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In a college entrance examination of my country, there was the following question:

Suppose that, in a galaxy, the dark matter, which is evenly distributed, can be removed. Suppose also that in the center of this galaxy there is a black hole with a star in circular orbit around him. Consider orbits of the same radius in the presence and absence of dark matter. On the resulting gravitational force exerted on the star and its effect on the movement of this star, it can be said that ...

The answer: "The force is attractive, and the orbital velocity of the star is greater in the presence of dark matter"

The answer I would give: "The force is attractive and the orbital velocity does not change"

My answer was based on the fact that dark matter is evenly distributed.

What am I missing?

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    $\begingroup$ Consider the dark matter in two regions, inside the orbital radius and outside. What is the net gravitational effect of the outer region on the star? $\endgroup$ – Triatticus Sep 14 '18 at 17:06
  • $\begingroup$ as Triatticus implies, the "evenly distributed includes all space, including the star and within the radius. The star itself will be heavier , the way the problem is worded. $\endgroup$ – anna v Sep 14 '18 at 18:30