Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 13 - Newton's Theory of Gravity - Exercises and Problems: 20

Answer

The radius of the event horizon is 14.7 km

Work Step by Step

We can use the equation for escape speed to find the radius $R$ of the event horizon. $v = \sqrt{\frac{2~G~M}{R}}$ $v^2 = \frac{2~G~M}{R}$ $R = \frac{2~G~M}{v^2}$ $R = \frac{(2)(6.67\times 10^{-11}~m^3/kg~s^2)(5.0)(1.99\times 10^{30}~kg)}{(3.00\times 10^8~m/s)^2}$ $R = 1.47\times 10^4~m$ $R = 14.7~km$ The radius of the event horizon is 14.7 km
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