Schwarzschild Radius

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:

$ R_S = \frac{2GM}{c^2} $

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:

Object Mass RS
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

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