system
Given the following post, respond as if you're commenting on Reddit:
human
Why doesn’t dark matter affect planetary motion like it affects the rotational velocity of stars at a larger scale?
gpt
The short answer is that it pulls the Sun and the planets by the same amount, so their relative motions within the solar system can ignore what's going on outside.

The dark matter halo of the Milky Way is very big and smooth. It's a big roughly spherical blob, that's denser in the middle, and less dense on the outside. Its net effect is that it an adds extra gravitational force towards the centre of the galaxy.

But this is all just classical gravity. The weirdness is that dark matter doesn't interact electromagnetically (although neutrinos don't do that either), but it's totally normal in how it interacts with gravity. If you had a big blob of gas with the same mass and distribution as the dark matter halo, it would produce exactly the same gravitational force (although this gas halo would be unstable, and would cool and collapse, as it can interact electromagnetically). The reason dark matter makes stars and gas orbit faster than you'd otherwise expect is just because there's more mass, and more force, and this mass is more spread out than the stars (which are more heavily concentrated in the centre), which means that the force drops off less slowly with distance than it would otherwise.

So the answer for why dark matter doesn't affect the orbits of the planets in the solar system is the same as why the combined gravity of all other stars and gas and black holes and everything else in the galaxy doesn't affect the orbits of these planets, or even why the Sun doesn't affect the trajectory of a football on Earth. If the gravitational force field varies only on a much bigger scale than the system you are looking at, then it pulls all objects in that system by the same amount. This means that, from within the system, you can't really tell that you're getting pulled at all, other than by looking at the overall motion of the whole system.

There is a middle ground where you get "tidal forces". This is where gravity differs *a bit* across some object. So, the Moon does pull the near side of the Earth more than the far side, which pulls Earth's oceans a little bit. But this is much smaller than the net total effect of the Moon on the Earth as a whole. But the gravitational force of the galaxy is on a way bigger scale than that, and we really can just ignore it if we only care about what's going on inside the solar system.