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where c is the speed of light, G is the gravitational constant, and M is the mass of the black hole. Note that in this formula, 2, G , and c are all constant; only the mass changes from black hole to black hole.
As we will see in the chapter on The Milky Way Galaxy , astronomers have traced the paths of several stars near the center of our Galaxy and found that they seem to be orbiting an unseen object—dubbed Sgr A* (pronounced “Sagittarius A-star”)—with a mass of about 4 million solar masses. What is the size of its Schwarzschild radius?
This distance is about one-fifth of the radius of Mercury’s orbit around the Sun, yet the object contains 4 million solar masses and cannot be seen with our largest telescopes. You can see why astronomers are convinced this object is a black hole.
Substituting the data into our equation gives
For comparison, the size of a proton is usually considered to be about 8 × 10
−16 m, which would be about ten million times larger.
Much of the modern folklore about black holes is misleading. One idea you may have heard is that black holes go about sucking things up with their gravity. Actually, it is only very close to a black hole that the strange effects we have been discussing come into play. The gravitational attraction far away from a black hole is the same as that of the star that collapsed to form it.
Remember that the gravity of any star some distance away acts as if all its mass were concentrated at a point in the center, which we call the center of gravity. For real stars, we merely imagine that all mass is concentrated there; for black holes, all the mass really is concentrated at a point in the center.
So, if you are a star or distant planet orbiting around a star that becomes a black hole, your orbit may not be significantly affected by the collapse of the star (although it may be affected by any mass loss that precedes the collapse). If, on the other hand, you venture close to the event horizon, it would be very hard for you to resist the “pull” of the warped spacetime near the black hole. You have to get really close to the black hole to experience any significant effect.
If another star or a spaceship were to pass one or two solar radii from a black hole, Newton’s laws would be adequate to describe what would happen to it. Only very near the event horizon of a black hole is the gravitation so strong that Newton’s laws break down. The black hole remnant of a massive star coming into our neighborhood would be far, far safer to us than its earlier incarnation as a brilliant, hot star.
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