Diameter in AU of a black hole with given mass?

AI Thread Summary
To determine the diameter of a black hole with a mass of approximately 3 x 10^6 solar masses in astronomical units (AU), the Schwarzschild radius must be considered. The calculation begins with the mass conversion, where 3,000,000 solar masses translates to a diameter of 3 x 10^12 km. Since one AU is 150 million km, dividing the total diameter by this value yields approximately 20,000 AU. The discussion also highlights the importance of referencing reliable sources, such as textbooks or Wikipedia, for the relationship between black hole mass and diameter. Understanding this relationship is crucial for accurate calculations.
PMelol22
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Homework Statement


The Galaxy has a black hole with about 3 x 10^6 M☉. What is its diameter in AU?

Homework Equations


Not sure.

The Attempt at a Solution


3,000,000 solar mass, but not sure how to figure out the diameter in AU. Let's see...diameter of the sun is 1,000,000km

3,000,000 x 1,000,000 = 3 x 10^12 km...one AU is 150 million km...1.5 x 10^8
3x10^12km/1.5x10^8 = 2x10^4 AU??
 
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PMelol22 said:

Homework Statement


The Galaxy has a black hole with about 3 x 10^6 M☉. What is its diameter in AU?

Homework Equations


Not sure.

The Attempt at a Solution


3,000,000 solar mass, but not sure how to figure out the diameter in AU. Let's see...diameter of the sun is 1,000,000km

3,000,000 x 1,000,000 = 3 x 10^12 km...one AU is 150 million km...1.5 x 10^8
3x10^12km/1.5x10^8 = 2x10^4 AU??

Welcome to the PF.

What does your textbook say the relation is between the mass of the BH and its diameter?

Alternately, you can look through the wikipedia article to find that relation... https://en.wikipedia.org/wiki/Black_hole

:smile:
 
I don't see it...
 
Is this question about finding the Schwarzschild radius?
 

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