astronomers have recently observed stars orbiting at very high speeds around an

Question

astronomers have recently observed stars orbiting at very high speeds around an unknown object near the center of our galaxy. for stars orbiting at distances of about 10^14 m from the object, the orbital velocities are about 10^6 m/s. assume the orbits are circular, and estimate the mass of the object, in units of the mass of the sun (Msun=2x10^30 kg). if the object was a tightly packed cluster of normal stars, it should be a very bright source of light. since no visible light is detected coming from it, it is instead believed to be a suppermassive black hole.

Explanation / Answer

Attractive force would provide necessary centripetal force to go in circle

Attracticve force = (G * m1 * m2)/ r^2

(G * m1 * m2)/ r^2 = m2*v^2 /r

6.67 * 10^(-11) * m1 = 10^12 * 10^14

m1 = 1.5 * 10^36

m1/ M sun = 1.5 * 10^36 / 2 * 10^30

m1 = 750000 M_sun

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