When the escape speed from the surface of a spherical object of mass M and radius R is equal to the speed of light, that radius is called the Schwarzschild radius for the given mass. What is the Schwarzschild radius of the Sun, whose mass is 2.0 × 10³⁰ kg? (i.e., if all the Sun's mass were compressed into a sphere of this radius, the escape speed from its surface would be the speed of light-it would become a black hole!) A) 4.5 km B) 1.5 km C) 5.9 km D) 3.0 km

Question

Quizplus · Accepted Answer

The Schwarzschild radius $ R_s $ is given by the formula $ R_s = \frac{2GM}{c^2} $. For the Sun, with $ G = 6.674 \times 10^{-11} \, \text{m}^3/\text{kg}\cdot\text{s}^2 $, $ M = 2.0 \times 10^{30} \, \text{kg} $, and $ c = 3.0 \times 10^8 \, \text{m/s} $, the calculation gives approximately 3.0 km.

When the Escape Speed from the Surface of a Spherical