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ss7ja [257]
2 years ago
6

Observations of the center of the Milky Way show the presence of a super massive black hole with a mass of 4.6 x 106 solar masse

s. Compute the Schwarzschild radius of this supermassive black hole. Give your answer in units of astronomical units (AU). At what distance does Mercury orbit from the Sun in AU? If we swapped out the Sun for this super massive black hole, would the event horizon extend beyond the orbit of Mercury? Be sure to show your calculations. 1 AU = 1.5 x 108 km.
Mathematics
1 answer:
natali 33 [55]2 years ago
6 0

The Schwarzschild radius of the black hole depends on its mass

The Schwarzschild radius of this supermassive black holeis 0.091 AU

<h3 /><h3>How to determine the Schwarzschild radius?</h3>

The Schwarzschild radius (r) is calculated using:

r_s = \frac{2GM}{c^2}

Where:

G =  Gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2

M = Mass of the object = 4.6 x 10^6 solar masses

c = Speed of light = 299792458 m / s

Express the mass in Kg

M = 4.6 x 10^6 * 9.2 * 10^18 = 9.15 * 10^36 kg

Substitute the above values in the equation

r_s = \frac{2 * 6.67408 * 10^{-11} * 9.15 * 10^36}{299792458 ^2}

Evaluate the expression

r_s = 13589425339.6 m

Express as km

r_s = 13589425.3396 km

Expressas AU

r_s = \frac{13589425.3396}{1.5 * 10^8}

Evaluate the quotient

r_s = 0.09059616893

Approximate

r_s = 0.091\ AU

Hence, the Schwarzschild radius of this supermassive black holeis 0.091 AU

Read more about gravitational radius at:

brainly.com/question/4208016

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