# National Aeronautics and Space Administration

## Life Cycles of Stars (Grades 9-12) - Page 12

Crossing the Event Horizon

If a black hole has no size, how do scientists talk about its surface? Well, we don�t really mean the physical surface of the black hole -- we mean the surface around the black hole at which the escape velocity is equal to the speed of light. In other words, if you are closer to the black hole than the distance to this surface, you cannot escape. If you are further away from the black hole than this distance, then there is still hope for you! The surface is called the event horizon, and its radius is the Schwarzschild radius. (Named for Karl Schwarzschild, an astronomer who was a member of the German army in World War I and died of illness on the Russian front in 1916. He applied the equations of general relativity to see what would happen to light near such a massive object.) It is important to keep in mind that the event horizon is not a physical boundary, but for all intents and purposes is the surface of the black hole. Once inside it, you are cut off from the rest of the Universe forever.

The relationship of the Schwarzschild radius to the black hole mass is simple:

This can be easily understood by looking at the equation for the escape velocity from any spherical body such as a planet or star, namely,, where M and R are the mass and radius of spherical object. For a black hole, the escape velocity is equal to c, the speed of light.

1. What would be the radius of a black hole with the mass of the planet Jupiter?
2. How would the period of the Earth's revolution change if the Sun suddenly collapsed into a black hole? Note that this can never happen!
3. Suppose the Earth were collapsed to the size of a golf ball...becoming a small black hole. What would be the revolution period of the Moon, at a distance of 381,500 km? Of a spacecraft that had been hovering 300 m above a point on the surface of the Earth before its collapse? Of a fly orbiting at 0.5 cm?