The Schwarzschild radius is the radius of the event horizon surrounding a non-rotating black hole. Any object with a physical radius smaller than its Schwarzschild radius will be a black hole. This quantity was first derived by Karl Schwarzschild in 1916:
where RS is the Schwarzschild radius, G is the gravitational constant, M is the mass of the object and c is the speed of light.
The following table gives the Schwarzschild radii of some familiar astronomical objects:
|Sun||2.0 × 1030 kg||3.0 × 103 m||= 3 km|
|Earth||6.0 × 1024 kg||8.7 × 10-3 m||= 8.7 mm|
|Moon||7.3 × 1022 kg||1.1 × 10-4 m||= 0.11 mm|
|Jupiter||1.9 × 1027 kg||2.2 m||= 2.2 m|
|Neutron Star||2.8 × 1030 kg||4.2 × 103 m||= 4.2 km|