Charon orbit)?
@chux Hadn't noticed that. I think it's supposed to be Pluto. It looks about ~2000 km on the graph and pluto is about 2200 km. The dot to the right must then be Eris, whose perihelion is 37 AU.
I'm not convinced by the 1/r^4 figure - would you really multiply? Surely it would scale with 1/(2r)^2, or 1/4r^2, which is still O(r^-2)