The Cosmic Perspective (9th Edition)
The Cosmic Perspective (9th Edition)
9th Edition
ISBN: 9780134874364
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter S3, Problem 44EAP

(a)

To determine

To Discuss:The change in the curvature of space-time in the region where the Sun used to be located if the Sun is replaced by a black hole of precisely the same mass.

(b)

To determine

The change in the curvature of space-time in the region of Earth’s orbit, if the Sun is replaced by a black hole of precisely the same mass.

(c)

To determine

The effect of the change on the Earth’s orbit, if the Sun is replaced by a black hole of precisely the same mass.

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Part 1. Stellar Mass Black Holes These are the collapsed cores of massive stars which end their life in supernova explosions. The stellar core can no longer use nuclear fusion to hold up the immense gravity, and collapses until its escape velocity rises higher than the speed of light. Voila! A black hole is formed. Part A: The Schwarzschild Radius The Schwarzschild Radius is defined as: 2GM (1) = c2 where r, is the Schwarzschild radius, G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. 1. Let's say we have a black hole with a mass 10 times that of the Sun (the Sun's mass is 2 x 1030 kg, so the mass of the black hole is then 2 x 1031 kg). Using the definitions for G and c, what would the Schwarzschild radius of this black hole be? 2. If the radius of the Sun is 7 x 108 m, how does the black hole's radius compare? (Divide the radius of the Sun by the Schwarzschild radius). Your answer should be in the form of times smaller/bigger than the…
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Chapter S3 Solutions

The Cosmic Perspective (9th Edition)

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