00:01
In this problem, we are alleged to have a black hole, and we're trying to figure out, well, we know that this is a black hole with a schwarzschild radius.
00:13
We'll call r sub s.
00:15
And schwarzschild's radius is 207 astronomical units.
00:20
One astronomical unit.
00:23
One astronomical unit, i'll write this at the bottom.
00:26
One au will be equal to 1 .496 times 10 to the 11th meters.
00:35
So this in terms of astronomical, or sorry, in terms of mass, or meters, astronomical units in terms of meters would be, well, we'll have to multiply by the 1 .496.
00:49
So that'll be 3 .1 times 10 to the 13th meters.
00:55
So that's the schwarzschild's radius, right? there's some supermassive body at the bottom here, and we have the black hole, alleged black hole, right? that's bending spacetime.
01:07
Okay, so this is the schwarzschild's radius.
01:09
We're trying to figure out what the mass is of this object that's causing this distortion, this singularity.
01:15
And so the way we find the mass is that we use the schwarzschild's equation, which says that the schwarzschild's radius is equal to twice the gravitational constant times the mass of the body divided by the speed of light squared.
01:30
And we know most of this stuff, right? we can go ahead and since we know the schwarzschild's radius, we're going to multiply the schwarzschild's radius by c squared.
01:40
It means that 2gm will be equal to, and this works out to be 2 .79 times 10 to the 30th.
01:49
I'm going to leave the units off because i'm using side units...