Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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 masses. 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.

Sagot :

MrRoyal

The Schwarzschild radius of the black hole depends on its mass

The Schwarzschild radius of this supermassive black holeis 0.091 AU

How to determine the Schwarzschild radius?

The Schwarzschild radius (r) is calculated using:

[tex]r_s = \frac{2GM}{c^2}[/tex]

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

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

Evaluate the expression

[tex]r_s = 13589425339.6[/tex] m

Express as km

[tex]r_s = 13589425.3396[/tex] km

Expressas AU

[tex]r_s = \frac{13589425.3396}{1.5 * 10^8}[/tex]

Evaluate the quotient

[tex]r_s = 0.09059616893[/tex]

Approximate

[tex]r_s = 0.091\ AU[/tex]

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

Read more about gravitational radius at:

https://brainly.com/question/4208016

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.