Proof that Gravitational Constant is not constant

So as these celestial bodies approached each other they would have originally been losing gravitational potential energy at the Universal Gravitational Constant rate, so it builds up a debt of negative energy. I propose that this negative energy has to be repaid when and if G of the binary (Gb) declines. Changing the G from 6.67384E-11 to 6.6721E-11 (Gb) will take a considerable amount of energy. Where does this energy come from?

 

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Hi AlexG.

Two things.

(1) This is "alternative theory" section which allows much latitude that is not allowed in the main Physics/Maths section; and...

(2) Robbity is doing no more than what arfa brane is doing in the main Physics/Maths section with his monologue "Cube Symmetry" exploration of his own ideas.

Why troll and criticize Robbity in this section when, by your same stated 'criterion', you should be more appropriately admonishing another in the main section? Personal bias and expedient double standards?

Just a relevant observation in the interests of fair play (I am assuming you know what "fair play" means).



Now to the topic:

Robbitybob1, since the increased speed of the closer orbits implies increased translational energy content overall of the respective bodies involved, then the increased energy content will increase gravitational effect between them at each successively smaller orbit, won't it? So any gravitational energy radiated away in order to reduce orbital altitude would result in energy gained by the overall system. Would this balance out? Is any gravitational energy radiated away, or is it only transformed into the additional speed/energy in closer orbits such that no net gravitational energy is lost from the system to remote locations across space? Sorry, that's all the time I have to speculate/comment on your topic/exploration on this.

Cheers!

 

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I know the thread is getting longer but I do feel we are getting closer to a resolution.
reasons I believe this is we have established the sum of the binary semi major axis'
we have established the semi major axis of the pulsar and its companion.
From its period we can determine how strong G is in the region.
And from these both and the fact that the orbital period changes by 67.5 microseconds per year we can calculate how much the sum of the binary semi major axis shortens by every year.
Accepting that G declines in systems that radiate gravity waves may be the answer to the next bit, for the dr/dt formula for gravitational radiation goes nowhere close to allowing for such a massive movement as is calculated in the orbital decay.
I'll get figures for this over the next few days, but this is confusing for it is roughly saying Hulse and Taylor should not have got their Nobel prize! So I am looking for a way so that we both still can be right. How can the the sum of the binary semi major axis shortens by 3.56 meters per year yet only move .29 meters/year (or so) from Gravitational radiation? and yet still be able to say "the only reason the orbit is decaying is due to energy and momentum loss through gravitational radiation"?????

It is going to be a difficult question to answer. I would like help if anyone cares to explore an interesting bit of science.
RC I will answer your questions too in the process. (All figures in this post are just from memory, don't treat them as accurate.)

 

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No problem, mate, in your own time. Good luck. Cheers.

 

"since the increased speed of the closer orbits implies increased translational energy content overall of the respective bodies involved, then the increased energy content will increase gravitational effect between them at each successively smaller orbit, won't it?"
I would stick to the convention that the gravitational force is inversely proportional to the distance between the bodies. And as you say the translational energy also rises. I'd tend to call this kinetic energy.

"So any gravitational energy radiated away in order to reduce orbital altitude would result in energy gained by the overall system. Would this balance out?" Energy lost is energy lost and it can't be recovered in any easy way. Gravitational potential energy is lost as the objects get closer together but for every meter drop there is exactly twice as much energy released as there needs for the extra kinetic energy to maintain an orbit. It won't fall unless energy is lost, but why gravitational radiation only accounts for a fraction of the released energy is the quest ahead. I can see it could be used to repay the negative GPE by reducing the strength of gravity between the bodies. What else can it do?
"Is any gravitational energy radiated away, or is it only transformed into the additional speed/energy in closer orbits such that no net gravitational energy is lost from the system to remote locations across space?" Gravity radiation is lost but only accounts for something like 1/11th of the available energy.
This means it might be possible to propose an amount or rate of change of G and we may see if the energy repayment accounts for the balance of the energy. Early days though.

 

Looking at "Orbital lifetime limits from gravitational radiation" http://en.wikipedia.org/wiki/Gravitational_wave plugging in the parameters G = 6.6721E-11
and the distance between the stars as 1949138400 meters the initial amount of movement attributable to Gravitational radiation = 0.29776 meters so the lifetime of the Binary would be 1,636,501,183 years. But from the change in orbital period of 76.5 milliseconds the change in distance between the stars = 3.56 m/year.
This magnitude of orbital decay is the more commonly reported one so the change in orbital distances can't be solely due to gravitational radiation.
The energy released from the loss of Gravitational potential energy is proportional to change in height (mgh) so 3.56/0.2823
= 12.607 so as I said before the gravitational radiation accounts for about 1/11th of the energy change and more accurately 1/12.607 of it using the different distance and strength of G.
Would anyone be interested in running and checking the Excel Macros with which these calculations have been done on. I can't write the equations as Tex (sorry).

 

You can quickly see there is a problem with the analysis as the movement per year has been calculated at 3.56 m/y and the distance between the stars is only an average of 1949138400 meters so even without looking at how the rate increases as they get closer, they will be touching in 534,010,520 years. So why is there so much confidence that gravitational radiation is the only thing removing orbital energy? Note the gravitational energy orbital lifetime formula says the binary will last for 1,636,501,183 years but that can't be so for it is collapsing at a rate way beyond that already.
PSR B1913+16 ["The system is also called the Hulse–Taylor binary pulsar after its discoverers."]
http://en.wikipedia.org/wiki/PSR_B1913+16

 

Can we look at how much the gravitational potential energy debt has been built up during the life of the binary. OK I haven't done or seen this type of analysis been done for a star system, so if anyone has a method or points of view please join in.
We will need to start with the position of the two masses at infinity. This seems bizarre as that is before the stars even formed and they have obviously gone through many changes over their lifetime and I wouldn't set myself as an expert on this, but despite all this we will just consider the mass of the stars as they are today and consider that residual masses as if they came in from infinity to end up in the position they are today.

 

gravitational potential energy U = -G*m1*M2/r + K, K by convention = 0. We will use the sum of the semi major axes as the average distance the stars are apart as r.
So work off r = 1949138400. Ok we should look at the GPE, U at normal G and then Ub at Gb (G for the binary) and see what sort of energy difference that is.
-2.708480280E+41 = U
-2.707787266E+41 = Ub
6.93014E+37 = Ub - U

So it is fair to say 6.93014E+37 Joules of energy have been repaid back to the negative GPE and the only source of energy the stars have is their Gravitational potential so one can see that to pay this back as the Gb continues to decline it would be easy to utilize the surplus energy to repay the debt. The debt is repaid when the gravitational attraction between the bodies declines. So something happens! What happens to make the gravitational attraction between the bodies decline? It is linked to Gravity waves obviously for it is not an everyday thing to lose gravitational attraction.

 

What we could do now is to look at the amount energy released as gravitational energy over the lifetime of the binary. I have seen how the rate of gravitational energy (GRN) release drops off quickly as the distance between the bodies increases.
The equation that we'll use is the one dE/dt = (32 / 5)*(GB^4 / c^5) * (m1 * m2)^2 *(m1 + m2)/r^5

See how the power released varies to inverse of the fifth power of "r" so if we run a macro backwards in time we should be able to find an "r" where the change in power is negligible.
I'll post this now and get back when i have run the macro.
At 57,983 times the current sum of semi major axis (r = 1.13017E+14 m) the amount of power radiated from GRN is below 1 Watt. Well I can guarantee that to come in from that distance would take millions of lifetimes of the Universe, so gravitational radiation is not the reason the masses of the stars came close together in the first place. The nebula that contracted to form the binary must have had two centres of density.

 

I think we should just look at the more recent history of the binary, say go back to when "r" is twice the current, and compare the amount of energy lost through GRN as compared to the loss of GPE over that distance.

 

Trying to get an idea of how the binary system formed and came across this passage

BINARY PULSARS AND RELATIVISTIC GRAVITY J Taylor http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/taylor-lecture.pdf

If I understand that correctly he says one star forms the other. That would seem in the first place to be very difficult.

 

Theories of the Birth of Binary Stars
http://www.astrophysicsspectator.com/topics/stars/BinaryStarBirth.html
has a understandable look at the four ways binary systems might form. The method expounded by J Taylor would be a fifth version "Their large orbital eccentricities are almost certainly the result of rapid ejection of mass in the supernova explosion creating the second neutron star." In fact I can't even begin to see how this would work!

 

That suggestion is just too stupid to contemplate really. For where would the orbital motion come from in that case? You could imagine if for any reason the debris clumped, it might just fall straight back down. Well when did this all happen and has there been enough time?

 

to get to the situation where there is a pulsar orbiting with a neutron star companion, there must be a real history of massive changes that have worked in unison which has allowed them to remain together. All this is a little too complex for me at this stage. I think there has been some estimate of the age of the binary, but where is it?

 

Maybe he didn't really mean creating, but more like "leading to"? "Result of rapid ejection of mass" in the supernova explosion (creating) "leading to" the supernova prior to "the second neutron star".

 

I would think J Taylor was of the opinion the stars were and have been a binary since their creation. What I find amazing is that one star can go through a supernova event and still maintain the binary. If the weight was more than halved it would have a such a reduction of gravitational attraction, that this would be like halving G. Wasn't one former argument proposed that if the force between two orbital bodies fell by more than half they would have gained their escape velocity and hence they would separate from each other ("fly apart")?

 

the formula for orbital speed and escape velocity are very similar and one has a value of twice the other.
Escape velocity = sqrt(2GM/r) whereas orbital speed = sqrt(GM/r), so I can see if the mass M which a star is in binary orbit with should halve instantaneously the orbital speed equals the escape velocity.
With a supernova I understand there is an enormous explosion and a lot of mass is exploded outward, but for a long time as the material shoots outward, the entire mass of the star is still acting through a centre of mass. Once the mass extends out far enough a lot of matter will be picked up by the gravity of the companion and the companion will be crashing through the debris and this will have an enormous slowing effect, so it is possible on the surface that a binary star system could survive a supernova of one of the stars.

The above was just the first attempt of understanding the process.

 

So then if one of the two stars lose a lot of mass the orbital of the "lighter" one will affected by the increased mass of it companion. It will have insufficient speed even though it will be lighter. The mass of itself doesn't come into orbital speed or escape velocity. So it will fall, but will it follow the "heavier" star?
At least I'm over my immediate fear that a supernova must cause a disruption of the binary.

 

Since it becomes extremely difficult to detail the binary's past let's just look at just the movement over the last billion years or so. How much further apart would they be?
We have a dr/dt formula that details the movement from gravitational radiation but this seems to account for 1/12 of the current movement. There is the dE/dt formula and if the movement has been calculated correctly it to underestimates the energy changes. I think the energy lost per meter lost from GRN is about right.
From the orbital lifetime formula we could look at what the distance was in the past, but surely this underestimated.
But Weisberg and Taylor calculated that the power loss from GRN perfectly matched the orbital period change??? I must still be on the wrong track.