Do stars' orbits in galaxies obey Kepler's Laws?
Subject: elliptical galaxies
An ellipse has 2 foci around which the bulk of stars flow. Let's assume that a huge star was pointed out in one of these foci.
Would it then be possible to give proof that all stars in the system, were circling around the focus, just as it is said by Kepler's first law.
Kepler's Laws were derived for the planets orbiting the Sun in our solar system. And they work for any situation in which you have one discrete object with a mass far greater than any of the the objects that orbit it. But with galaxies you have a very different situation. The mass of a galaxy is not all concentrated at the center. It's spread out among all the constituents of the galaxy, across hundreds of thousands of light years. As explained here, even the supermassive black hole at the center of the Milky Way isn't massive enough to greatly affect the orbits of the stars in our galaxy (except for those very close to the center).
So you can't really say that the stars in an elliptical galaxy are orbiting about one of the foci of the ellipse as the planets do when they orbit the Sun. In fact, a star in an elliptical galaxy won't even necessarily trace out the same path in space each time it makes an orbit.
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