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We know that the speed with which the planets go around our sun decreases as a function of the distance they are from the sun. Since stars are not planets, and presumably do not behave like planets, why do we relate the revolving of planets around our star, on the one hand, with the revolving of stars in a spiral galaxy, on the other hand? When we find that stars move with constant speed regardless of distance from the centre of the galaxy, why does this surprise us on the basis that planets move with differing speeds around the centre of a solar system? In other words, are we not comparing apples with oranges when we have to posit dark matter as an explanation of stars all moving at constant speed unrelated to distance? I suppose that an object revolving around something else is common to both situations, but a planet is not a star and our sun is not the centre of a spiral galaxy. So, why reach for an explanation of the latter on the basis of our knowledge of the former?

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    $\begingroup$ The orbital velocity does decrease with distance, it just doesn't decrease as much as we would expect based on the visible mass in galaxies. This was originally why the existence of dark matter was proposed. See this answer. $\endgroup$ – lemon May 2 '15 at 16:17
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    $\begingroup$ You have, indeed, two theoretical choices. Either you assume that gravity behaves the same at inter-galactic distances as it does within the solar system and then you need dark matter to explain the rotation curves, or you modify the laws that govern gravity. Either way you need something new. Most physicists feel that dark matter is the better choice. Cosmological data seems to bear that choice out. In terms of staying close to Occam's razor (and this is more of a motivational than a scientific argument), dark matter wins, because nature seems to "like" stealthy particles like neutrinos. $\endgroup$ – CuriousOne May 2 '15 at 16:27
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    $\begingroup$ Essentially a duplicate of physics.stackexchange.com/q/6561/2451 and links therein. $\endgroup$ – Qmechanic May 2 '15 at 16:31
  • $\begingroup$ lemon, thank you for your link to your earlier answer, which I found most helpful. $\endgroup$ – Ignor Ramus May 2 '15 at 16:40
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    $\begingroup$ "Since stars are not planets, and presumably do not behave like planets..." Could you elaborate on the distinction between the two, at least that is relevant to the question? For example, you can put two large brown dwarfs together and get a small star, which alone seems to indicate the only physical difference is mass - which is already accounted for in our (generally accurate) theories of gravity. $\endgroup$ – Asher May 2 '15 at 18:39

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