Black Holes

This is a reference to what a black hole is.

The definition of a black hole is an object that is so dense that the velocity needed to escape from the object is grater then the speed of light.

Lets start with this ‘escape velocity’ thing. In order to leave the orbit of an object you must reach a specific velocity. The equation is:

Where G is the gravitation constant, M is the mass of the object, and r is the radius of the object. All of the variables are based on the object you are trying to escape.

The equation is easiest to derived from the conservation of energy law:

K(i) is the initial kinetic energy of the escaping object, U(gi) is the initial potential energy induced by gravity on the excepting object. And K(f) and U(gf) and the final. In step 2 I plug in the variables. They are the same as above except m is the mass of the escaping object. Now in step 3 I say that the final distance is infinite (because if you escape the gravity you will forever float away form the object) and that the final velocity is 0 (because if we have more velocity after we are an infinite distance form the object then we will have been going to fast.). Because of this the entire right side of the equation becomes 0. So then steps 3-7 are all high school algebra.

So earth has an escape velocity of 11.2 km/s (M=5.9736×10^24 kg, G=9.8m/s^2, r≈6,372km)

Now lest make a black hole. If the escape velocity must be grater then the speed of light then we have a starting point v(e)=c. so now we can work our equation backwards:

M/r in this case is a fancy way of saying density of the object because the radius is the only variable in the volume of a sphere (4/3πr^3). This ‘magic’ density is 6.736x10^26kg/m^3. That’s shrinking the earth to a radius of 8.8mm... so like a peanut.

So u can see that a black hole is only dependent of the density of an object. This is why black holes are the densest things in the universe. But also notice that the mass can be anything.

Let’s say we have a sun exactly like ours in the same type of solar system. For some reason the sun becomes a black hole without any of the high energy processes happing that would disturb the orbit of the planets. In this impossible situation the planets would continue to orbit the black hole as if noting has happened. This is because the black hole still have the same mass as the sun its just in a smaller space now.

Also size does not matter. If you take the mass of an atom and crush it down to the correct density you still have a black hole. It is immensely smaller the any atom and have the same gravitational attraction of the original atom but it is still a black hole.

The size of the black hole is measured by the radius of the event horizon. The event horizon is just the point at which the escape velocity is the speed of light.

It should also be noted that black holes decay over time. This is due to very advance mathematics that I can’t prove with out coping someone’s work (Steven Hawkings) and would probably confuse most people reading this (including my self). But an extremely simple rate is 2.28x10^5kg=a one second long black hole. So anything that weighs less will evaporate faster.