The Black Hole Event Horizon calculator computes the distance from the center of the black hole to the event horizon based on the mass of the black hole using the escape velocity equation.
INSTRUCTIONS: Choose units and enter the following:
Event Horizon (RBH): The event horizon radius is returned in kilometers. However, this can be automatically converted to compatible units via the pull-down menu.
This vCalc physics equation builds on the very simple principle of the gravitational attraction of any two masses to define the radius of a black hole. The calculated radius, R, defines the event horizon of a black hole, in that any mass, M, that is compressed smaller than this radius, R, becomes a black hole.
Given that the escape velocity of a body can be computed as: `v_"(escape)" = sqrt((2*M*G)/R)` we can recognize that this velocity must not exceed the speed of light. Therefore we can re-write the equation as `v_"(escape)" = sqrt((2*M*G)/R) < c`. Rewriting this again to solve for R, which represents the radius of the black hole, we get:
`R < (2 * M * G)/c^2` ; where G is the universal gravitational constant and M is the input mass of the black hole. Interpreting this in terms of a mass compressed by gravity, it tells us any mass, M, with a radius less than R is by definition a black hole.
If we were to calculate the radius of the sun, were the sun's present mass became a black hole, we would get the following radius:
`M_"(SUN)" = 1.989*10^30 kg`
And if we enter this mass into this equation, we find the sun's radius as a black hole would be approximately: 2953.9 meters.
Since the sun's present radius is approximated as 696,342 km, this equation would tell us the sun's radius as a black hole would be about `4.24 *10^-6` of its present size (0.00000624 of its present size, which is about 6 millionths of the sun's present size).
University Physics 12th Edition, Chapter 12, Equation #12.29