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ramriot t1_itbs3tv 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

Thank you for this extensive explanation but unfortunately calculation of gravitational interaction in symmetrical smooth objects is I think independent of configuration.

All matter outside of an object's orbit should affect it equally, while that inside can just as well be treated as a point object at the barycenter.

A better answer to the original question is to say that the fraction of dark matter to visible matter within the Earth's orbit is much smaller than that of the sun's orbit around our host galaxy. Thus the latter shows a greater anomalous velocity.

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Astrokiwi t1_itbslwp wrote

That's only for spherical concentric shells. If, for instance, a star passed within 2 AU of the Sun, it would definitely affect the Earth's orbit, even though all the mass is outside the Earth's orbit.

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