[Rich]

One of the problems with the standard physics model, is that as you move out from the centre of a galaxy the angular momentum of the stars around the galactic centre is constant or increases slightly. I think I have got this right. If you look at the our solar system or a moon system like the moons of Jupiter the angular momentum falls as you move out from the gravitational centre. The absolute velocity falls as well but not by the same factor. So for example Neptune at 30.1 astronomical units from the Sun (the Earth is at 1 Astronomical unit from the Sun) revolves in a period of 164.8 Earth years. Hence its angular velocity is approximately 165 times slower than the Earth's. This means that Neptune absolute velocity relative to the Sun is a less than a fifth of the Earth's. This accords with predictions of Newtons inverse square law.

To explain this anomaly, Physicists have invented Dark matter. there is a lot of mass we can't see. But how does this help, because increasing the mass of the Galaxy's will not change the gradient of the velocity against the distance from the gravitational centre?

[lucky]

Kepler's third law only holds when all the mass that's pulling things is assumed to be at the center of mass (or spherically symmetric around it). This does not hold for galaxies, especially so because of dark matter.

[mikema63]

I'm more interested in what dark matter is, but from my understanding dark matter is in a cloud around the galaxy not at the center.

[Rich]

Kepler's third law only holds when all the mass that's pulling things is assumed to be at the center of mass (or spherically symmetric around it). This does not hold for galaxies, especially so because of dark matter.

The Time period is proportional to the radius raised to the power of 3 over 2. (Is there a Unicode way to print that nicely?)

Yes but surely if there is circular symmetry and the matter is concentrated in the plane of rotation that will increase the fall off in angular velocity (as you move outwards from the centre) not reduce it.

I'm more interested in what dark matter is, but from my understanding dark matter is in a cloud around the galaxy not at the centre.

Even if the dark matter is outside the visible Galaxy that wouldn't necessarily break spherical symmetry. The absolute velocity of the stars (in a stable circular orbit) is proportion to their gravitational acceleration. Therefore for any given absolute velocity, the further out a star's orbit the faster it is falling towards the galaxy centre. So why should matter (whether dark or light) outside of the visible Galaxy increase the rate of falling?

[mikema63]

I have no idea, hopefully someone with a better understanding of physics will come by.

[One Degree]

The 'Death Star' is composed of dark matter and is hiding next to the sun.
This accounts for the discrepancies and I can prove it mathematically.

Actually, I am totally ignorant of this science and would be curious to hear an answer.
I know dark matter distorts the shape of the galaxy, so it is not as it appears to us.
Is this the cause of the discrepancies in the formulas?

[lucky]

Suppose that the galaxy is mostly a big ball of dark matter with radius R and density ρ.

Consider a circular orbit inside that ball, at radius r < R around the center.

For a circular orbit we have: a = v^2 / r, where a is gravitational acceleration and v is velocity.

Thanks to the Shell theorem, we have:
a = G*M / r^2, where M is the total mass inside the sphere of radius r.

Since we have assumed uniform density:
M = 4/3 * π * ρ * r^3
a = G * M / r^2 = 4/3 * G * π * ρ * r
v = (a * r)^(1/2) = (4/3 * G * π * ρ * r^2)^(1/2) = (4/3 * G * π * ρ)^(1/2) * r
Angular velocity:
ω = v / r = (4/3 * G * π * ρ)^(1/2)

Hence the velocity is proportional to r and angular velocity is constant, as long as you're inside the ball.

[One Degree]

Next week they are suppose to fire up the large Hadron collider and possibly prove the existence of dark matter.
Maybe their explanation will be an answer I can understand.

[mikema63]

Dark matter definitely exists, it must unless everything from newton on is completely wrong. The problem is that we have only the faintest idea of what it might be.

[Decky]

Sounds like nonsensical hocus pocus. Science gets on it's high horse but really it is no more reasonable than creationism.

[Saeko]

Everything depends on how dark matter is supposed to be distributed. Dark matter is also hypothesized to be weakly interacting, meaning that dark matter particles don't bounce off of each other or ordinary matter particles, but instead almost go right through each other. Therefore, dark matter clouds can exhibit behaviors that ordinary matter clouds can't, which allow them to achieve the mass distributions necessary to produce the observed effects on galaxies.

[Rancid]

Dark matter is just a place holder term for the fact that we can detect extraneous gravity fields outside of detectable matter.

[Rich]

Dark matter is just a place holder term for the fact that we can detect extraneous gravity fields outside of detectable matter.

Lucky has persuaded me, that Dark matter is a fairly reasonable presumption. i would say rather that Dark Energy is much more of a place-holder for stuff scientists don't understand. A cosmic constant that's not constant.