An alien spaceship, passing through our solar system, observes us by reflected sunlight from earth’s surface. We know the escape velocity from earth’s surface is vesc = √(2GME/RE). Suppose we can (magically) compress earth radius to a very small size RS so that the escape velocity equals the speed of light c. In that case, nothing, not even light, can escape earth’s gravity and the alien spaceship will observe us as a “dark black hole”! What would be the value of RS? (RS is called the Schwarzschild radius.)

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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An alien spaceship, passing through our solar system, observes us by reflected sunlight from earth’s surface. We know the escape velocity from earth’s surface is vesc = √(2GME/RE). Suppose we can (magically) compress earth radius to a very small size RS so that the escape velocity equals the speed of light c. In that case, nothing, not even light, can escape earth’s gravity and the alien spaceship will observe us as a “dark black hole”! What would be the value of RS? (RS is called the Schwarzschild radius.)

a) 8.8 cm

b) 8.8 mm                                      

c) 8.8 m

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