How did astronomers establish the existence of a supermassive black hole in the center of the Milky Way galaxy?
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Answer:
By observing objects orbiting around it, it was possible to get an estimate on the mass, and an upper limit on the diameter. It is believed that the only possibility to have such a high amount of mass (about 4 million times the mass of the Sun) in such a small space is either a black hole, or something that will needs convert to a black hole within a short time.
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