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Chapter 22: Problem 45

Find the Schwarzschild radius for an object having a mass equal to that of the planet Saturn.

Short Answer

Expert verified
\(r_s\) is approximately 842715 meters or roughly 843 kilometers.

Step by step solution

01

Identifying the Known Variables

The mass of Saturn (M) is known, approximately 5.683 × 10^26 kg. The gravitational constant (G) is 6.674×10^-11 m^3 kg^-1 s^-2, and the speed of light (c), a fundamental physical constant, is about 3 x 10^8 m/s. These will be the values plugged into the formula.
02

Apply the Schwarzschild Radius Formula

We use the formula for the Schwarzschild radius \(r_s = 2GM/c^2\). Plugging in our known values, we get \(r_s = 2 * 6.674×10^-11 m^3 kg^-1 s^-2 * 5.683 × 10^26kg / (3 x 10^8 m/s)^2\).
03

Solving the equation

Performing the indicated operations, you obtain a numerical result for the Schwarzschild radius \(r_s\).

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