I’m not an astronomer so I ask this in ignorance, how is it that we can detect planets around other stars (if my understanding is correct we’ve discovered about 4,000 so far) at great distances but not one so much (relatively) closer?
We can detect planets that are close to stars. We can’t (or only with great difficulty) detect planets far away from stars. All exoplanet discoveries are based, in some way or another, on watching the parent star, not on directly watching the planet itself.
If I understand correctly, the way we detect planets of stars that are very far away is by monitoring how much of their light coming towards us is blocked by a planet passing in front. This obviously wouldn’t be possible with Planet 9. That said, it sure does seem odd that bodies thousands of light years away are easier to detect than something much much closer.
What are you talking about? We’ve detected lots and lots of planets and smaller bodies in this system. 
And to add to Chronos’ point, there’s a wide range of planets we’ve discovered around other stars, but many of those systems are bound to have lots of tiny bodies whose influence on their star are to insignificant to be noticed above the noise and the influence of their larger siblings.
That’s one method. Another is to analyze the doppler shift of the star and figure out what kind of planets are needed to explain its specific wobble.
I recently stumbled onto a “news” site with a double-translated version of a Los Angeles Times article. The original source wasn’t named, but I recognized the article despite its peculiar phrasing and word choices. I’m guessing there is a lot of that going on; it’s an easy way to generate web content without paying for it.
The “weird news” tangent has this spin-off page:
I hope you’re kidding with this silly tilting at windmills, but if you’re not …
A [size=adjective] [object] is an [object]
A [sub-class=noun] [object] is a [subclass object]
The compound term “dwarf planet” is a noun describing a class of objects with certain traits. Traits that are different from the traits of a “planet”. The traits are disjoint enough that no planet has all the traits of a dwarf planet, and no dwarf planet has all the traits of a planet.
The compound term “dwarf planet” is not synonymous with the qualitative description “smallish planet”.
In further news, we may say that “Texas is flat”. That doesn’t mean the Earth is flat. One hopes you agree.
A German Shepherd is not a dog. A German Shepherd Dog is a dog.
This why I support classing dogs as oddballs and meatballs.
Apparently so. Their “editorial policy” section includes information for aspiring writers on how to write and submit an article which includes this wonderful statement: “When an article is accepted, we will intimidate you with our decision.” 
Great find.
A website published by bots, for bots!
The situation is a bit more complicated than that. Mercury is in fact made of denser material than Earth, but Earth is more compressed by its own weight.
From Wikipedia
Cool find!
So Earth gravity is adding 25% to Earth’s density (4.4 → 5.5).
To my non-expert intuition that’s a gigantically big multiplier when you consider how incompressible most of Earth’s materials are. And that some of the stiffest densest stuff is where the pressures are greatest.
Which raises an interesting thought …
Earth’s gravity is highest at the surface and decreases as you go down towards the center whereat gravity is zero. The pressure goes up monotonically as you descend because there’s an ever-increasing pile of stuff above you pressing down. Given the various densities of the stuff, from atmosphere to ocean to crustal rock to mantle rock to core materials, the pressure should increase at different rates at different depths as those two factors play off against each other.
So how does the pressure vary by depth? Here’s what I found after just a bit of reading:
This wiki has some informative graphs on density and gravity by depth, but not one of pressure. Here’s a pressure graph, but with the X-axis reversed vs the wiki graphs. There’s a distinct bump in the rate of pressure increase as you transition from the mantle into the outer core. And the declining gravity isn’t really a factor until you’re very close to the center.
Cool! Still surprised it’s worth 25% though.
Personally I would not be surprised if there were half a dozen large planets in the Oort cloud, Earth-sized or bigger. We aren’t going to see them because they are far away, small, cold, and poorly-lit by the Sun.
That is acceptable! 
Note to Board: We now have ten planets.
Ida is a chunk of rock with a boulder “trapped” in a gravity field so weak that an athlete could reach escape velocity with simply a standing jump.
The bigger a solid planet is the more dense it is likely to be because of gravitational compression, too.
But what if all of this discussion about Pluto being a planet is moot? Some researchers think Pluto might be a comet!
If being downgraded from planet to dwarf planet back in 2006 was one identity crisis for Pluto, here’s another: Scientists now say the ninth rock from the sun could be a sort of giant comet, having formed when a billion or so comets clumped together in the solar system’s early days.