Glossary of Astronomical Terms/Schwarzschild radius

Schwarzschild radius is the radius of a non-rotating body, if compressed sufficiently, would collapse into a singularity - a point where matter has infinite density and zero volume. It is also at this point that gravity becomes so strong, not even light can escape it. The Schwarzschild radius can be often be thought of as the minimum radius a body must have in order to become a black hole.

Formula for the Schwarzschild Radius

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The formula is quite straight forward to use and is not in the least scary looking:

$r_s=2Gm/c^2$

Where :

r_s is the Schwarzchild radius (in meters)
G is the Gravitational constant
m is the mass of the body (in kg)
c is the speed of light

We can make $2Gm/c^2$ a lot simpler as G and c are well defined constants, so we now have :

$r_s=m\times 1.48\times 10^{-27}$

So the Earth, which has a mass of 5.9742×10²⁴kgs, would have a Schwarzchild radius of just 9mm (from a radius of 6,372,797 m)!

John Beckett 14:10, 17 November 2006 (UTC)