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a) How large is the Schwartzschild radius for a black hole of a million solar masses? b) What about a billion (10°) solar masses? c) How do these sizes compare with the radius of the sun (the actual sun, not the sun as a black hole), and the size of the solar system? Remember you must compare the sizes in kilometers. The radius of the solar system is about 100 AU. 1 AU is 150 million kilometers.

a) How large is the Schwartzschild radius for a black hole of a million solar masses? b) What about a billion (10°) solar masses? c) How do these sizes compare with the radius of the sun (the actual sun, not the sun as a black hole), and the size of the solar system? Remember you must compare the sizes in kilometers. The radius of the solar system is about 100 AU. 1 AU is 150 million kilometers.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
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### The Schwarzschild Radius and Black Holes A black hole has an event horizon, also known as the Schwarzschild radius, which is proportional to its mass. We can write a handy version of this equation for stars in terms of solar masses as follows: \[ R = 3M \] Where \( R \) is measured in kilometers and \( M \) in solar masses. So a 1 solar mass object (the Sun, for example) if turned into a black hole would have a Schwarzschild radius of 3 km. We believe galaxies have supermassive black holes at their centers with masses that can be a million, or even a billion times the mass of the Sun. **Questions:** a) How large is the Schwarzschild radius for a black hole of a million solar masses? b) What about a billion (\( 10^9 \)) solar masses? c) How do these sizes compare with the radius of the Sun (the actual Sun, not the Sun as a black hole), and the size of the solar system? Remember you must compare the sizes in kilometers. The radius of the solar system is about 100 AU. 1 AU is 150 million kilometers. ### Explanation - **Schwarzschild Radius Calculation:** - For a black hole of a million solar masses: \( R = 3 \times 1,000,000 = 3,000,000 \) km - For a black hole of a billion solar masses: \( R = 3 \times 1,000,000,000 = 3,000,000,000 \) km - **Comparison:** - The radius of the Sun is about 696,340 km. - The size of the solar system is about 100 AU, which is approximately 15 billion km (100 AU \(\times\) 150 million km/AU). These calculations help us understand the immense scale of black holes compared to familiar astronomical objects.
Transcribed Image Text:### The Schwarzschild Radius and Black Holes A black hole has an event horizon, also known as the Schwarzschild radius, which is proportional to its mass. We can write a handy version of this equation for stars in terms of solar masses as follows: \[ R = 3M \] Where \( R \) is measured in kilometers and \( M \) in solar masses. So a 1 solar mass object (the Sun, for example) if turned into a black hole would have a Schwarzschild radius of 3 km. We believe galaxies have supermassive black holes at their centers with masses that can be a million, or even a billion times the mass of the Sun. **Questions:** a) How large is the Schwarzschild radius for a black hole of a million solar masses? b) What about a billion (\( 10^9 \)) solar masses? c) How do these sizes compare with the radius of the Sun (the actual Sun, not the Sun as a black hole), and the size of the solar system? Remember you must compare the sizes in kilometers. The radius of the solar system is about 100 AU. 1 AU is 150 million kilometers. ### Explanation - **Schwarzschild Radius Calculation:** - For a black hole of a million solar masses: \( R = 3 \times 1,000,000 = 3,000,000 \) km - For a black hole of a billion solar masses: \( R = 3 \times 1,000,000,000 = 3,000,000,000 \) km - **Comparison:** - The radius of the Sun is about 696,340 km. - The size of the solar system is about 100 AU, which is approximately 15 billion km (100 AU \(\times\) 150 million km/AU). These calculations help us understand the immense scale of black holes compared to familiar astronomical objects.
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