What I love about this chart is that back in the XIX century we actually thought that there was indeed a mysterious planet inside Mercury's orbit. We even gave it a name: Vulcan.
As you know, planets follow elliptical orbits around the Sun. But Mercury's orbit is weird, as the ellipse itself rotates. This is called "precession", and other bodies do that too. Except the precession of Mercury's orbit can't be explained with Newton's laws.
In the XIX century, the French astronomer and mathematician Urbain Le Verrier proposed that this could be due to the presence of an as of then unknown planet, located inside the orbit of Mercury. This mysterious planet was named Vulcan.
This was a good idea. After all, Le Verrier had successfully used the same trick earlier to predict the existence of Neptune, based on observations of the orbit of Uranus. So, if Mercury's orbit was doing weird things, an unseen planet seemed obvious. Except that it wasn't.
Repeated attempts to observe Vulcan failed over and over. Some observers claimed to have found it, but there was never compelling evidence. How could this be possible? Newton couldn't be wrong, right? Well, turns out that he was.
The precession of Mercury's orbit was eventually explained by Einstein's General Relativity. Newton was, in a way, right. It's just that his law of gravitation is just an approximation that breaks down when you get very close to massive objects, like the Sun in this case.
What I love about this story is that it perfectly mirrors what's going on today with dark matter. General Relativity fails to explain the observed universe if all matter is what we call baryons. For the sake of simplicity, let's say that baryons are "normal stuff" :-)
We have a good idea of the amount of baryons in galaxies and in the universe as a whole. But they're not enough to explain how stars rotate within galaxies, or how galaxies are spread in the universe. Not even close.
One possibility is to follow Le Verrier's approach, and assume that there's unseen stuff that makes up for the unexplained motions of the normal stuff. We call this dark matter (a terrible name for reasons that deserve their own thread).
The question is whether dark matter is like Neptune --it exists-- or like Vulcan --just a moniker for weird things going on with gravity.
Most astronomer would go with the first option, which could very well be true. The problem with that option is that it can't be proven wrong: even if dark matter doesn't exist, we would never know. We can disprove specific kinds of DM, but not DM as a concept.
The alternative, attempts to modify gravity, are tricky too. They fail to explain many large scale properties of the universe, but they work great at smaller scales, explaining --even predicting-- rather tight correlations we see in galaxies.
Many experiments have tried to find DM particles, unsuccessfully so far. After each experiment, the properties of DM particles are readjusted to put them below the detection limits of the previous experiments. This is akin to making Vulcan smaller and smaller each time.
The problem with Vulcan and DM is that there's no emergency exit, no criteria for when to stop. Searches of Vulcan extended well into the XX century. If we'd never come up with General Relativity, we'd still be looking for Vulcan.
Do dark matter particles exist? I have no clue. Probably. I hope not, because the alternative is much more fun, but the universe doesn't care how we want it to be. I'm just a puny observer :-)
To conclude, I leave you with this fantastic article by David Merritt, which explores the ins and outs of both approaches to the missing mass problem, including this analogy with Neptune and Vulcan:
sciencedirect.com/science/articl…
sciencedirect.com/science/articl…
