## wtorek, 1 maja 2012

### If you are bored start counting R of black hole!

Last time I was very bored. And I start counting R of black hole (of course in the easiest way I found). It's very simple. You just need one formula ( R= 2GM/c2) and the part 2GM/c2 you can take as 1,48 * 10-27 because (2 * 1,67 * 10-11/ (3*108) it's approximately exactly 1,48 * 10-27.

﻿
 Top: simulation of absorption of the star by a supermassive black hole. Below: an observation of this process in galaxy RXJ 1242-11
The formula is correct when mass used by you is smaller than R (radius of black hole) which has been counted. But, let's make an a simple example.
We can take mass of our Sun, and let's checked how small should be radius of our Sun, to make it like a black hole. Wikipedia reported that the mass of the Sun is 1.9891 × 1030 kg, so...

R= 1,48 * 10-27 * 1.9891 × 1030 = 2,9438 * 103

So as we can see our Sun should shrink very much, and have less than 2943,8 meters of radius to start be a black hole. Now our Sun have 0,696 * 106 of radius, so it should shrink  236 times.

In fact if you will conduct many calculations for different masses, and after these you can count density of these objects and you can see, that density is decreasing if mass and radius of black hole rising. Strange? Not exactly. If anywhere will exist black hole of radius large like one light year, the mass of these object will be something about 6,39 * 1042 kg, but the density of that will be about 0,0018*10 -3 km/m3. This follows from the fact that the radius of the black hole increases linearly with the increase in mass, and consequently its mean density decreases much faster.