Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 68Q
To determine

To explain:

The reason for the requirement of careful piloting to direct a spacecraft into a black hole.

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The Schwarzschild radius RBH for an object of mass M is defined as (See image.) where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole.   1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass?   2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass?   3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?
In 1999 scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun but occupying less space than our moon. Suppose that of these black holes has a mass of 1x10^3 sun's and radius equal to one-half the radius of our moon. What is the density in grams per cubic centimeter? The mass of the sun is 2.0x10^30 kg and the radius of the moon is 2.16x10^3 mi.
Devise a way for the occupants of a spaceship to know whether they are being pulled into a black hole. What can they do if they determine they are within the Schwarzschild radius?
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