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Aseyhe t1_itb7ezq wrote

Reply to comment by Astrokiwi in Why doesn’t dark matter affect planetary motion like it affects the rotational velocity of stars at a larger scale? by quantumshrarry

The smoothness of the dark matter isn't the full explanation. A completely uniform distribution of dark matter would affect planetary orbits if there were enough of it. It would source a harmonic oscillator potential.

The main reason dark matter does not significantly affect planetary orbits is that there is simply not enough of it. Stars and star systems form when gas cools and condenses. Since dark matter does not cool, it does not participate in this process. Consequently, whereas the average density of the solar system within Neptune's orbital radius is about 3*10^12 GeV/cm^3, the average density of dark matter in our neighborhood is about 0.4 GeV/cm^(3), ten trillion times smaller.

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Astrokiwi t1_itb9l9n wrote

So yes, that's another good point. Part of the answer is a gravitational force can affect a system without affecting the motions within that system - and that does come down to the smoothness of the potential. I also wanted to clarify that dark matter isn't a magic thing that just speeds up orbits - in terms of gravity, it's just a distribution of matter, that acts like any other distribution matter. But yes, the other part is that there isn't an additional local effect, as the local density of dark matter really is very low.

Though I would want to clarify for other readers (as I assume you know this of course) that while there is locally not much dark matter (it has a very low density), but because it's smoothly spread out over such a huge 3D structure, its total mass is much larger than the mass of the stars and gas in the Galaxy.

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