## Horizon

Although light cannot escape from a black hole, the black hole has certainly not ceased to exist. It is still a physical object with mass. That is the reason it creates a gravitational field, just as the earth or any other object with mass does. But how do we talk about the size of a black hole when we have just described it collapsing without end? Is it infinitely small?

It turns out that there is a dimension to ascribe to a black hole. We can talk about the mass of a black hole, and its radius, but it is a very different kind of radius, as we'll see in a moment. First, a quick detour.

In Chapter 9, "Space Race: From Sputnik to the International Space Station," we described the fundamental difficulty of getting rockets into space. Building a rocket capable of escaping the earth's gravitational pull requires an engine capable of delivering sufficient thrust to achieve a velocity of about 7 miles per second (11 km/s). This escape velocity (as Newton determined in the eighteenth century) depends upon two factors: the mass of the planet, and its radius. For a fixed-mass object, the smaller the radius, the greater the escape velocity required to get free of its gravitational field.

So as the core of a star collapses (with its mass remaining constant), the escape velocity from its surface increases rapidly. But what about when it has no more "surface" that we can talk about? What is the surface of a black hole? And what is the limit to the increase in the velocity?

Nature has one very strict speed limit: the speed of light. Nothing in the universe, not even photons carrying information from distant reaches of the

universe, can move faster than the speed of light, or 984,000,000 feet per second (300,000,000 m/s). So there is an upper limit to escape velocity as well. When a body of a given mass reaches a certainâ€”very smallâ€”size, objects would have to be moving faster than the speed of light to escape. It makes Alcatraz look like a piece of cake.

Star Words

### Star Words

The Schwarzschild radius of a black hole is the radius of an object with a given mass at which the escape velocity equals the speed of light. As a rule of thumb: The Schwarzschild radius of a black hole (in km) is approximately 3 times its mass in solar masses. So a 5-solar mass black hole has a Schwarzschild radius of about 5 x 3 = 15 km. The event horizon coincides with the Schwarzschild radius and is an imaginary boundary surrounding a collapsing star or black hole. Within the event horizon, no information of the events occurring there can be communicated to the outside.

## Telescopes Mastery

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