Enter all but one of the mass, gravitational constant, and speed of light in a vacuum into the calculator to determine the Schwarzschild radius; this calculator can also evaluate any of the variables given the others are known.
Schwarzschild Radius Formula
The following formula is used to calculate the Schwarzschild radius:
R = (2 * G * M) / c^2
Variables:
- R is the Schwarzschild radius
- G is the gravitational constant
- M is the mass of the object
- c is the speed of light in a vacuum
To calculate the Schwarzschild radius, multiply the mass of the object by 2 times the gravitational constant. Divide the result by the speed of light in a vacuum squared.
What is a Schwarzschild Radius?
The Schwarzschild radius is a concept that comes from general relativity, named after the German physicist Karl Schwarzschild who first proposed the concept in 1916. It is the radius of a sphere such that, if all the mass of an object is compressed within that sphere, the escape speed from the surface of the sphere would equal the speed of light. This means that not even light could escape from inside this sphere, making it a black hole. The Schwarzschild radius of an object is proportional to its mass, with the proportionality constant being 2G/c^2, where G is the gravitational constant and c is the speed of light. For example, the Schwarzschild radius of the Earth is about 9 millimeters, meaning that if all the Earth’s mass were compressed into a sphere with a radius of 9 millimeters, it would become a black hole.
How to Calculate Schwarzschild Radius?
The following steps outline how to calculate the Schwarzschild Radius:
- First, determine the mass of the object (M) in kilograms.
- Next, use the formula Rs = (2GM) / (c^2) to calculate the Schwarzschild Radius.
- Finally, substitute the values of G (gravitational constant) and c (speed of light) into the formula and calculate the result.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge:
mass (M) = 5 x 10^30 kg
gravitational constant (G) = 6.67430 x 10^-11 m^3 kg^-1 s^-2
speed of light (c) = 299,792,458 m/s
