There’s a good answer for that. And we’re going to explain it. Right now! How exciting.
Planets outside the Solar System, or exoplanets, are comparatively easy to find because we can see the effects of their orbit on stars. We have a number of methods for finding exoplanets, but pretty much all of them are related to this.
The most famous, and perhaps the one you’ve heard of, is the transit method. From our position, if a planet crosses across its star, we can see the dip in light that causes.
Measuring three of these dips, we can work out the mass and orbit of the planet. Not all planets transit their star with respect to us, however, so we can’t use this for every star.
Another method is called radial velocity. This involves noting the tiny, tiny gravitational tug a planet exerts on its star. For smaller planets in wide orbits, this is incredibly difficult, but for larger planets in tighter orbits, such as hot Jupiters, this can be quite useful.
Then there’s gravitational microlensing, where we can see a more distant star being magnified by the gravity of a closer star. If there’s a planet in orbit, we can sometimes see a small deviation in the light from the distant star. This method is pretty much the only way we’re able to find rogue planets, those wandering without a star, by noting their gravitational effects as they pass in front of other stars.
But in our own Solar System, things are a bit more tricky. We can’t really use these methods to see Planet Nine or Planet Ten, except maybe microlensing, because they don’t pass near the Sun relative to us. We can, however, guess where they should be.
The existence of Planet Nine and Planet Ten is suggested by the movements of objects in the outer Solar System, namely Kuiper Belt Objects (KBOs). We can see that the orbits of these KBOs are “warped”, or pulled slightly out of position, which suggests unseen bodies are gravitationally influencing them.
Planet Ten is thought to be located just beyond Neptune’s orbit, about 60 times Earth’s distance to the Sun (1 AU, or astronomical unit), and between Earth and Mars in mass. That’s based on the warping of KBOs in that location. Planet Nine, meanwhile, is thought to be quite a bit further out, between 500 and 700 AU, and half the mass of Neptune.
(Note, these are informal names and unlikely to stick if the planets are confirmed to exist. Planet Nine was theorized first and Planet Ten second, hence them being backwards in arrangement)
Now, while we can see the effects of these planets, finding them is a different matter. We can’t use the transit method, because they don’t cross the Sun, and other stars are too distant. We can’t use the radial velocity method, because they don’t have much effect on the Sun.
So our best bets are either microlensing, hoping they pass in front of a distant star and warp its light, or more promisingly direct imaging. The latter is, as its name suggests, seeing light reflected by the planets in actual images. We’ve already seen a few exoplanets via this method.
Doing so takes time, however. We’ve essentially got to look across the whole sky (although the area is a bit smaller, based on where we think the planets are). As we speak, people are trawling through images of the sky to find glints of light from these planets. There’s even a citizen science project to find Planet Nine that you can get involved with.
If Planet Nine and Ten are out there, there’s a good chance we’ll find them given enough time. And some estimates suggest there could be many more planetary bodies hiding in the outer Solar System. Finding them will be just as tricky, though.
Looking for exoplanets is much easier, as strange as that may seem. It’s like trying to see someone in the silhouette of a window very far away, compared to seeing someone in pitch black much closer to you. As such, we know of thousands of exoplanets, but comparatively little large bodies in the outer Solar System.