QUESTION: Why do planet ratios employing Orbital Energy, Black Body Kelvin, orbital periodicity, and square root of AU, gives an answer that appears to be something of a constant?
(This had been discussed on another forum, posted (Jan. 29, 2010): http://www.humancafe.com/discus/mess....html#POST5413 about Spin Ratios where the ratio of about "one" keeps coming up, if divided (multiplied in the denominator) by a spin-ratio (Earth's) of SR =~2.32, when figuring the interrelations of Planet's Kelvin black-body and orbital Energy.)
In fact, the long original equation can be reduced and better written as:
Spin = [PK^2 x Ev^2 x 365 x (AU^0.5)] x 1/ [(231.7K^2) x (PE * 17.33E+16J) x orbit days x ~SR] = ~1
In words, it means:
Planet Kelvin squared, times Venus orbital Energy squared, times 365 Earth days, times square root of AU distance from the Sun; all divided by Venus Kelvin squared, times planet Energy, times Venus orbit Energy, times orbit days, times (inverse) Spin Ratio 2.32, equals aprox =~1.
Note: Planet orbital Energy is a value derived from Solar radiance received by planet (W/m^2), times 1/2 mean distance from the Sun, times mean orbital velocity squared, to give us Energy E' for that planet.
When calculated for Earth's orbital Energy, taking data from "Nasa Planetary Fact Sheet" [ http://nssdc.gsfc.nasa.gov/planetary/planetfact.html ] per equation:
E' = solar irradiance x 1/2 Rv^2
Earth's E' is:
Solar irradiance: 1367.6 W/m^2
Mean distance from Sun: 149.6E+9 meters
Mean orbital velocity: v = 29.78 km/s
(1367.6) (149.6E+9) = 204592.96E+9 = 2.046E+14 W/m = solar radiance energy
KE = (1/2) (1) (29.78)^2 = (1/2)(1)(886.85) = 443.4 m^2.kg.s^-2 (Joules)
KE * W/m = ( 443.4 J) (2.046E+14 W/m) = 9.07e16 Joules (times Newton force N) = Earth's total orbital Energy. (Please note m = 1 is a net function of planet mass already in orbital motion, and the planet KE is 'template' function only.)
Earth's E = ~9.07E+16 J (which is close to E = mc^2 = 90 petajoules). This Energy level (for Earth) then sets the basic template for like Energy E' levels for the other planets, using the same methodology:
MERCURY: 60.55E+16 J
VENUS: 17.33E+16 J
EARTH: 9.0E+16 J
MARS: 3.66E+16 J
JUPITER: 0.335E+16 J
NEPTUNE: 0.01E+16 J
This was then found true for all the planets, from Mercury to Neptune (Pluto was left out as an odd-ball, not in same orbital plane with the Sun as the others). When these ratios are worked out for Earth, the spin-ratio is SR=2.32, a dimensionless number. When all the other planets have their ratios worked out by same equation, if divided (1/multiplied) by Earths 2.32 ratio, they then approximate SR=~1. Why?
Maybe there is something that nets out I can't see? (BTW, I had mentioned this 5-6 years ago briefly on this forum when I first calculated it, but nothing was resolved then.)
That is the question posed here for readers of Against the Mainstream. Nothing like this exists in current astronomical/astrophysical literature, to my knowledge, so it is obviously NOT Mainstream. However, it is not even Against Mainstream, since it is not a theory nor hypothesis, merely a play on numbers using known planetary data that just happen to stack up this weird way, where all the SR spin-ratios for all the planets approximate unity (except Venus). Why would it be?
Here is an example of how those numbers work:
Taking the stats for the planets (from NASA page), with above equation for Spin:
AU; PLANET; P-KELVIN; P-ENERGY; ORBIT DAYS; SPIN; (AU)^1/2;
0.39 ; Mercury; 442K ; 60.55E16 J; 88 days; 58.8 ; 0.624 ;
0.72 ; Venus ; 231.7K ; 17.33E16 J; 244 ; -245 (retro?); 0.850 ;
1.0 ; Earth ; 254.3K ; 9E16 J ; 365 days; 1 ; (2.32 base SR)
1.5 ; Mars ; 210.1K ; 3.86E16 J; 687 ; 1.03 ; 1.225 ;
5.2 ; Jupiter ; 110K ; 0.335E16 J; 4329 ; 0.415 ; 2.28 ;
9.5 ; Saturn ; 81.1 K; 0.1004E16J; 10753 ; 0.455 ; 3.08 ;
19.2; Uranus ; 58.1K ; 0.024E16J; 30660 ; 0.718 ; 4.38 ;
30 ; Neptune ; 46.6K ; 0.01E16J ; 60225 ; 0.673 ; 5.48
By the numbers, where planet's orbital Energy is in bold:
Spin = [PK^2 x Ev^2 x 365 x (AU^0.5)] x 1/ [(231.7K^2) x (PE * 17.33E+16J) x orbit x ~SR]
Mercury: [442K^2*17.33E16J^2*365*0.624] x 1/[231.7K^2*60.55E16J*17.33E16J*88*2.32 =?
[195364K*300.3E32J*227.8] x 1/[53684.9K*1049.33E32J*204.2] = ?
[13354530 / 11503230 = 1.16 (slightly high)
Venus: [231.7K^2*17.33E16J^2*365*0.85] x 1/[231.7K^2*17.33E16J*17.33E16J*244*2.32=?
canceling likes = [310.25] / [566.1] = 0.548 (off unity by ~ half)*
Earth: [(254.3K^2*17.33E16^2*365*1)] x 1/[231.7K^2*(9E16 J*17.33E+16J)*365*2.32] = Spin
[64668.5*17.33E16J^2*365] x 1/[53684.9*9E16J*17.33E+16J*365*2.32] = Spin
[64668.5*300E32J] x 1/[53684.5*9E16J*17.33E+16J*2.32] = Spin
[20005500E32J/ 19425898E32J = 1.03 (vs. Earth = 1 spin)
Mars: [210.1K^2*17.33E16J^2*365*1.225] x 1/[231.7K^2*(3.86E16J*17.33E16J)*(687?)*2.32 = ?
[44142K*300E16J*447.1] x 1/[53684.9K*3.86E16J*17.33E16j*687*2.32] = 5920766.5 / 5723777.43 = 1.034
Jupiter: [110K^2*17.33E16J^2*365*2.28] x 1/[231.7K^2*(0.335E16J*17.33E+16J)*4329*2.32 =?
[12100*300.3E32J*832] x 1/[53684.9K*5.8E32J*10043.3] = 3023180160 / 3127106626 = 0.967
Saturn: [81.1K^2*17.33E16J^2*365*3.08] x 1/[231.7K^2* (0.1004E16J*17.33E16J)*10753*2.32 =?
[6577.2K*300.3E32J*1124] x 1/[53684.9K*1.74E32J*24947] = 2220049672 / 2330342329 = 0.95267
Uranus: [58.1K^2*17.33E16J^2*365*4.38] x 1/[231.7K^2*(0.024E16J*17.33E+16J)*30660*2.32 =?
[3375.6K*300.3E32L*1598.7] x 1/[53684.9K*0.416E16J*71131] =?
[1620590488 / 1588562819 = 1.02
Neptune: [46.6K^2*17.33E16J^2*365*5.48] x 1/[231.7K^2*(0.01E16J*17.33E16J)*60225*2.32] =?
[2171.6*300.3E32J*2000] x 1/[53684.9K*0.1733E16J*139722] = 1302600000 / 12999916645 = 1.00
Why would this happen?
I think the most puzzling aspect of this exercise is that of all variables, I would not expect the square root of planet's distance from the Sun, expressed in AUs, to be part of this 'unity' result. Again, why this variable (AU^1/2) need be included? Wouldn't a simple ratio of planet orbital energy and planet's back body Kelvin give similar results? But they don't. That appears a real mystery to me! Hope it is to you too.
Ps: I will be leaving in a few days for a two month trip in Italy and Europe, so may not always be able to answer queries, it depends on Wi-Fi availability on my iPhone. I surely will not be back within the 30 day window this thread might run, but hope to look in and try to respond as I am able.