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barnabas_trumanI'll assume that you accept these premises:
1) The gravitational force exerted by an object gets stronger the more massive the object is.
2) The gravitational force exerted by an object gets stronger the closer you are to its center.
Imagine that we have a planet that has a constant mass, but we can vary its radius (and thus its density) however we like. Now suppose we build 299,792,458 cannons on the surface, all aimed straight up. The first cannon, on the far left, launches its projectile at 1 m/s, the second at 2 m/s, the third at 3 m/s, and so on, so the final cannon, on the far right, launches its projectile at the speed of light (if that bothers you, we can stop at the 299,792,457th cannon).
For any planet, there is a certain speed called the escape velocity. This is the speed with which a projectile must be launched in order to never fall back to the planet due to gravity. One of these cannons must be launching its projectile at (or very close to) this planet's escape velocity. Let's call this the Escape Boundary, because all the cannons to the left will be launching (slower) projectiles that fall back down to the planet, and all the cannons to the right will be launching (faster) projectiles that escape the planet's gravity and never fall back.
With me so far?
Now let's shrink the planet's radius (holding its mass constant, remember?) a bit. Since the cannons on the surface are now closer to the center of the planet, they're subject to stronger gravity. This means that the required escape velocity is higher! In other words, the cannon at the previous Escape Boundary is now too slow and its projectile (eventually) falls back to the planet, so the new Escape Boundary is a little further to the right.
Shrink the planet's radius further, gravity at the surface becomes stronger again, the Escape Boundary moves further to the right, and more projectiles are falling back to the planet while fewer are escaping--again, with stronger gravity, a faster speed is required to escape.
Keep shrinking the radius smaller and smaller, and eventually we get to a point where the Escape Boundary is exactly on the final cannon. In other words, at a certain radius, the required escape velocity is c, the speed of light itself! This radius is called the Schwarzchild radius (after the physicist and astronomer Karl Schwarzchild) or rs. The exact value of rs depends on the mass of the planet (or star or whatever), and represents the radius that would be required to produce an escape velocity of c, meaning only light can escape the gravitational field--anything slower (i.e. everything else) will fall back in.
So what happens if we shrink the radius further, making it even smaller than rs? At that point the Escape Boundary moves past the fastest cannon, meaning that nothing, not even light, can escape gravity! This is what is meant by a "black hole."
Any questions?
1) The gravitational force exerted by an object gets stronger the more massive the object is.
2) The gravitational force exerted by an object gets stronger the closer you are to its center.
Imagine that we have a planet that has a constant mass, but we can vary its radius (and thus its density) however we like. Now suppose we build 299,792,458 cannons on the surface, all aimed straight up. The first cannon, on the far left, launches its projectile at 1 m/s, the second at 2 m/s, the third at 3 m/s, and so on, so the final cannon, on the far right, launches its projectile at the speed of light (if that bothers you, we can stop at the 299,792,457th cannon).
For any planet, there is a certain speed called the escape velocity. This is the speed with which a projectile must be launched in order to never fall back to the planet due to gravity. One of these cannons must be launching its projectile at (or very close to) this planet's escape velocity. Let's call this the Escape Boundary, because all the cannons to the left will be launching (slower) projectiles that fall back down to the planet, and all the cannons to the right will be launching (faster) projectiles that escape the planet's gravity and never fall back.
With me so far?
Now let's shrink the planet's radius (holding its mass constant, remember?) a bit. Since the cannons on the surface are now closer to the center of the planet, they're subject to stronger gravity. This means that the required escape velocity is higher! In other words, the cannon at the previous Escape Boundary is now too slow and its projectile (eventually) falls back to the planet, so the new Escape Boundary is a little further to the right.
Shrink the planet's radius further, gravity at the surface becomes stronger again, the Escape Boundary moves further to the right, and more projectiles are falling back to the planet while fewer are escaping--again, with stronger gravity, a faster speed is required to escape.
Keep shrinking the radius smaller and smaller, and eventually we get to a point where the Escape Boundary is exactly on the final cannon. In other words, at a certain radius, the required escape velocity is c, the speed of light itself! This radius is called the Schwarzchild radius (after the physicist and astronomer Karl Schwarzchild) or rs. The exact value of rs depends on the mass of the planet (or star or whatever), and represents the radius that would be required to produce an escape velocity of c, meaning only light can escape the gravitational field--anything slower (i.e. everything else) will fall back in.
So what happens if we shrink the radius further, making it even smaller than rs? At that point the Escape Boundary moves past the fastest cannon, meaning that nothing, not even light, can escape gravity! This is what is meant by a "black hole."
Any questions?
