Crossing the Event Horizon
If a black hole has no size, how do scientists talk about its surface? They dont really mean the physical surface of the black hole when they use the phrase "surface of a black hole", they mean the imaginary 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:
R = 2GM/c2
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, v = sqrt(2GM/R), 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.
- What would be the radius of a black hole with the mass of the planet Jupiter?
- How would the period of the Earths revolution change if the Sun suddenly collapsed into a black hole? Note that this can never happen!
- 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?
- How large in mass would an object have to be in order to become a black hole with an event horizon the size of a basketball (consider the diameter of the ball to be 35 cm)?
How Much Do You Know?
There are many popular myths concerning black holes, many of them perpetuated by Hollywood. Television and movies have portrayed them as time-traveling tunnels to another dimension, cosmic vacuum cleaners, and so on. Here is your chance to show what you know
or think you know! Decide if each of the following statements is either true or false. Explain how you came to your conclusions.
- Black holes move around the Universe sucking up everything in sight.
- Black holes will eventually suck in all the matter in the Universe.
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