Frontiers and Controversies in Astrophysics: Lecture 8 Transcript
February 13, 2007
Professor Charles Bailyn:
Okay, welcome to the second part of Astro 160. This is going to be about black
holes and relativity. And just to give you kind of a preview, the whole point of black holes is that, of course,
they emit no light, so you can't see them directly. And so, the question arises, "How do you know that they're
there?" And the reason you can demonstrate that black holes exist is because they're in orbit around other
things and you can see the motion of the other things that interact gravitationally with the black hole.
This concept should be familiar, to a certain extent, because it's exactly the same thing we've been doing for
discovering exoplanets. You don't see the exoplanet directly. What happens is that there's something else that
you can see that's affected by the presence of the exoplanet. So, exactly the same thing happens with black
holes. And so, we're going to use the same equations, the same concepts, to explore this very different
context. So, black holes can't be seen directly. And so, instead of detecting them directly, you use this
combination of orbital dynamics and things like the Doppler shift to infer their presence, and more than just
inferring their presence, to infer their properties.
Now, the context is more complicated. And, in particular, we're no longer going to be using Newton's laws
â€“ Newton's Law of Gravity, Newton's Laws of Motion--because there is a more comprehensive theory that
replaced Newton, which is necessary to understand these things. That more complex theory is Einstein's
Theory of Relativity. So, we're going to be using some relativity rather than Newtonian physics. This gets
weird very fast, okay? And so, I'm not going to start there. I'm going to start with a kind of Newtonian
explanation for what black holes are, we'll do that this time, and then the weirdness will start on Thursday.
So, the first concept and the easiest way, I think, to understand black holes is the concept of the escape
velocity. This is a piece of high school physics. Some of you may have encountered it before. And it just
means how fast you have to go to escape from the gravitational field of a given object. If you go outside and
you shoot up a rocket ship or something like that, how fast do you have to shoot it up so that it doesn't fall
back to the Earth? And so, you can define an escape velocity for the Earth, or for any other object for that
matter, which is just how fast you have to go to escape its gravitational field.
There is an equation associated with this. It looks like this,
, that's the escape velocity, 2
the 1/2 power. And this is the speed required to escape the gravitational field of an object; supposing that the
object has mass equal to
and radius equal to
. Oh, one other assumption, I'm assuming here that you're
standing on the--that you start from standing on the surface of the object. If you are on the surface. Okay.