[stephensonsco]

The dark matter is a gas not a solid. It's not orbiting the sun, it's orbiting the galaxy (technically, not even the galaxy, it's orbiting inside it's own halo mostly). The orbits of the particles would be highly irregular, going in all directions, many with very eccentric orbits, etc. The sun is moving through the "rest frame" of the galaxy at a ~constant speed, but the earth is orbiting the sun so it has fractionally varying relative speed compared to the rest frame (speeding up and down every year relative to the rest frame).