So in the last lecture, we talked about the idea of the distortion of space time.
And how that is really, in Einstein's view, equivalent to gravity.
Or that is what we should think about when we think about gravity.
Now, we want to think about what happens to a really massive star when it dies and
that neutron star that forms at the center is the quantum mechanical forces
are too strong to even allow it to support itself against its own weight.
What happens then?
And before we go there, we need one very important concept.
Which is on our way towards black holes and as the concept of escape velocity.
And the question here you want to ask yourself is what do you need in order to
launch something into space?
What do you need in order to escape a massive object?
To be able to travel freely out into space.
How fast does it have to be moving?
And as it turns out, there's a simple formula that we can use based on
conservation of energy that tells us that a massive object with some mass r and
some radius r that the escape velocity has a very simple form.
The v escape is equal to the square root of 2 times Newton's gravitational
constant G times the mass of the object, divided by the radius.
The important thing about this to see is that the escape velocity increases, for
example, if the mass goes up.
And that certainly makes sense, if I have a rocket that can produce or
that can launch something into space from the Earth, and then I suddenly,
magically, double or triple or quadruple the mass of the Earth.
I'd expect I'd need a more powerful rocket now to get that satellite into space.
But likewise, we could imagine taking the Earth and shrinking it down, making
the Earth half the size of its present value or a quarter or a tenth of the size.
What we see from this formula is that the escape velocity would still go up.
That smaller more compact objects, have very high escape velocities as well.
So the important thing to understand, is there's three possibilities here.
If I launch a probe or
I launch a rocket from the surface of a gravitational object or a massive object.
If v, if the velocity I'm launching with is less than the escaped velocity
it'll fall back to Earth.
It's just like when you take a ball and throw it in the air.
Eventually it goes up and then it comes down.
If I launch it with exactly the escaped velocity what
will happen is I will be able to get that object to go into orbit.
It will continually circle the gravitational object.
If, however, the velocity is greater than the escaped velocity I will actually be
able to get that probe out to infinity.
Of course it will take an infinite amount of time to get there, but
I will essentially be able to escape the gravitational object.
So that idea of escape velocity's going to be very important for
us to be able to define the all-important quantities associated, or
physical structures, associated with a black hole.
So that's what we'll do next.
Adam FrankProfessor
