# Thread: Planet Spin as Function of Interior Heat?

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## Planet Spin as Function of Interior Heat?

FROM THE HUYGENs THREAD, I OFFERED THIS SET OF EQUATIONS TO SHOW PLANETARY SPIN RATIOS AS A FUNCTION OF VARIABLE E &amp; G, as per below.

The purpose for this equation was to find a relationship between planetary interior heat and the energy levels within which planets orbit. There seems to be a relatively good fit, if not exact, so I solicit any ideas that might expose possible flaws in this reasoning.

If anyone has any comments or criticisms, they would be appreciated. Thanks.

Ivan/ aka 'Lunatik'
---------------------------------------------------------------------------
Originally Posted by Lunatik
PLANETARY SPIN RATIOS PER AXIOMATIC EQUATIONS AS A FUNCTION OF OF VARIABLE E &amp; 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 &amp; spin days.]

2. I had thought that planetary rotation was a function in relation to mass, density, and volume. Planets rotate in the same direction of their revolution, which is shown in almost every major body in the system. The major difference is in Venus, which has a very slow retrograde rotation. Methinks a large impactor collided with Venus early on, causing the rotation to slow dramatically, even stopping it and reversing the rotation. Keep in mind that the Venusian day is longer than the Venusian year. That must have been one hell of a show to watch. Whatever hit Venus must have been big, and hit it at the right angle. With the impactor that collided with the Earth, the ejecta coalesced into the Moon, and helped stablize the rotation of the Earth.

3. What about satellites (like Jupiter's and Saturn's)?

4. 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.

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...

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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.
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 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...
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.

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... something to look for if variable G and variable E are real. That's what this equation seems to be saying here.

One very easy way to disprove this theory is by working out a similar equation with 'non-variable', universal constant Newton's G. If you get spin results that more closely match observed spin, you're in!

6. 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...
What is a "planet" in your theory. The nine named planets? Large moons too? Large asteroids? All masses?

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

8. Originally Posted by Lunatik
Originally Posted by pghnative
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...
What is a "planet" in your theory. The nine named planets? Large moons too? Large asteroids? All masses?
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.
I'm not asking if you've done the calculations, I'm asking if you would hypothesize that interior heat energy somehow drives the spin of moons, asteroids, comets, etc.

Or do you hypothesize that it is only the nine planets whose spin is driven by interior heat energy.

9. Originally Posted by Lunatik
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.
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.
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!

10. Originally Posted by Lunatik
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...
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.
That was not my question. Have you calculated the numbers for Venus? If so, how come that you end up with a positive number? You can only get a negative result with the numbers that you give. So your calculation is wrong. What reason do we have to look into the rest of them if you can't even see that, and don't understand how you can simplify your calculation?
Have you made that formula yourself? Do you understand it? Have you checked it in any way?

11. Originally Posted by Fram
Originally Posted by Lunatik
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.
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.
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!
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).

12. Originally Posted by pghnative
Originally Posted by Fram
Originally Posted by Lunatik
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.
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.
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!
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).
Ah, thanks, that might explain it. I thought his :/: was the 'lower' priority, meaning that you first made the calculations between those, and then the :/: calculations. This was in line with the first element, (PK/PE), which has to be done before the first :/: can be done, as it is included in brackets.

Lunatik, care to write your formulas a bit more clear the next time? The mathematicians use the parentheses for this reason... You use them as well, but not in the right way (putting a constant on its own between brackets is useless, for example). And by using / and :/: indifferently, you only confused me further.

Well, assuming that this is the correct explanation, that only leaves the questions: why use three constants, why use spin in a calculation to calculate spin, and why a positive result for Venus?

13. 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
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

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

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

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

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)

edited once to remove a mean-spirited remark on my part, and a second time to correct spelling

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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!
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.

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Originally Posted by pghnative
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
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
--italics mine

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

This should be: SR = P * C/ spin * orbit

Originally Posted by pghnative
That is
P = PK*PK*AU^0.5 / PE
C = C3 / (C1*C2)
Should be: P = PK*PK*AU^0.5 / PE*orbit*spin

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
--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?

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

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).

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
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:

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

The real equation is ..[DELETED]

That's what I think this Planetary Spin Ratio equations says.

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)
[/quote]
Actually, spin-e and spin-b are on both sides of the equation, why wouldn't they be? If I knew why you dropped out 'orbit' and later 'spin-e', I might better understand your conclusion. Still looking at it...

It's the variables that runs the results, not the constants which are there only to 'normalize' for Venus 'zero' spin and Earth's one day spin. That's why I fall back upon using actual numbers, because otherwise it is easily confusing. Have not yet had chance to work on your new simplified version, but will check it out futher. Thanks.

{Edited for delete of: SRe/ SRp = 1/ spin-p, which is wrong, and spell.]

16. Originally Posted by Lunatik
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!
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.
I think pghnative has explained my mistake quite good, but your explanation makes no sense to me. Are you seriously saying that in one equation where you use twice PK, it doesn't have twice the same value?
That is what you are saying, but I seriously hope that is not true.
I know PK is not a constant, and that was not what I said. The way I interpreted your equation, due to the very confusing way you had written it down, gave the result that you could just take out PK as you ended up with PK / PK, which is 1.
As pghnative pointed out, that probably was not your intention. But your explanation here is quite ridiculous.
I'll sit back for a while and see how you and pghnative make sense of this equation, because we clearly have problems understanding one another. I'll chime back in when I have another question or remark.
Pghnative has adressed two of my points, the use of constants and the fact that you use spin at both sides. Thanks for that.
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?

17. Originally Posted by Lunatik
Originally Posted by pghnative
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
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
--italics mine

Hmm, looks like you left out 'orbit', which is a variable.
You're right, I excluded orbit by accident. This doesn't, however, change my conclusion.

Originally Posted by Lunatik
Originally Posted by pghnative
That is
P = PK*PK*AU^0.5 / PE
C = C3 / (C1*C2)
Should be: P = PK*PK*AU^0.5 / PE*orbit*spin
My explanation is easier to follow if you stay with my convention and keep spin out of the lumped parameter "P". (This is my fault --- since I accidentally left "orbit" out of the lumped parameter "P", it makes my equations confusing)

Originally Posted by lunatik
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
--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?

SRe/ SRp =? spin-e/ spin-p
No, it shouldn't. Your premise is that if you take the spin ratio of earth and divide it by the spin ratio of another planet, you obtain the rotational period of that planet. In math form, this is SRe / SRp = 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).

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
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:
You've done the equations wrong. spin-p is in the numerator on the right side.
Originally Posted by Lunatik

Pe/ Pp = 1. Is this what you were trying to say?
Yes, that is exactly my point. Take your values for PK, PE, and orbit, and forget completely about spin. Don't take my work on the math, do it your self. The ratio of P for earth to any other planet is about 1.

Recall that my definition of P is this (this time, including "orbit", as you've duly pointed out )

P = PK * PK * AU^0.5 / (PE * orbit)

For earth, P = 19.69
For murcury, p = 22.88

The ratio is 0.86, or about equal to 1. Note that when you did your calcs you noted that by dividing earth's spin ratio by mercury's, you obtained 51 days, close to Mercury's actual of 58.8.

But 51 / 58.8 = 0.86. Exactly the same (excluding rounding effects.). This is not a coincidence, it is a mathematical certainty, as my algebraic manipulation proves.

Spin has nothing to do with it. I repeat, spin has nothing to do with it. Calculate P for every planet. It will be very close to 19.7. I haven't done the calculation yet, but it will be off for Venus and Pluto to exactly the same degree as your original calculations.

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Intriguing. Now I see what you're getting at. Thanks.

I believe Fram had said earlier that what would happen if I dropped the 'spin' from the left side of the equation. I could, and did, where the numbers came out within some margin of error of 2.32, which is Earth's number. But then can I still call it a "spin ratio"? Or is it now merely a "ratio", of which I'm not sure what it represents, except that there seems to be some sort of parity with Earth: A ratio of what?

Will have to think on this some more, since something is represented here, but not sure what it is, if anything. ops:

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] ???

It would simplify it, but not make it right, unless I can figure what "ratio" without including spin is all about. Fram, pghnative, thanks for your help, Vermonter and papageno thanks for your points. Obviously this needs work... :-?

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## Mass.

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.

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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?
I'm working on this as we speak. What happens if I take out Venus's temp 231.7K from the 13.36E-16 orbit Energy number? Rationale here is that Venus is 'different' from the other planet since we're using it as a base "zero spin", implying that by this hypothesis if Kelvin equals Energy, there is no energy differential to cause spin. Let's see... if I drop 231.7K from (VK/VE) the Venus Kelvin divided by Venus Energy, then the second function in the equation is merely VE = 17.33E-16. So dividing the first function (231.7K/ 17.33E-16) by the second (1/17.33E-16) leaves us with only Venus Kelvin VK = 231.7K

Now, if I run the equation with that, the final SR (I left spin in for this just for comparrison) we get a number of SR = 1.20 ... but what is that? If I take out the spin, I get 292.8, which is even a more meaningless ratio than the first result. So this idea is out. So I don't know why Venus is so misbehaving. If I go backwards to see what is Venus's spin ratio vs. Earth's SR = 2.32, I get 2.32/244 = 0.0095. So you can see the SR = 0.005 number for Venus is in the 'ball park', but not good enough. So it remains a mystery, either with or without spin on the left side of the equation. Without the spin number, the result is ?ratio= 1.22. I feel like I'm missing something here, but can't see it...

And as said above, without spin, I don't really know what these numbers represent anyway! Cheers.

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## Re: Mass.

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.
If you look at black-body heat for the planets you'll see that the giants are not hotter. In fact, Jupiter at 110K, and Saturn at 81K, are both cooler than Earth's 254.3K. However, as you point out there may not be a 'causal' relationship between interior planet heat and rotational speed. But it is curious that there seems to be something going on, just don't really know what. Thanks, let's keep thinking to see if we can figure out what it is... :-?

22. 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] ???
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.

By the way, I suspect that the reason these are equal is that all of the variables (PK, PE, AU, orbit) are dependant on distance from the sun. So taking a bunch of variables that are dependant on distance from the sun, and then multiplying and/or dividing them, it doesn't really surprise me that they are similar for all nine planets.

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## Yes.

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.

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## Re: Yes.

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.
You got it right. I was working with black-body radiation of the planets, as per http://nssdc.gsfc.nasa.gov/planetary/ , so didn't know what interior heat temps were, only radiation heat, which is many K below interior heat. I figured they could measure radiating heat fairly well, but not sure about interior heat. How do you stick a thermometer into Jupiter?

All this is up in the air right now, still trying to get a fix on what the ratios mean. Stay tuned, but "enlightenment" may not come for a long time. Fun thinking about it, though not garanteed for results. As pointed out above, this may be just no more than some relationship to distance. So still working on it...

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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.
Taking this piece by piece:

1. PK^2 is planet's black-body radiation squared.
2. AU^0.5 is square root of distance, (also hypothetical square root of linear increase in G per AU, in my thinking per Axiomatic Equation).
3. PE is hypothetical planet's orbit Energy expressed as: E = solar irradiance x 1/2 Rv^2. where R is distance from the Sun.
4. Orbit is orbital days (vs. Earth's 365 days)

The constants are there to bring the equation back into Earth's rotation of one day from Venus's "flat" K to E relationship, where virtually no spin.

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. So that's where I'm at, just about throwing in the towel for now since I simply cannot see it. Sometimes after months go by, it dawns on me, so will need to do a lot of sleeping on it.

Appreciate all the things you pointed out. That all the planets come in close using these variables has me head scratching, especially planet Kelvin, so it is becoming quite an interesting puzzle, with no reasonable outcome assured.

26. 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.
Where did you obtain your values for PK (aka, black-body temp). Based on your values, I presumed that they were the equilibrium temperature for an arbitrary black-body in the orbit of the planet.

They are obviously not measured values --- Earth is given at ~ -20C, which (if my memory serves me) is about right for a black-body at Earth's AU. It obviously isn't Earth's average actual temp (which I believe is in the vicinity of 0 C), due to greenhouse effect.

If my presumption is right, PK is directly related to distance.

27. Lunatik, just checking your data a bit, and shouldn't both Uranus and Pluto also have a negative number of days for their spin?

28. 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-
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.

29. Originally Posted by Nicolas
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-
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.
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.

30. Originally Posted by pghnative
Originally Posted by Nicolas
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-
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.
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.
Maybe I should have formulated my thoughts a bit more clearly for myself before posting them (and losing another part of clearness on translation to "English").

What I meant was in short that when taking data from elements of the same system, trends are found whenever dependent data is used in the formula. As long as you haven't come to a conclusion about what your formula expresses (in which case I wonder how you came to the formula), you don't know which trend you are seeing. It could be a new discovery (dependence of 2 variables previously thought unrelated), a trivial dependence (mass/volume/density) not relevant for the research, or a "false dependence".

Like you said: Say you've got a formula with luminosity, distance and orbital period. You could conclude from the trends seen that orbital period is influenced by luminosity, while both seem dependent only because they both are a function of distance to the sun; this does not mean they directly influence each other (in either direction). And if there is pure dependence (so not via a shared variable), the direction of dependence is of importance. Clear example: Luminosity at Mars depends on sun activity, but the luminosity at Mars will not influence the activity of the sun.

So a very good understanding of the formula used is needed to be able to conclude just what trend is seen in results.

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