Re: Flaw in Stowe/LeSage Heating

From: Paul Stowe (ps_at_acompletelyjunkaddress.net)
Date: 03/01/05 

Date: Tue, 01 Mar 2005 15:15:58 GMT

On 1 Mar 2005 06:11:20 -0800, "TC" <tclarke@ist.ucf.edu> wrote:

>Bilge wrote:
>> TC:
>>> I was looking at Paul Stowe's
>>> "An Overview of the Concept of Attenuation [Pushing] Gravity"
>>> http://www.mountainman.com.au/index_ps.htm
>
>>> He derives from the LeSage theory that the heat output
>>> of a body resulting from gravity should be
>>> q = kM/R where k is a constant, M the mass and R the radius
>>> of the body.
>
> Stowe has clarified that q is heat flux/unit area, not total
> heat flux as I had misread.
>
>>> It occured to me to ask what the temperature of a laboratory
>>> scale body would be from this mechanism
>
> It seems that there will be a small effect using Stowe's formulas.
> A 1 meter radius sphere of iron would have a minimum temperature
> of 0.19K absent other heating or cooling.

 Ummm, 0.019 °K but, OK...

> But I remain troubled. Stowe's formulas just do not ring true
> for me. The energy flux/area is proportional to M/r which in
> gravitational context is escape velocity/potential when multiplied
> by proper constant, a property of the whole body, not of a
> differential area of the body.

 Indeed. An analogous example, you have a distributed radioactive
 gas such that there existing in space a gamma flux of q'/z (where
 q' is the source term in energy per unit volume & z the linear
 attenuation coefficient in inverse meters) and an embedded piece
 of spherical matter (a gamma ray attenuator) such that its radius
 [r] yields a a total mean free path of 2zr of 0.0001. Thus,
 the attenuating of gammas passing thru the sphere deposits energy
 into the sphere. This is, for a 2zr of 0.0001, a uniform process
 affecting every volume element equally. This is called (and known
 in the trade) as the weak solution. Mathematically the weak
 solution is when the condition,

                         e^-zt = 1 - zt

 For a situation where the above condition is not met, the energy is
 dopsited in an exponential manner with the most in the first mean
 free path. In the case of LeSagian gravity, as have been formally
 proven, Newton's equation IS the weak solution to this problem.

> I also wonder where the original data for table in
> http://www.mountainman.com.au/news99_b.htm comes from.

 That data is readily available.

> Also in http://www.mountainman.com.au/le_sage.htm
> "Derivation of Newtonian Gravitation from LeSage's Attenuation Concept"
> The derivation of the the expression for energy input is not given
> "Big step here derivation not shown!" Is the derivation available
> anywhere?
> In the book "Pushing Gravity"?

 Look just above that section. You'll find,

                      f_d = f_in[2GM/c^2r_o]

 Where f is power flux (watts/m^2) and the other terms are as
 expected. Then f_d is the corresponding observed power emission
 and f_in the LeSagian full field input value. You don't have
 either of these thus you say, IF the equation is true and we have
 a good measured value for f_d we can solve for f_in. I originally
 used the Earth's value since it is very well known. I dicovered
 however that a body as big, and as poor a thermal conductor as the
 Earth requires ~25 Billon years to reach a thermal equilibrium
 state. Thus, I then used data from the Moon (taken in the Apollo
 heat flow experiments) ~0.01. This gives a f_in of ~1.6E+08. Then
 k is,

                          k = (2G/c^2)f_in

 Now, you can instead use Jupiter and get the same basic value.
 We switched to Jupiter for the normalizer in our piublished paper
 since its values is better sustantiated that just two measurements
 from Moon.

 Now, once you have this, you ask the next question, does it match
 others. Thus the table. Now to your specific question, the answer
 is no, I abandoned this soon after I posted that piece. Dimensionally
 it is correct (assuming q has dimensions of kg/sec) and numerically
 it matches. But, I never was able to fully derive it since a piece
 of the puzzle is still missing. I thought it 'cool' enough to
 mention, in hopes that someone else might get it.

> Also Bilge supplies:
>
>> http://www.mathpages.com/home/kmath131/kmath131.htm
>
> Which derives very different conclusions from the LeSage model at
> great odds with Stowe's results.
>
> Has Stowe ever refuted these arguments?

 See "Pushing Gravity". It DOES address several of these issues (and
 not just our papers). Also Barry went to a significant effort to
 address the in the following series.

http://groups-beta.google.com/group/sci.physics.relativity/browse_frm/thread/1afcda5a7882c43/b437f7783528c72f?q=%22LeSage+Shadows%22&_done=%2Fgroups%3Fas_q%3D%26num%3D100%26scoring%3Dd%26hl%3Den%26ie%3DUTF-8%26as_epq%3DLeSage+Shadows%26as_oq%3D%26as_eq%3D%26as_ugroup%3D%26as_usubject%3D%26as_uauthors%3D%26lr%3D%26as_drrb%3Dq%26as_qdr%3D%26as_mind%3D1%26as_minm%3D1%26as_miny%3D1981%26as_maxd%3D1%26as_maxm%3D3%26as_maxy%3D2005%26safe%3Doff%26&_doneTitle=Back+to+Search&&d#b437f7783528c72f

 Shadow, a.k.a. Bilge just blew smoke in response...

 Paul Stowe

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