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There Could be a Problem with Dark Matter?

A while ago it was discovered that stars go around the galaxy at "the wrong speed". How do you mean? Well, planets are in orbit around the sun, and they go around at speeds which fit well with their distance from the sun. The planets close to the sun go around in orbit quite fast, and the planets further away from the sun go much slower. Newton's laws of motion describe the orbits of planets around the sun quite well. In contrast, what goes on at the galactic scale doesn't quite look right.

In the rotation of the galaxy, stars go around at various speeds, but there's a problem, which is that they go round at a rate which seems too fast, in consideration of the amount of matter there is for them to orbit around. It is as if, for every kilogramme of material that can be seen, there's five kilogrammes of invisible material. Only by that sort of proposition is it possible to explain how there can be so much gravity that the stars can be kept in such fast, close rotation. Thus, "Dark Matter" was born. The idea is that there exists the star-stuff which is visible through telescopes, and then there's some invisible material dubbed "Dark Matter" which has a mass of five times the normal matter, and yet it somehow doesn't interact much with the normal matter.

This is the conventional theory so far.

Of course scientists are on the hunt for Dark Matter and would dearly like to get some into test-tubes to find out what it's about. However, the stuff is rather elusive.

For all we know so far, dark matter could be real, and could exist in some odd way or other, a kind of different type of stuff which behaves the way it does and its existence explains the odd rotations of stars about the galaxy. However, I have spotted an odd anomaly which I'd like to resolve. I'll explain the logic...

Supposing
that the galaxy is made up of stars, and that they weigh about
the same on average as the sun, 2 x 10^{30}Kg
(exponential notation). Also,
let's suppose they are spread out at a distance of about four
light-years from each other (which is a guess that's probably
good enough for the calculations). In the Milky Way Galaxy there
are estimated to be one hundred thousand million stars, which
would mean the total mass of the
galaxy is 2 x 10^{30}Kg x (1 x 10^{11}) = 2 x 10^{41}Kg.
If cosmologists claim the mass would have to be five times that
amount in order to get the gravity right, ie **10**^{42}**Kg**,
then somehow there would have to be a hidden, invisible, amount
of material, either in some ineffable form (dark matter), or in
the form of normal matter that's just "hidden". (Followers
of The Hitch Hiker's Guide to the Galaxy will note the poetic
irony that the galaxy weighs 10 to the power of **42**
kilogrammes).

So, first of all, let's subtract the mass of the Interstellar Medium. What's that? It's just finely spread-out gas and stuff that's very diffuse, inbetween the stars. No-one really bothers about it, and in various science fiction, spaceships just whoosh through space at immense speed with no problems of drag or friction, so the Interstellar Medium can generally be ignored. But wait, let's factor things into the equations. If the sun is sitting there in a cubic piece of interstellar space 4 light years by 4 light years by 4 light years, then that's 64 cubic light years of interstellar medium to consider.

A light year is the
distance that light can travel in a year at the speed of light, so that's
a distance of almost 10^{16} metres.

Supposing
we take the original dark-matter fudge-factor of five times the
stellar mass, and spread it out nice and evenly in that 64 cubic
light years, we get... 2 x 10^{30}Kg x 5 divided by (4 x
10^{16})cubed, we get an average galactic density of 1.56
x 10^{-19}Kg per cubic metre. That may not sound a lot,
but when you multiply it by Avogadro's number (6.6 x 10^{23})
to get the number of atoms it would be if it was monatomic
hydrogen, it comes to about 100,000 atoms per cubic metre.

So, what's wrong with that? Well, on the one hand you have Dark Matter estimated to be the equivalent of 100,000 atoms per cubic metre, but when you look up the data for "The Interstellar Medium", many good science books say that the interstellar medium consists of about 1 million atoms per cubic metre, or thereabouts. Take a look at http://en.wikipedia.org/wiki/Interstellar_medium for example, which agrees with the concise encyclopaedia of science in saying it's about a million particles per cubic metre.

So, to sum it up, hypothetical Dark Matter would have to be at least 100,000 atoms per cubic metre, which is an uncomfortable and unexplained thing, and yet we already have an accepted idea that there's an interstellar medium with 1,000,000 atoms per cubic metre. Or, to put it another way, it would mean that there's plenty of stuff already there without inventing "dark matter".

It may be that someone can explain this, and I can't help thinking that surely some cosmologists must know about such calculations. Surely there's a mistake I am making somewhere in the figures? The numbers may be mindbogglingly big, but for all cosmologists to have failed to spot the inconsistency would be even more mindboggling?! Or, is it somehow that I am one of the few people who does this sort of calculation in my head when I can't get to sleep!?

If you know the answer, please tell me. I'm interested to hear constructive scientific ideas on this sort of thing, and I will update the page if news comes in on answers to the mystery.

(Please don't write in if you can't do the sums. This isn't a political or religious argument. It's a matter of whether the matter is there or not, and that's a matter of whether the numbers on a scientific calculator match up to consistent sense with already-known science).

I have pointed out this anomaly a while ago and so far no-one has written in. Curious, because the conventional figures seem to conflict with each-other and can't be entirely right!