Sunday 30 March 2014

Something on Gravitational waves p1

Power Radiated by orbiting bodies:

As two or more bodies orbit each other, some amount of energy is released from the system via gravitational waves. This in turn causes an inspiral or decrease in orbit. So after losing all energy the two objects fall in too each other! This same is happening with the earth and sun system at a rate of 200W (I didnt bother to calculate this as it was done on Wikipedia ;) ) but as per wiki it will take 10^13 times the current age of universe for the earth to fall in and before that ever happens the sun will eat us in red giant phase(or will it...).

So in the formula of radiated power via G-waves we take two masses orbiting around each other $m_1,m_2$. For simplicity we can take standard keplarian orbits in x-y plane or in 2-D plane.
This is our formula: P = \frac{\mathrm{d}E}{\mathrm{d}t} = - \frac{32}{5}\, \frac{G^4}{c^5}\, \frac{(m_1m_2)^2 (m_1+m_2)}{r^5}
where $\frac{dE}{dt}$ is the derivative or rate of change of energy with respect to $t$.
$G$ is our gravitational constant and $G=6.673*10^{-11}m^3kg^{-1}s^{-2}$
$c$ is speed of light and $c=300000000m/s$
$r$ is the separation between the two orbiting bodies

(note: The answers will be minus because it is power lost!)

First of all I am going to make a 2-D graph in the x-y plane where y-axis will be $P$ and the x-axis will be $m_1$, we will take $r$ as to be constant, so we can take $r=1.5*10^11meters$. $m_2$ will also be constant and we can take that as earths mass so $m_2=6*10^{24}kg$

In this graph with mass $m_1$ ranging from $2*10^{30}kg$ to $3*10^{30}kg$ we can see that at mass $m_1=2*10^{30}kg$ and the contstant mass $m_2= 6*10^{24}kg$ or earths mass, the power lost by G-waves is 200W!!

If you notice that as $m_1$ increases with all other stuff constant then the power lost is increasing logarithamically as you can see in this graph:
you can see that at ten times the mass of sun how much the energy release by G-waves increase to 600,000W! Still not so much!
If we take two neutron stars with mass of sun at a distance of 2*10^8m away then see the graph as r increases or decreases.
This is a graph of Power radiated with respect to distance between objects. The mass is 1 Solar mass  for both objects and they are neutron stars. at $2*10^8m$ is about $10^{30}W!!!$ that means in a few days or months the stars would collide!
The graph might look flat or constant near 10^30W or as r increase but dont be fooled by that and look at the Power axis and see the scale ratio. the graph looks like this over their.
again dont be fooled that the power is gone positive, keep your eyes open and look at the axis,
it shows it in this way for understanding. 
And the graph will never go positive unless mass is negative!! which cant happen. 

Now we are going to see the graph with respect to two variables. First with $m_1$ and $m_2$;
hmmm, not such an interesting graph but it has a lot of info in it.
The vertical axis is the Power, the rest two axis are the masses of the two bodies, As you can see that as  $m_1$ which is the top horizontal axis increases along with $m_2$ increasing the power radiated is exponentially increasing and then it suddenly does a strange thing and becomes a fold!
again, not to be fooled it looks like this at that fold:
But again note that these graphs axis ratios are not the same, so the graph looks different a bit.
Now we shall look at a 3D graph of our neutron star case. here the x and z axis will have equal rates of change( or axis ratio ). taking again with respect to $m_1$ and $m_2$:

basically its the same thing :(

Now taking the graph with respect to $m_1$ and $r$:
BTW: no this is not a waterfall model but it can be (Moral: different formulas make different real world models!)
Now that is interesting :)! This time I added some colour to show the heights in it.
As you can see another fold in these graphs too!! In the colour coded graph we can clearly see grey for the fold, so ill call it a well!(The water one)
The graph will be similar for neutron star case.


, so $$  
. we will take this as simple keplarian orbit in x-y or 2-D space.

Sunday 2 March 2014

History repeats itself, my speech

Think about it, “Does history repeat itself?”                                   
History most certainly does repeat itself, or you can say, “It rhymes with the future. “. It's all based on power & money.  
You will notice when you Look at History. Germany was depressed financially during the 1930's. It took but one man (Hitler) to have millions of people look the other way while millions were murdered. Same for the killing of many scientists, they all were killed for opposing the laws of the church, people were in a way enraged against them in the blame that they were opposing religion, religion was used in history again and again by the people who used it for their own vested interests.
People will never learn, they will always be hostage to their extremist ideas they will always oppose science and technology in the name of religion.
I always ponder and feel so sad when I read the history. Pythagoras, a great mathematician of Greece, who gave us the well known Pythagorean Theorem. His ideas were rejected by extremists in Greece who later manipulated people, which led to his killing by an angry mob, a great mind wasted. But this didn’t stop and over the years history kept repeating itself. Centuries later Boltzmann suffered the same fate as his theories and ideas were ridiculed and mocked so much that he went into extreme depression which later forced him to take his own life.
It was after his death did people realize that his theories were correct, yet another waste of a brilliant mind.
History keeps repeating itself since it is human nature. Humans will forever make mistakes, out of jealousy, out of intolerance and lack of knowledge.  We just can't help ourselves.
Greed will always poison man’s soul, as it did it in the past, we will always be locked up in the abyss of hate. We have acquired technology and knowledge over the years but it did it not change us, instead it made us more cynical and unkind.
 Wars will always happen because not everyone is the same, and people have their own opinions on things. I find it funny that people think history doesn't repeat. Why is it that no matter how many times we're told not to do something, and we do it anyways? Because it's human nature.
I do not have the power to single-handedly change history. But I will be a public voice saying “No!” when I see these sorts of things transpiring, when I see signs of history repeating itself. And thanks to today's technology, each voice can be heard not only in its own location, but around the world.
Do not be among those who stand quietly by. Let your voice be heard.