Is it a Black Hole?
Learn how to find out and check other objects.
You can read about the formula we use here, or, jump down to the calculator and start using it.
The Schwarzschild Radius Formula
A characteristic of black holes is the distance around them from which nothing can escape. This is called the Event Horizon or Schwarzschild Radius.
One way of characterizing a black hole is by determining whether its Schwarzschild Radius is larger than its actual radius. The formula for the Schwarzchild Radius can be used to determine this. You can even find out whether you are a black hole by using it.
The formula looks like this:
r_{s} = | 2GM |
c^{2} |
Here is what the letters stand for:
r_{s} is the Schwarzschild Radius
G is the gravitational constant: 6.674 x 10^{-11} m^{3} · kg^{-1} · s^{-1}
M is the mass of the object in question, in kilograms
c is the speed of light: 299,792,458 m · s^{-1}
Let's see what it looks like after these values get plugged in and its ready to use.
r_{s} = | 2 · M · 6.674 x 10^{-11} m^{3} · kg^{-1} · s^{-1} |
299,792,458^{2} m^{2} · s^{-1} |
That's a bit better. We can plug in a mass in kilograms now. We'll use Sagittarius A*, the black hole in the center of the Milky Way It has a mass of 8.2 x 10^{36}kg
r_{s} = | 2 · 8.2 x 10^{36} kg · 6.674 x 10^{-11} m^{3} · kg^{-1} · s^{-1} |
299,792,458^{2} m^{2} · s^{-1} |
Now we can get rid of some of these units that cancel with one another
r_{s} = | 2 · 8.2 x 10^{36} kg · 6.674 x 10^{-11} m^{3} · kg^{-1} · s^{-1} |
299,792,458^{2} m^{2} · s^{-1} |
The rest can be plugged into a calculator.
r_{s} = | 1.0945359 x 10^{27} m |
299,792,458^{2} |
This leaves us with one huge number divided by another huge number. So, we should get a number that is somewhat less huge.
It comes out to 12,178,355,417 m which we can write as 1.2 x 10^{10} m.
We know Sagittarius A* is a black hole, so its radius must be smaller than 1.2 x 10^{10} m.
Black Hole Calculator
With the mass and radius of an object, you can find out whether it is a black hole.
Radius of object in meters: x 10 ^{}
Results:
If you need some examples to try, here are a few:
Object | Mass in kilograms | Radius in meters |
---|---|---|
A Navel Orange | 0.27 | 0.042 |
A 155 pound, six foot tall human | 70 | 0.47 |
The Sun | 1.9885 x 10^{30} | 6.957 x 10^{5} |
Jupiter | 1.9 x 10^{27} | 6.9911 x 10^{4} |
Earth | 5.972 x 10^{24} | 6.378 x 10^{3} |
How to code it
We used JavaScript to code this calculator. It is the language of the web and runs inside web browsers.
Here is what you would code if you wanted to solve the Schwarzschild Radius formula.
//first we'll set up our values that we need
//the variable G will have the gravitational constant
let G = 6.674 * Math.pow(10,-11);
//the variable c will have the speed of light
let c = 299792458;
//now the variable M will have the mass of the object in question
let M = 8.2 * Math.pow(10,36);
//put it all in the equation, and store the result in the variable rs
let rs = (2 * G * M)/Math.pow(c,2);