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Question

The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light. a) What is the radius of a black hole with a mass twice that of the Sun? b) At what radius from the center of the black hole in part (a) would the orbital speed be equal to the speed of light? c) What is the radius of a black hole with the same mass as that of the Earth?

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1 of 10### Knowns & Concept

$(a)$

- The escape speed is the speed of the light $\color{#c34632} v=3.00\times 10^8\, \dfrac{\text{m}}{\text{s}}$
- The mass of the black hole is $\color{#c34632} M=2M_S=2(1.99\times 10^{30}\, \text{kg})=3.98\times 10^{30}\, \text{kg}$
- The gravitational constant is $\color{#c34632} G=6.67\times 10^{-11}\, \dfrac{\text{Nm}^2}{\text{kg}^2}$
- We need to find a radius $\color{#c34632} R$ of the black hole

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