Change in angular velocity of the following system

[Dale]

Do gravitational waves emit from symmetric bodies rotating around an axis of symmetry?

No, you need at least a changing quadrupole moment.

 

[Matt Benesi]

So it seems like you and mfb are saying there wouldn't be GWs.

How much does frame dragging contribute when the system is isolated or far enough away from other massive bodies (so there isn't reciprocal torque)?

 

[mfb]

How much does frame dragging contribute to what?

Your questions are unclear.

 

[Dale]

So it seems like you and mfb are saying there wouldn't be GWs

This scenario is not an axisymmeteic body rotating about its axis of symmetry.

I can't speak for mfb, but I am not certain if there would be GWs or not.

 

[Matt Benesi]

K. On frame dragging: I'm under the impression that an external object has to be orbiting or close to the system for torque to be applied to the system (reduction or increase in angular momentum due to frame dragging).

I rewrote the code (still looking at the math side of the problem- fixed a couple angle errors which resulted in skewed values when I made a generalized function for rings with any number of objects greater than 1).

I noticed a neat mathematical property of ring acceleration increase when increasing # of bodies while using the same total mass. I restricted the mass of all bodies on the ring to 1 gram, divided between the bodies. 2 body/3 body ratio ~ 3/10; 3 body/4 body ration ~ 10/21; 4 body/5 body ratio ~21/36...

Sticks pretty close to those ratios, even with ring velocity getting really close to c. Obviously there is a mathematical explanation for 2n^2+n turning up...


fiterall is the function. usage in WxMaxima is:

fiterall(r,v,mass,number,iter,skippy)$

r= radius of body ring
v= tangential velocity of ring in direction of rotation
mass= total mass of point bodies
number= number of point bodies
iter= # of iterations to perform the homing function** set it>300 for accuracy
skippy= number of iterations between displaying iteration number (set for >444 to avoid notifications)

**each iteration of the homing function reduces error in position
of acceleration sourcefpprec:128$fpprintprec:32$
fiterall(r,v,mass,number,iter,skippy):=[
pi:bfloat(%pi),mpb:mass/number,
c:299792458b0*100b0,
t:v/(2b0*r*pi*2b0),
array(times,number),
k:1,
for k thru (number-1) do [
i:1,angle:k*pi/number,
ss:2b0*r*sin(angle)/c,zz: r*2b0*sin(angle-ss*t)-c*s,
steppy:ss*.1b0,
for i thru iter do[zold:abs(zz),
if (zz>0b0) then [ss:ss+steppy] else [ss:ss-steppy],

zz: r*2b0*sin(angle-ss*t)-c*ss,
if (abs(zz)>zold) then steppy:steppy/2b0,
if integerp(i/skippy) then disp(sconcat(" iterations: ",(i)))],

disp(sconcat(" Time #", k, " (from perfect time): ", float(zz))),
times[k]:ss
],

acctotal[number]:0b0,
array(acc,number),
k:1,
for k thru (number-1) do [
sr:times[k]*c,
accpart:(sqrt(sr/(sr-2b0*mpb*6.67408b-14/c^2b0))
*mpb*6.67408b-14*(100b0/sr)^2b0),
acc[k]:accpart*sin(t*times[k]+(pi/2-pi/number*k)),


acctotal[number]:(number)*acc[k]+acctotal[number],
disp(sconcat (" Acceleration#",k,": ",float(accpart))),
disp(sconcat (" Tangential Acc#",k,": ",float(acc[k])))

],

disp(" "),

disp(sconcat(" angular acc: ", float(acctotal[number]))),
disp(sconcat(" ang acc per mass: ", float(acctotal[number]/(mass)))),
disp(" ")

]$

 

[Dale]

still looking at the math side of the problem

The math side of the problem starts with using a consistent theory of gravity. This approach is fundamentally wrong. You need a field theory to make it relativistic and it needs to be a tensor field to be consistent.

 

[Matt Benesi]

It looks like you're saying that non-tensorial line element solutions (Schwarzschild and Kerr), which are the only actual confirmations of GR, are not good enough.

 

[Dale]

It looks like you're saying

I never said anything remotely similar.

non-tensorial line element solutions (Schwarzschild and Kerr),

Those are both tensor solutions.

which are the only actual confirmations of GR

This isn't true either.

Please stop posting misinformation about physics and please don't misrepresent my comments.

 

[Matt Benesi]

I found a solution for angular momentum loss due to gravitational waves for 2 bodies. Since I rewrote the math to include #s of bodies other than 4, I can apply the relativistic angular momentum loss equation to the 2 body problem (although a 4 body problem is still a problem).

I'll let you know how it turns out.

So much for that. It's over 10^-70 too small to account for the angular acceleration, unless I totally coded it wrong.