Quote:
Originally Posted by Insane Climber
Imagine two stars orbiting each other. A binary i think you call it. If a third star was orbiting the two, would it orbit the biggest star or would it orbit the center of mass of the two stars.
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Actually, the third star would orbit neither of those options - it would orbit the centre of mass of all three stars. But depending on the mass of each of the stars and their angular velocity, that centre could be anywhere in the space enclosed by the three stars - even at the centre of one of the stars themselves.
Adding a million stars of varying mass into the equation makes it muddier - the centre of mass could be anywhere at all and only by observing from outside the system could an estimation be made where the centre is.
However, it would be unlikely the centre of such a system would be dark as there would be lots of stars with low angular velocities and/or mass orbiting a very short distance from the centre of gravity of the system.
Unless there was a large, super-heavy, unobservable object at the centre sucking away these "rogue" stars, making them in turn unobservable, our observations of a hole in the centre of galaxies would be the exception instead of the norm.