“To disagree leads to study, to study leads to understanding, to understand is to appreciate, to appreciate is to love. So maybe I’ll end up loving your theory.” -John Wheeler
Out there in the Universe, there’s a lot to marvel at. Over billions of years, gravity has attracted different portions of the expanding Universe together into large superclusters and filaments, each made up of clusters, groups, and individual galaxies separated by great cosmic voids.
From the observations of this structure on both large-and-small scales and comparison with simulations, we know that in addition to the normal matter in the Universe — protons, neutrons, and electrons — there needs to be some type of dark matter, or massive matter that’s affected by gravitation, but not by electromagnetic forces or photons.
An entire suite of observations, including the motions of individual galaxies within clusters,
the rotation speeds of individual galaxies at various distances from their galactic center,
using the gravitational lensing effect of different galaxy clusters,
and the spectrum of fluctuations in the cosmic microwave background, among others,
all show the same thing: that in addition to protons, neutrons, and electrons, there’s about five times as much mass in this new form of matter — dark matter — that exerts a well-understood gravitational force but neither absorbs nor emits light, and doesn’t collide (as far as we can tell) with protons, neutrons or electrons. So while normal matter (in pink, below) slows down and can even stick together when it runs into other normal matter, dark matter (in blue, below) just passes right through both itself and all other forms of matter.
Whereas a spiral galaxy like our Milky Way may be a few thousand light years thick and maybe 100,000 light years in diameter, the dark matter halo superimposed on our galaxy (and, as far as we can tell, all comparable galaxies) extends for maybe a million light-years in all directions. It’s more massive than the normal matter in our galaxy, but it’s far more spread out, and it also doesn’t clump together into the clumps that are so important to us, like stars, planets, and human beings.
When I first heard about dark matter, I was a prospective graduate student, teaching full-time in California, and while I was visiting the University of Florida, one of the professors was telling me about his experiment searching for one particular theoretical variant of dark matter.
“Hold on,” I said to him, “if this dark matter is spread out throughout the entire galaxy, then there should be some of it in our Solar System, too, right? So shouldn’t we be able to detect its gravitational effects on the outer planets as compared to the inner ones?”
He brushed my question off, dismissively, and continued on talking about his research. Needless to say, I was unimpressed.
The next day, I told this story to another professor there, and he immediately understood what I was asking, and why it was important. You see, the Sun is by far the dominant mass in the Solar System; to an outstanding approximation, it determines the orbits of the planets. But for Venus, the planet Mercury is interior to it; to a first approximation, Venus’ orbit is determined by the combined masses of the Sun plus Mercury. For Jupiter, its orbit is determined by the Sun plus the inner, rocky planets and the asteroid belt. And for any orbiting object in general, its orbit is determined by the total mass enclosed by an imaginary sphere centered on the Sun, with that object at the edge of the sphere.
So if there’s a sea of dark matter that permeates space where we are — all through the Solar System — the outer planets should see a slightly different (greater) mass than the inner planets. And if there’s enough dark matter, it should be detectable.
“Let’s calculate it,” the professor said to me, and so we spent the next half-hour doing just that. When we finished, we’d found that about 1013 kg of dark matter ought to be felt by Earth’s orbit, while around 1017 kg would be felt by a planet like Neptune. These values are tiny; the Sun has a mass of 2 ✕ 1030 kg, while values in the 1013 - 1017 kg range are the mass of a single modest asteroid. Someday, we may understand the Solar System well enough that such tiny differences will be detectable, but we’re a good factor of 100,000+ away from that right now.
And that number is only down to around 100,000 now thanks to some new observations, which were egregiously misrepresented by MIT Technology Review. Dark matter is negligible when it comes to Solar System orbits, and it isn’t even close to being detectable. In fact, one of the last scientific papers I wrote looked at what happens if all the dark matter that’s gravitationally captured by the Solar System over its 4.5 billion year history is (somehow) never re-ejected by the same process that allowed its capture. That’s a safe upper limit on the amount of dark matter that the Solar System could conceivably have.
And even in that (admittedly overly) optimistic scenario, at all distances from the Sun, there’s still not enough dark matter to even approach the observational limits.
It’s a calculation that’s accessible to any beginning graduate student, and it’s also my own story of how I met the professor who’d wind up becoming my Ph.D. advisor, and the one person who I probably had the best working relationship with in my entire life. But don’t be fooled by claims that we haven’t detected dark matter in our Solar System gravitationally; we shouldn’t at the level of sensitivity we’re currently capable of.
But if we put an object whose mass was definitively known into orbit around the Sun a light-year away, and we mapped out all the mass that existed out to that distance around the Sun, that’d be a different story. Hopefully, that’s a test we’ll someday be able to perform!