MarkBour wrote:neufer wrote: . . .

- 1) Time to the first power

2) Mass squared

3) Frequency cubed and

4) Size to the fourth power.

. . .

Not to quibble, but would it be better to say "size to the

*negative* fourth power" ?

Actually, I have made an error

It should read:

- 1) Time to the first power

2) Mass squared

3) Size to the fourth power and

4) Frequency to the FIFTH power

The

**strong sensitivity to frequency** dominates in a binary gravitational situations such a merging black holes since Kepler tells us that Frequency = "size to the

*negative* 3/2 power"

Allowing for this effect the graviton production = "size to the

*negative* 7/2 power" [= 4 - 5x(3/2)]

and the power P = "size to the

*negative* 5 power" as in the Wikipedia formula below.

(Note that each graviton has an increasing quantum energy = "size to the

*negative* 3/2 power")

https://en.wikipedia.org/wiki/Gravitational_wave wrote:
<<Suppose that [two orbiting masses] are m

_{1} and m

_{2}, and they are separated by a distance r. The power given off (radiated) by this system is:

where G is the gravitational constant, c is the speed of light in vacuum and where the negative sign means that power is being given off by the system, rather than received. For a system like the Sun and Earth, r is about 1.5×10

^{11} m and m

_{1} and m

_{2} are about 2×10

^{30} and 6×10

^{24} kg respectively. In this case, the power is about 200 watts.>>

- So the Sun / Earth system radiates only about 200 watts or ~9.5x10
^{42} gravitons per second.

But what if we substituted a

**full sized orrery model** with a Sun & Earth of masses 2000 kg & 6 g respectively?

-----------------------------------------------------------------------------------------

The power depends upon the masses squared and the masses have dropped by a factor of 10

^{27}; hence the radiation drops by a factor of 10

^{54} resulting in a radiation of ~9.5x10

^{-12} gravitons per second or 3x10

^{-4} gravitons per year.

-----------------------------------------------------------------------------------------

Things get even worse if we make the orrery a

more feasible (1 AU => 150 m) size since gravitational radiation depends upon distances to the fourth power! Now our realistic yearly orrery puts out just 3x10

^{-32} gravitons per year. Clearly there is not enough time in the life of the universe for our realistic yearly orrery model to emit even a single graviton.

-----------------------------------------------------------------------------------------

Now what if we speed our realistic orrery model up to make an orbit in just one second? Now radiation depends upon frequency to the sixth power whereas graviton energy (= hv) only depends upon frequency to the first power such that graviton production increases as frequency to the fifth power.

Our **realistic very fast orrery** now puts out ~12 gravitons per hour.
-----------------------------------------------------------------------------------------

Hence...I concede that humans with masses 10

^{4} larger than the orrery's 6 g "Earth" (the main generator) but sizes 10

^{2} smaller than the orrery are capable of generating a few gravitons per hour on a good day.

However, heart pumping with blood masses 10

^{3} smaller and sizes 10

^{1} smaller will require 10

^{10} hours to produce a single graviton.