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View Full Version : Black holes, escape velocity and super-luminal speed.



Cronos
08-17-2009, 06:51 AM
I wrote this whole thing back in year nine a year ago in science. Everything is my words and the two diagrams are self made.

People have permission to use it as a learning reference, and I give permission for it to be posted on any site as long as I am credited. You also have permission to print this out or use its exact words aslong as it is quoted to 'Jayden Traynor'.

When I recovered this from my computer, I was annoyed to find that the 9th and 10th page (mostly covering superluminal speed) were missing. So I will supply a link that should cover what I started to explain.

Black holes, escape velocity and super luminal speed.


Black holes Introduction

A black hole is a region of space with a gravitational pull so great that not even electromagnetic radiation can escape from it (e.g. light), after having past its event horizon.

In 1783 John Mitchell proposed of an object with a gravitational pull so strong that nothing could escape it. Black holes can be described by the general theory of relativity:

When a large amount of mass gathers in a small region of space all paths through space are warped inwards towards the center of its mass, preventing all matter and radiation within it from escaping.

Black holes have in invisible interior but can still be revealed for example, a star orbiting its center has its gas being drawn into the black hole it spirals towards the center heating up and emitting large amounts of radiation that can be picked up by Earth orbiting telescopes.


Escape velocity (Ve)

Escape velocity is the term used when the kinetic energy of an object is equal to the magnitude of its gravitational potential energy.
For example someone throws a ball into the air and it falls back down this is because Earths gravitational pull exceeded the moving balls kinetic energy.
The Earths escape velocity is 11.2km/s and to escape the Suns gravity from Earth 42.1km/s is required. (As shown in the diagram below).
11.2km/s is around 34 times the speed of sound and 10 times faster than the speed of a bullet shot from a rifle.
Many people think that a rocket trying to leave Earths gravitational field requires a certain speed but this can be acquired at any speed as long as constant propulsion is used. However the second the propulsion stops the rocket can only escape by achieving Earths escape velocity 11.2km/s depending on its altitude (escape velocity lowers the further away from the surface the object is).
An object having left the Earth’s gravitational field can still be drawn in by the Sun’s gravitational field (Ve 42.1km/s).
All planets and stars have gravitational fields and they all weaken the further away from the center. For example to reach Ve on the Suns surface 617.5km/s is the speed required, the Suns Ve from Earth is 42.1km/s and its Ve from Neptune is 7.7km/s.

Here is a diagram showing the surface Ve of all the planets and the suns surface Ve/its Ve from the surface of all the planets.

http://img256.imageshack.us/img256/4641/blackholeone.jpg


Why is it impossible for anything to escape a black holes gravitational pull?

1. A black holes Ve is too fast for even the speed of light, which travels at 300,000km/s and since nothing is faster than the speed of light then nothing can escape a black holes gravity.

2. Why cant an object powered by propulsion escape after having past the event horizon? Space and time are not two separate things they are one, spacetime. In spacetime information (objects, radiation ect.) can only move forward in time and cannot change position faster than light.

3. Normally information is free to move in any direction through spacetime. However the gravitational field of a black hole tilts the directions towards its center and the closer the information is the more paths that are titled towards the center. When all possible paths for the information to take are heading into the black hole this is called the event horizon. Anything before the event horizon still had available paths away from the black hole but this doesn’t mean they had the required Ve or propulsion power to avoid the event horizon. (Refer to the third paragraph in the Black Holes Introduction section).

http://img151.imageshack.us/img151/8382/blackhole2.jpg


What would happen if you fell into a black hole?


Outside the event horizon

If you are within the range of the black holes gravitational pull and you are not using any methods of propulsion you will slowly drift towards the black holes center. At this point it is still possible to escape from the black holes gravitational pull. You feel weightless as everything is pulling you in the same direction. As you approach the event horizon time will start to slow down.

If this were a small black hole you would have been torn apart by now.


Inside the event horizon

At this point it is impossible escape the black hole. Assuming this is a large black hole after passing the event horizon around 600,000km from the center you will begin to feel tidal force. Tidal force is a gravitational force that gets stronger and stronger the closer you are to the center. The part of your body closest to the center for e.g. your feet, will feel a stronger pull than your head, this will get more and more dramatic as you approach the center eventually tearing you apart.


Spaghettification

An object in a very strong gravitational field feels a tidal pull stretching it in the direction of the object generating the gravitational field. This causes the nearer parts of the streched object to feel a stronger pull than the others. When tidal force is strong enough to deform and tear apart atoms and other particals it is called spaghettification. Spaghettification starts with an object breaking into 2 separate pieces, then those 2 pieces breaking into 4 separate pieces, then 8, 16, 32 ect. This will continue until the object is a cloud of separate elements, this stage is right before singularity.


Singularity

Singularity is in your future and there is no possible way to change that. You will already have been torn apart before reaching singularity.

As an object approaches singularity tidal forces reach infinite meaning they tear the object apart with infinite power. All atoms and components that make up the object are torn away from each other before reaching the singularity. What happens when the singularity itself is reached is currently unknown.


What does it look like when heading into a black hole?


Outside the event horizon

Everything looks the same and the event horizon will not be visible for light that travels into the black hole can never return and be processed by your eyes.


Inside the event horizon

Nothing particularly interesting can be seen; objects in the distance may be distorted because the black holes gravity bends the light (much the same as looking at your finger through water or a glass cup).


Singularity

The singularity is not visible until you hit it and someone observing from a distance of even 1cm away would not see it due to gravitational time dilation. Although you wouldn’t live long enough to reach singularity.


What would an observer from outside the horizon see as you fell into it?

From the observers view the closer you get to the event horizon the slower and slower you appear to be moving and eventually to will appear to be frozen and not moving anywhere, the observer will never see you cross the horizon. Why?

The observer is witnessing an optical illusion, and its simple, simply the light that you emit takes longer and longer to reach the observers eyes the closer you get to the horizon so you appear to move slower. The second you pass the horizon it will appear to the observer that you’re are frozen, this is because the photons (light) and other radiation you emit just after you cross the event horizon will not escape and will never return to the observer because all paths in space time from that location lead into the black hole (refer to paragraph 1 and 3 of the Black Holes Introduction section), so the observer will see the last photons you released and you will appear frozen.

Also time slows down the nearer you get to the horizon so if you hover just outside the horizon for an hour and then rejoin the observer, who is watching from outside the gravitational field, will have aged a lot more than you.


Black hole sizes

Black holes are classified according to their mass and size, which is determined by the radius of the event horizon.

Astronomical unit (au) = 149,597,870.691 km
Au = distance from the Earth to the Sun
Solar mass = mass of our sun (about 2 nonillion kg)
(Nonillion =1,000,000,000,000,000,000,000,000,000,000) (10 to the power of 30 )


Supermassive black hole

Mass - ~100, 000 – 1,000,000,000 solar masses
Size - ~0.001 – 10 astronomical units


Intermediate-mass black hole

Mass - ~1000 – 999,999,999 solar masses
Size - ~0.000006685 astronomical units


Stellar-mass black hole

Mass - ~10 – 9,999 solar masses
Size - ~0.000000201astronomical units


Primordial black hole

Mass - ~Moon
Size - as small as 1mm


Meanings for Singularity, Event horizon and Gravitational Time Dilation


Singularity Explained

In the center of a spherical black hole there is a region where all of its mass is concentrated into a region with no volume making its density infinite, this is called a gravitation singularity.

Singularity is a point in the center of a black hole with no length, height or width. Singularity signals the breakdown of the general relativity theory.


Event Horizon Explained

The event horizon marks the point in a black holes gravitational field where after crossing over is impossible to cross back over to the other side. The event horizon is not solid nor is it any different from the rest of space; it is merely an invisible line surrounding a black hole such as Earths equator.

Anything having crossed the event horizon an object can never return to the other side because all available paths in spacetime are pointing towards singularity. Gravitational pull outside the event horizon is no different to that of an object of the same mass.

Someone looking into the black hole would see nothing because the light from inside the event horizon cannot cross it.


Gravitational time dilation

Gravitational time dilation is the effect of time passing at different rates in areas of different gravitational potential. The higher the distortion of spacetime the slower time will pass. Spacetime is distorted and tilted towards large masses in concentrated areas.

In other words time will travel slightly faster on Earth than on Jupiter. Time even travels slightly faster for a person in a merry-go-round than it does for someone standing still however this can only be a matter of mere nano seconds or less. This happens because spinning objects also create gravitational time dilation.


Ergosphere

The ergosphere is a region of spacetime where it is impossible to stand still. This is caused by frame dragging in this case the black holes ergosphere is dragging spacetime along in the direction the black hole is spinning.

An object in the ergosphere would get dragged around with the spacetime with the black holes rotation. In the ergosphere spacetime is moving faster than the speed of light (nothing is aloud to move faster than light accept spacetime itself) and to stand still the object would have to move faster than the speed of light in the opposite direction of the rotation.


Black holes are no more powerful than ordinary stars

Black holes don’t have stronger gravitational pull than normal stars and planets of the same mass. For example if our sun collapsed into a black hole (which would never happen because the sun is too small) the black holes center of mass would be in an extremely smaller area than the sun (possible only a few kilometers across) but would still have the exact same gravitational pull.

On the surface of the sun the escape velocity is 617.5 km/s and it is still quite possible to escape out of the gravitational field.

The power of a gravitational field is stronger the closer to the source and weaker the further away and since the suns mass is spread out in an area with a diameter of 1380000 km the gravitational fields strength wont be maximized.

However in the case of the sun collapsing into a black hole all of the mass will be concentrated into an area around 300,000 times smaller allowing objects to get far closer to the mass as a whole until a point where the gravitational pull is too strong for anything to escape (event horizon).


Forming and evaporation of a black hole


Forming from gravitational collapse

When an object or star for example has insufficient internal pressure to resist its own gravity it will collapse into itself inevitably turning into a black hole. This is usually because of a lack of fuel resulting in low temperature, which is related to the stars ability to withstand its gravity.

Also if a significantly sized star blows up in a supernova and leaves remnants of 3-4 or more solar masses they could still collapse into black holes.


Growth

Black holes can continue to grow in mass by absorbing interstellar dust and cosmic background radiation. Black holes formed in a binary star system can steal a lot of matter from its partner. Also black holes can gain a significant amount of mass from other stars and planets and perhaps another black hole. This is a likely explanation of how supermassive black holes are formed.


Evaporation

Black holes emit hawkings radiation, which will decrease its mass and makes it shrink. Large black holes emit less radiation then smaller black holes. Eventually the black hole will have fully evaporated and will disappear.


Super Luminal Speed

* Unfortunetly I am missing most of this section, I dont know why, so most of it wont make sence because it abruptly finishes. I will try to recover the last pages.

Suppose our sun died, where would we go? Alpha Centauri?

Even moving at the speed of light at 300,000 km/s it would still take us four years to get to the nearest star Alpha Centauri not to mention the extra year it would take to accelerate up to SOF and decelerate back down to normal speed.

This wouldn’t be so bad if the human race depended on it but lets not forget we don’t have technology nearly advanced enough to even think about travelling anywhere near the speed of light.

But lets suppose we had the technology to reach the speed of light and could we go any faster? The answer? Relativity says no, spacetime is constructed so that no matter can go faster than the speed of light.


What would happen if I approached the speed of light?

Ok first consider this:

I am in a car race against another driver and to make it fair we both have the same car and the same engine, they are both identical cars. The winner should come down to know has the better driving skills right? No I filled the trunk of his car with cement before the race. I win the race and my competitor runs out of petrol I also notice that I travel much faster down the straights than he does.

This is because his car weighs far more than mine therefore making him travel slower and burn up more energy trying to maintain a high speed in turn he ran out of petrol.

This shows us that the higher the mass of an object the more energy it needs to reach a certain speed, and to maintain that speed.

So to reach the highest possible speed minimum mass and maximum power for acceleration are required.

Now with that in mind consider this:

Special theory of relativity – As an object gains speed it gains mass
Lorentz contraction – As an object gains speed it shortens in the direction of its motion
Time dilation – As an object gains speed time slows down

* Missing from here onwards, sorry, trying to recover.

For now ill just add a brief outline of what what missing:

Basicly, the faster an object moves, the more mass it gains, the smaller it gets and the more energy it requires to continue being propelled. Moving faster than the speed of light (super-luminal speed) is impossible. As we approached the speed of light the objects mass would aproach infinite, the object would be infinitely small and the object would require an infinite amount of energy to continue at that speed.

That was just a brief outline of what I can remember.




Finally: If you honestly read this whole thing, you are a legend.

Bonk
08-17-2009, 07:12 AM
This is worse than cutting out the last few pages of a thriller

Nah, good effort. If only I could be bother reading it, there lies your challenge!

Cronos
08-17-2009, 07:16 AM
Haha thanks. I really cant see anyone reading the whole thing (accept me, obviously, since i made it). When I submitted this in science it never got returned. Science teacher probly took one look at it, and was like "**** that, too much effort!".

Too bad i never got the paper copy back, that would of had the missing pages...

Cool new sig by the way :3.

Rival
08-17-2009, 07:40 AM
If only I were English.. I'm dutch so I don't understand much of the terms you use. I read trough half of it but then I coulnd't understand certain stuff anymore.

Still, it's very well explained, and I already knew most of the theory, so I could follow most of it. Nicely done.

Cronos
08-17-2009, 07:52 AM
Thanks :3 You are only half a legend though.

Rival
08-17-2009, 08:01 AM
Oh noes >_< I RELLY wanted too bee epix.

MaxZ
08-17-2009, 12:42 PM
(nothing is aloud to move faster than light accept spacetime itself)

Badly written, spelling mistakes.

'As we approached the speed of light the objects mass would aproach infinite'

How can something approach infinite, infinite isn't a number. It can be an incomprehensibly large amount. But it can't be infinite.

I think...

Rival
08-17-2009, 01:43 PM
Thats a way to say it, for when you approach it, you are timeless.

Cronos
08-17-2009, 06:10 PM
Maxz: And that is exactly why the faster than the speed of light is impossible.

MaxZ
08-18-2009, 01:37 AM
: O

Cronos
08-18-2009, 01:44 AM
Accept other photons of coarse. Some types of light can move faster/slower.

Howcome your not active on GA anymore :3?

MaxZ
08-18-2009, 03:27 AM
Because I'm just back from France and I'm busy with other things. Like animating.

Rival
08-18-2009, 04:10 AM
You are? wow.