10:23 PM ooooo AT&T; LTE session masteringphysics.com Exercise 13.37 MasteringPh

Question

10:23 PM ooooo AT&T; LTE session masteringphysics.com Exercise 13.37 MasteringPhysics Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light years and an orbital speed of about 250 km/s. Part A Determine the mass of the massive obiect at the center of Way galaxy. Give your answer in kilograms. Express your answer using two significant figures. kg Submit Give Up Part B Give your answer in solar masses (one solar mass is the mass of the sun). Express your answer using two significant figures. mas Give Up Submit

Explanation / Answer

a) radius = 7.5 light years

distance of one light year = 9.461 * 1015 m

G M m / r2 = m v2 / r

G M / r2 = v2 / r

GM / r = v2

6.67 * 10-11 * M / (7.5 * 9.461 * 1015) = 2500002

M = 6.65 * 1037 kg

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b) In solar masses

(6.65 * 1037) / (1.99 * 1030) = 3.34 * 107

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c) no

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d) Schwarzschild radius Rs = 2 G M / c2

= (2 * 6.67 * 10-11 * 6.65 * 1037 ) / (3.0 * 108)2

Rs = 9.86 * 1010 m

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