Originally Posted by Lunatik

PLANETARY SPIN RATIOS PER AXIOMATIC EQUATIONS AS A FUNCTION OF OF VARIABLE E & G:

Taking planetary black-body heat in Kelvin and planet's orbit Energy, per Axiomatic, we can arrive at a spin ratio, SR, which will yield each planet's spin as measured in earth days. The resulting equation is:

(PK/PE) :/: (13.36E-16) x (PK/231.7K) :/: (planetary orbit/365) :/: (planet spin) x (AU)^1/2 = SR

where:
SR = Spin Ratio for planets
PK = Planet Kelvin, black-body heat
PE = Planet orbit solar Energy, per Axiomatic
VK = Venus Kelvin, base planet spin (245 days retro spin, per 244 days orbit), here as base spin "zero" (where Kelvin and Energy nearly equal)
VE = Venus Energy, per Axiomatic
planetary orbit = in Earth days
planet spin = in Earth days (or fraction of Earth day)
AU = G'/G, ratio of planet's G' and Earth's G, linear deltaG = ~7.2E-11 per AU
(AU)^1/2 = same as square root of (G'/G)
Spin Ratio = SR, a Kelvin and Energy dependent number, which when Earth's SR (2.32) is divided by planet's SR yields daily planet spin.
x = times
:/: = divided by
VK/VE = (2.317K/17.33E+16 J) = 13.36E-16 , which is a ratio, used in SR equation above, as a base for Venus (near zero) parity.

The above equation for Earth yields:

(254.3K/9E+16J) :/: (13.36E-16) x (254.3K/231.7K) :/: (365/365) :/: (1) x (1) = 2.32

Tables of above values, where orbit and spin are in Earth days, and SR is as calculated per equation above:

AU; PLANET; P-KELVIN; P-ENERGY; ORBIT; SPIN; (AU)^1/2; SPIN RATIO

0.39 ; Mercury; 442K ; 60.55E16 J; 88 days; 58.8 ; 0.624 ; 0.0456
0.72 ; Venus ; 231.7K ; 17.33E16 J; 245 ; -244 ; 0.850 ; 0.005 (this is is way off - retro) ?
1.0 ; EArth ; 254,3K ; 9E16 J ; 365 days; -1- ; 1 ; 2.32 (base SR)
1.5 ; Mars ; 210.1K ; 3.86E16 J; 687 ; 1.03 ; 1.225 ; 2.246
5.2 ; Jupiter ; 110K ; 0.335E16 J; 4329 ; 0.415 ; 2.28 ; 5.41
9.5 ; Saturn ; 81.1 K; 0.1004E16J; 10753 ; 0.455 ; 3.08 ; 4.97
19.2; Uranus ; 58.1K ; 0.024E16J; 30660 ; 0.718 ; 4.38 ; 3.21
30 ; Neptune ; 46.6K ; 0.01E16J ; 60225 ; 0.673 ; 5.48 ; 3.69
39.5 ; Pluto ; ~37.5K ; 0.006E16J ; 90520 ; 6.3 ; 6.28 ; 0.304

Divide Earth's SR = 2.32 (which is our1 day spin) by any of the above planetary SR's, and you will find a close match to actual spin in Earth days. Here's the lineup:

Merc: 2.32/0.0456 = ~51 (vs. actual 58.8 )
Ven: 2.32/ 0.005 = ~464 (way off by ~x2! vs. actual -245)?
Ear: 2.32/2.32 = 1 day (our home planet's spin)
Mar: 2.32/ 2.246 = ~1.033 (vs. 1.03 actual)
Jup: 2.32/ 5.41 = ~0.428 (vs. 0.415 actual)
Sat: 2.32/ 4.97 = ~0.467 (vs. 0.455 actual)
Uran: 2.32/3.21 = ~0.723 (vs. 0.718 actual)
Nept: 2.32/ 3.69 = ~0.629 (vs. 0.673 actual)
Plut: 2.32/ 0.304 = ~7.63 (vs. 6.3 actual) ?

You can see from the above that Venus is way out of line (it has retro spin) and Pluto are off by more than 20%, Mercury is off by 12%, but the other planets are a fairly close fit. Consering I am working with rough estimates, taken from Nasa Planet tables, and used mean distances for the planets, the spin ratios as a function of planetary heat and orbit Energy come in fairly close to actual spin.

Coincidence? Numerology? Handwaving? Woowoo? Against the Mainstream? Some will think it odd, others will dislike intensely, or not believe it, and call it gibberish. Fine error? Gross error? But these are the numbers as they work out. They clearly show that there seems to be a relationship between planetary interior heat and the Energy levels in which their orbits reside, factoring in a variable G, as per the equation above. I think it interesting enough to think about some more, maybe get better K numbers, especially Mercury and Pluto, and work it out with better orbital numbers. New physics? Maybe... I am sure "careful eyes will be narrowly watching"...

Does this prove the Axiomatic Equation? Not to my mind. But it offers one more reason to go out there and look for a variable Newton's G 'proportional'. What say you now? Hogwash? I'll be curious to see your reactions. I suggest we start a different thread, since this one's run pretty deep already. This above is not a formal paper, which I will write at another time with full explanations.


Sorry guys, you won't find any of this in any textbook, it's a BABB first!

[Edited to fix Venus orbit & spin days.]

Originally Posted by Fram

I have given my comments so far in the erratically named 'Potential threat' thread.
Basically, from a mathematical point of view the equation is way too complicated (you don't need PK, for example, and the need for all the constants isn't clear either), and from a logical point of view, you use spin in the equation and you use the result of the equation to calculate spin again.

Originally Posted by Fram

A third criticism, that I haven't posted there: how can your result (spin ratio) for Venus be positive, if one of the elements you are multiplying with is negative? Perhaps you better check the equation and all the calculations, and come back again then...

Originally Posted by Lunatik

This is all based on an assumption that interior heat energy somehow drives planetary spin, though we do not understand why it should. So planetary spin is not merely conserved angular momentum, ad infinitum, but actually a function of energy. Can it be so? Maybe...

Originally Posted by pghnative

What is a "planet" in your theory. The nine named planets? Large moons too? Large asteroids? All masses?

Originally Posted by Lunatik

the nine planets. Haven't done the work on moons, which may be complicated by home planet energy outputs. So don't know moons for now, only nine planets.

Originally Posted by Lunatik

When I reworked it the way you suggested, rather than PK dropping out, it came out (PK)^2, and got same results, so the original equation:

(PK/PE) :/: (13.36E-16) x (PK/231.7K) :/: (planetary orbit/365) :/: (planet spin) x (AU)^1/2 = SR became:

(PK)^2/PE :/: (13.36E-16/231.7K) :/: (planetary orbit/365) :/: (planet spin) x (AU)^1/2 = SR

I'm doing this from memory (notes not with me) but got same results (but not 100% sure I got it right). But this way may be easier to deal with, though results should be the same.

Originally Posted by Lunatik

Venus is off the charts, because of its retro spin, so used it only as a best guess basis for near zero spin, though I confess that is only a rough estimate. The results for Venus puts it off the charts, but other planets are okay, more or less.

Originally Posted by Fram

Wait. You have (A/B) / (C * (A/D))
Now, C * (A/D) = (C*A) / D
So you get (A/B) * (D / (C*A))
This is the same as (A*D)/ (B*C*A),
and this is again the same as D / (B*C).
Hey, no longer is there an A!

Can please someone else confirm that I have this basic basic math rules still correct, and if I do, please tell it to Lunatik, because if you get even this wrong, why bother with anything else, and if I get even this wrong, please ignore my criticisms. But this is quite crucial!

Originally Posted by pghnative

Fram
The problem here is that Lunatik's equation is tough to decipher based on what he/she typed. More parenthesis (parenthesi??) should have been used to clarify.

This:
(PK/PE) :/: (13.36E-16) x (PK/231.7K) :/: (planetary orbit/365) :/: (planet spin) x (AU)^1/2 = SR

is better represented as:
(PK/PE) * (1/C1) * (PK/C2) * (C3/orbit) * (1/spin) * (AU^0.5)
where c1 = 13.36E-16; C2 = 231.7; C3 = 365

As you've pointed out, the use of 3 separate constants is confusing.

Also confusing is the lack of units analysis. By my best guess, the units of this "ratio" are (length^0.5 / time).

Originally Posted by pghnative

This:
(PK/PE) :/: (13.36E-16) x (PK/231.7K) :/: (planetary orbit/365) :/: (planet spin) x (AU)^1/2 = SR

is better represented as:
(PK/PE) * (1/C1) * (PK/C2) * (C3/orbit) * (1/spin) * (AU^0.5)
where c1 = 13.36E-16; C2 = 231.7; C3 = 365

Originally Posted by Fram

Wait. You have (A/B) / (C * (A/D))
Now, C * (A/D) = (C*A) / D
So you get (A/B) * (D / (C*A))
This is the same as (A*D)/ (B*C*A),
and this is again the same as D / (B*C).
Hey, no longer is there an A!

Originally Posted by pghnative

Taking this further,

SR = (PK * PK * C3 * AU^0.5) / (PE * C1 * C2 * orbit * spin)

Lumping some terms together gives:

SR = P * C */ spin
Where P = planetary terms (excluding spin)
Where C = constants

Originally Posted by pghnative

That is
P = PK*PK*AU^0.5 / PE
C = C3 / (C1*C2)

Originally Posted by pghnative

So let's look at lunatik's conclusions. Supposedly it is compelling that if you take earth's spin ratio, divide it by another planet's spin ratio, you obtain the planet's rotational period (within ~15% for 75% of planets)

So, let's let:
SRp = SR for the planet of interest
SRe = SR for earth
Pe = P (my P, above) for Earth
Pp = P for planet of interest
spin-e = Earth's spin (ie, rotation rate)
spin - p = Planet of interest's spin

Then,
SRe = Pe * C * / spin-e
SRp = Pp * C * / spin-p

Again, it is said to be compelling that SRe / SRp is nearly equal to the rotation rate of the planet of interest. Because of this, a link between internal heat and rotation rate is hypothesized. Let's calculate this:

SRe / SRp =? spin -p
(This means "Does SRp / SRp equal spin-p"


substituting for SRe and SRm gives:
(Pe * C * / spin-e) / (Pp * C * / spin-p) =? spin-p

Originally Posted by pghnative

Since spin-E = 1 (by definition --- we're calculating the spin of the relevent planet in earth days), and since you can cancelling the C's and rearrange the left side, you get:
(Pe * spin-p) / (Pp) = spin-p

Originally Posted by pghnative

But spin-p is on both sides of the equation!!!! This means that spin has nothing to do with it.

So, while I cannot (yet) explain why Pe / Pp would be ~1 for any planet, I can at least state conclusively that the hypothesis that spin is related to internal heat is baseless.

(By the way, since all of the terms in Pe and Pp are variations on planet distance, internal temperature, and orbital period, I suspect that there is nothing earth-shattering with regard to why Pe / Pp is ~1 for most planets)

Originally Posted by Lunatik

I think I can see where the problem is. You think PK is the same everywhere, but it is not. PK, which is Kelvin temp for each planet, is a different value for each planet, so these would have to be PK1, PK2, PK3..., each one a separate value. Taking the equation:

(PK/PE) :/: (13.36E-16) x (PK/231.7K) :/: (planetary orbit/365) :/: (planet spin) x (AU)^1/2 = SR

As pghnative says, these are ratios, so each parenthesis is a separate value, not necessarily algebraic, so that (PK1/231K) is not same as (PK2/231.7K), if that helps. This was why I had those values in parenthesis, because each one represented a value unique to the planet being calculated for spin, as a ratio of Kelvin to Energy, then 'normalized' for Venus near zero spin and Earth's one day spin. That's why it does not lend itself easily to algebraic equivalents, so using actual numbers makes for easier to understand results: Kelvin, E, spin, orbit in days, are in my original post; see Nasa Planetary link for more data. Then put in on a spread sheet and see what you get.

Addendum: in rereading pghnative's I can see what he's getting at. Like I said before elsewhere, there are some very smart people here! I'l check it over later and get back. Thanks for simplifying it! I'll run some numbers on it to see how it goes.

Originally Posted by Lunatik

--italics mine

Hmm, looks like you left out 'orbit', which is a variable.

Originally Posted by Lunatik

Should be: P = PK*PK*AU^0.5 / PE*orbit*spin

Originally Posted by lunatik

--italics mine

So far so good, except for missing 'orbit' and a minor typo, SRp (as SRm).
However, SRe / SRp =? spin-p may not be totally correct. Why did you drop out the spin-e?

It should read as:

SRe/ SRp =? spin-e/ spin-p

Originally Posted by lunatik

which gives us: (Pe*C/ spin-e) / (Pp*C/ spin-p) =? spin-e/ spin-p

if I follow what you are doing correctly. Of course both sides will have spin in them, since they are ratios of spin. Remember SR is only a number showing the relationship of PK/ PE, for all the planets, Earth included, where it is = 2.32. When you take this 2.32 for Earth and divided it by itself, you get spin of one day. For all the other planets, it is different, which results in approx. their spin (in Earth days).

That no longer applies. It should now read, if spin-E =m 1, as:

(Pe * spin-p) / (Pp) = 1/ spin-p, where the spin-p cancels into:

Originally Posted by Lunatik

Pe/ Pp = 1. Is this what you were trying to say?

Originally Posted by Fram

I hope Lunatik will find time to watch the third question again as well: why do you get a positive result for Venus, when you can with your numbers only get a negative result?

Originally Posted by Bathcat

It seems to me that large planets would be expected to....

1. Be hotter inside, if only because their volume-to-surface-area ratio means they can radiate away less heat per cubic meter of interior volume, and

2. Conserve angular momentum in the face of various gravitational perturbations.

(On the last point, obviously small bodies closely orbiting large ones tend to become tidally locked fairly quickly -- like our Moon. What I mean in point 2 is that a large body, like Jupiter, would have a great deal more angular momentum for the mechanism of tidal friction to overcome before its rotation could be slowed toward tidal lock.)

So empirically speaking it seems to me that there should be a correlation between interior heat and rotational speed but not a causal link.

Originally Posted by Lunatik

Can this odd formula be rewritten as:

SR = [(PK^2 x 365 x (AU^0.5)] / [(231.k^2) x (PE * 17.33E+16) x orbit x spin] ???

Originally Posted by Bathcat

Are you talking about radiative temperature or interior temperature? Lunatik wrote: "The purpose for this equation was to find a relationship between planetary interior heat..." (emphasis added)

"The interior of Jupiter is hot: the core is probably about 20,000 K." Reference: Nineplanets

*shrugs*

It seemed to me that you were indeed interested in interior heat and not the radiative black-body temperature, which is another kettle of carp. A blackbody spectrum would only represent a planet's interior temperature if the planet were the same temperature throughout, yes? A spectral analysis of the Sun or another star as a blackbody only gives the surface temperature -- the temperature of the radiating surface.

If you're using the temperature of Jupiter's radiating surface, you're not using interior heat. So it seems to me.

*shrugs again*

But I'm probably misunderstanding your argument. I haven't been following the Huygen thread.

Originally Posted by pghnative

You can write any formula that you like, but keep in mind that the value of (PK^2 x AU^0.5 / PE * orbit) is nearly equal for each of the nine planets. So taking this, multiplying it by some constants (in your case, 365 / (231 * 231 * 17.33E16), still results in a number that is nearly equal for each of the nine planets.

Originally Posted by Lunatik

What I can't see, which is why I puzzle over it, is why PK^2 would be "distance related". I can see AU, or PE (R is distance), and orbit as distance related, but not Kelvin temps.

Originally Posted by Lunatik

-snip-
As pghnative says, these are ratios, so each parenthesis is a separate value, not necessarily algebraic, so that (PK1/231K) is not same as (PK2/231.7K), if that helps. This was why I had those values in parenthesis, because each one represented a value unique to the planet being calculated for spin, as a ratio of Kelvin to Energy, then 'normalized' for Venus near zero spin and Earth's one day spin. -snip-

Originally Posted by Nicolas

Just a thought here:

if you have any formula using planet specific data, and normalize this formula for 2 planets in the system, doesn't the relation found say "all planets are elements of the same system, influenced by the same factors"? I mean isn't it logical that a trend is found? What the trend represents here isn't clear to me however. It represents "something", but whether that's some new finding, a standard relation or a "trivial" (irrelevant) relation isn't clear to me at the time.

Originally Posted by pghnative

I'm not exactly sure what you are saying here. In the general sense, I think it does make sense to look for relationships among things. If ratios of certain, specific, data all equal the same number for most objects in a system, then that justifies forming a hypothesis.

For instance, Keplar noted that there was a relationship between the orbital period and distance from the sun. The cube of one divided by the square of the other is a constant. Ultimately this led to Newton's theory of gravity.

In this case, I don't think there is anything new here. The ratio of PK, PE, AU^0.5 and orbit are all the same for most of the nine planets. But since PK, PE appear to be related to solar luminosity (which in turn is related to solar distance) and since AU^0.5 and orbit are also related to solar distance, it is to be expected that combinations of these variables will equal a constant.

To reword this (and possibly beat this dead horse into the ground), I have no doubt that you could find a ratio between solar luminosity and orbital period for all nine planets. Can one conclude that solar luminosity drives orbital motion? That would be a reasonable hypothesis. But then you'd look at moons, and see that this didn't hold up. Alter you hypothesis to say that both luminosity and orbital period are both functions of distance, and then you'd see that the data holds for all systems. You'd then call it a theory, and go home and drink your grog.