Dark Matter and Rotational Velocity Curves of Galaxies and Stellar Systems

Question

The way dark matter is introduced to documentary watchers such as myself is to account for the difference between the rotational velocity of the stars in a galaxy compared to that of planets in stellar systems or even planetary systems (e.g. Jovian moons).

There is an apparent paradox here however: stellar and planetary systems do live in galaxies as well, right? So that these smaller systems should not exhibit any difference of velocity curves.

Said otherwise, one could jokingly ask: does dark matter mischievously avoid stellar systems (just to give us a clue and get noticed at last I presume).

Browsing through this forum to get some answer I stumbled upon this former question distribution of dark matter and I thought that was the explanation: dark matter would be mainly confined to the outer rim of galaxies.

But then I also came across this other question is dark matter really present around the sun.

I think I really need some insight of people more in the know.

Answer 1

The contribution of dark matter on the gravitational dynamics is negligible for relatively dense systems such as planetary systems.

Some rough figures: a planetary system like our solar system typically contains a solar mass of stellar matter within a light day cubed. Galaxies are much less dense: in our Milky Way you need a volume of about a hundred cubed light years to have a solid chance that the volume contains a solar mass.

So, even if dark matter would be distributed uniformly in and around galaxies, it is evident that star dynamics in galaxies is much more sensitive to dark matter than planetary dynamics.