How elusive is dark matter?

Your mind can wander into some strange areas when lying in bed in the early hours of the morning, in the quiet before the kookaburras start laughing their heads off.

When we read about dark matter, it often easy to think that it's out there, far away from Earth, like black holes, neutron stars, and little green men. But it's important to remember that the orbit of the Sun around the Galaxy depends upon not only the stars we see, but the dark matter we don't.

In fact, we have to remember that dark matter surrounds and threads our Solar System. But just how much?

Anyone who has done any university physics knows that within the Solar System we can happily use Newton's laws of gravitation and laws of motion to calculate the paths of the planets, with the Sun as the massively dominant source of gravitational pull, with the planets just providing additional little tugs. If there is dark matter in the Solar System, it seems to be irrelevant.

Just how much dark matter is there then?

By looking at the motions of stars, we can estimate how much dark matter there is. The density reported by this study is that within the Solar System is

This is in units of Solar masses (which are big) and parsecs (which are also big). What's this in "normal" units (and for our american cousins, I mean metric).

The wonderful Wolfram Alpha tells us that 1 Solar Mass, spread over a cubic parsec is

and the local dark matter density is

Ouch! This is small. No wonder we don't have to worry about the dark matter in the Solar System.

So, if dark matter is made of particles, how massive would they be? Well, there's a lot of speculation on this, but let's take a look at some recent suggestions that it's about 30 billion electron volts. Huh, you say, how is that a mass? In science, you choose units that are useful to you. In astronomy, we use Solar masses, as that makes it easier to talk about stars (it's a pain in kgs!), and in particle physics, they use electron volts.

 How big is an electron volt? Well, wikipedia tells us that it's

which is pretty small, and so 30 billion of these are

Ooooh - this is getting interesting. This means that there are roughly 10,000 dark matter particles per cubic metre in the Solar System. And don't forget that the room in which you sit, or field in which you are lying down in, are in the Solar System. And in every cubic metre about you there are roughly 10,000 dark matter particles, about 10 per litre.

When you reach this point, cup your hands together. In there there is probably a dark matter particle or two. Dark matter doesn't seem remotely as elusive now, does it.