It is believed that, at the center of our galaxy, is a \"super-massive\" black h

Question

It is believed that, at the center of our galaxy, is a "super-massive" black hole. One datum that leads to this conclusion is the important recent observation of stellar motion in the vicinity of the galactic center. If one such star moves in an elliptical orbit with a period of 16.4 years and has a semi-major axis of 4.8 light-days (the distance light travels in 4.8 days), what is the mass around which the star moves in its Keplerian orbit? You can apply Kepler's third law to the orbital motion of the star to find the effective mass around which it is moving.

Explanation / Answer

Kepler's law is T^2/R^3=4 pi^2/(G*M) so M = 4 pi^2 R^3/(G*T^2) we know T = 16.4 years = 517533586 seconds R= 4.8 light days = 4.8 * 24 *60*60*3E8=1.24E14 so M = 4* pi^2 *(1.24E14)^3/ (6.67E-11* 517533586 ^2)=4.21E36 kg

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