Wednesday, 23 April 2014

Something on G-waves p2

Orbital Decay from Gravitational Radiation:

(Note: Remember those folds forming in the graph in Part one? Well those showed continuity...No strange effect in that...)

In part 2 we will use Power Radiated, which we found in Part one to find the rate of decrease of Orbit Radius with respect to time. In other words we will find $\frac{dr}{dt}$, the derivative or rate of change.
The formula for finding this stuff is \frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ .
The orbit decays at a rate proportional to the inverse third power of the radius. 
The variables are same as in part 1.
Well Im going to take $r=1.5*10^{11}m$ and $m2=6*10^{24}kg$ and $m1$ is our variable from $2*10^{29} \text{  to  } 3*10^{30}kg $:
A similar graph like in part 1. The unit for orbital decay is m/s. Earth with our sun is $1.1*10^{-20}m/s$ . 

Now lets take our 2 solar mass Neutron stars and plot their orbit decay with Radius as our variable:
So as the orbit radius decreases the decay increases exponentially.
Now for 3D:
We are going to only take our Neutron star case as graphs are similar.
So with relation to $m1,m2$ the graph is:
and for $m1,r$: