Let’s take a virtual trip to the Moon with an idea of Johannes Kepler to guide us. In this image we have the Moon placed next to the Earth – what are we seeing?
The triangle has one side running from the centre of the Moon to the centre of the Earth, one running at right angles to it from the Earth’s centre point to the edge of the Earth, and the third side completing the triangle.
Since it’s a right-angled triangle, the third side is also the hypotenuse of a Pythagorean triangle. But it’s a bit more than that too.
According to NASA’s Moon factsheet, the ratio of the equatorial radius of the Moon to that of the Earth is 0.2725.
That means if the Earth radius is given a value of 1, the Moon radius will be 0.2725 on the same scale (i.e. as a ratio), making a combined Earth+Moon radius of 1.2725, which is almost identical to the square root of phi (1.27202) – a 99.96% match.
http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
In a Pythagorean triangle, the square of the two shorter sides must equal the square of the third side i.e. the hypotenuse. So if the two shorter sides of our triangle are 1 (Earth radius) and the square root of phi(combined radii) we have:
1² + [sqrt(phi)]² = 1 + phi = 1 + 1.618034 = 2.618034 = phi²
So the squares of the three sides of our triangle are: 1, phi and phi²
We have in fact a Kepler triangle – the black area inside the squares in this diagram.
‘A Kepler triangle is a right triangle formed by three squares with areas in geometric progression according to the golden ratio.’
http://en.wikipedia.org/wiki/Kepler_triangle
So that’s what the illustrated triangle of the Moon and Earth (above) is showing.
‘Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into mean and extreme ratio. The first we may compare to a mass of gold, the second we may call a precious jewel.’
— Johannes Kepler
More about the great astronomer and mathematician here:
http://en.wikipedia.org/wiki/Johannes_Kepler
Footnote: if the Moon is shrinking, as appears to be the case (see link), the radius ratio to Earth is moving closer to the ‘square root of phi, minus one’.
http://news.bbc.co.uk/cbbcnews/hi/newsid_8930000/newsid_8931900/8931960.stm
Tallbloke's Talkshop 
Both the diagrams seem to be wrong.
The one with the moon and the earth needs a φ replacing with a φ².
The one with the yellow squares needs a φ replacing with a √φ.
[mod note: comment withdrawn later – see below]
See…..this proves man is warming the earth with carbon dioxide……….
gc: have another look. The moon graphic shows the ‘unsquared’ values and the Kepler diagram has the squared values – hence the yellow squares.
Gee. Googling this phi thing. You just get lost in the God and creation phi blogs.
Mind blowing stuff..
Looking for something for you ‘oldbrew’.Maths that is
from one of the phi religion blogs
http://www.davidjayjordan.com/MoonExactness.html
Many of them have studied the phi maths
quote
“The sun acts on the earth and its moon as one entity with its center at the barycenter.
This barycenter being exactly 216,000 miles from the Earth, which is why the ancients knowingly or unknowingly
always used the 216 number as their length between Moon and the Earth, as well as its 2160 mile diameter as the
fundamental of its size
———————————.
is this phi related? 216?
————————————
Lots of links about the moon/earth phi relationship and Egyptian pyramids and the ark of the covenant and the Bible and and .and. infinity
Here is a forum discussion looks ok
http://www.oztrance.net/forum/showthread.php?21143-Is-there-a-PHI-link-between-earth-and-moon
weathercycles says: ‘is this phi related? 216?’
Only indirectly: 216 x 3/2 = 144 which is a Fibonacci number.
http://en.wikipedia.org/wiki/Fibonacci_number
So for example 2160 = 144 x 5 x 3 (all Fibonacci numbers).
Important to stick to actual data or it can all get a bit ‘woolly’ 😉
Miles Mathis has an interesting paper on the density of the Earth and Moon.
http://milesmathis.com/phi.html
He concludes:
‘Of course there is much more to be said on this problem, but I think I have shown that phi in nature is not a coincidence. There are numerical coincidences in Nature to be sure, but most of the number relations that have been passed off as coincidence or numerology are, I believe, simply mechanical phenomena yet to be explained.’
The strange reocccurence of various numbers (like Pi) and ratios in astronomical and physical sciences makes me wonder if we aren’t dealing with additional dimensions that intrude or make themselves known in our 4 dimensions in odd ways. “Flatland” kind of weird ways. So that the relationships are not weird or fixed by odd fudge factors (constants) when the other dimensions are taken into account.
Have you no sense of responsibility to the environment? If you leave the moon there it will crush the Arctic ice cap. The ice will drift down into warmer waters, melt, and swamp coastal areas. Put the moon back in its proper place at once.
[reply] Good point, hadn’t thought of that 😉
Mathis theory very interesting OB
I am proud of myself that l understood the concept he was presenting.
I noted that Mathis had the density of moon and earth as
quote
And if we look at the known densities of the Earth and Moon, we find the numbers 5.515 and 3.3464. The ratio there is 1.648
——————————————–
Maybe related to…
3.3464 * 5.515 = 18.45
longitude of ascending node = 18.6
18.6 node cycles
The periodicity and recurrence of eclipses of the Sun by the Moon, and of the Moon by Earth, is described by the saros, which has a period of approximately 18 years.
——————————————–
Getting back to the 2160… couldn’t make links here
144 * 5.515 * 3.3464 = 2657
try again
117 * 18.45 = 2158.65
————————————–
117? looking for a connection?
For example, the Moon does not orbit the exact center of the Earth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun.
http://en.wikipedia.org/wiki/Earth-Moon_barycenter
————————————————
some fractal stuff here
“From the above analysis, then, the radius of the Earth [6378 kilometers] to the barycenter of the Earth:Moon system [4641 kilometers] is similarly proportional as the boiling point of water [373.16] is to the freezing point of water [273.16]. Consider the variations below:”
http://www.earthmatrix.com/sciencetoday/moon/barycenter.html
———————————–
that’s all could find tonight.
Night all …from Gold coast Australia
@ weathercycles: the NASA fact sheet says the Moon-Earth density ratio is 0.606
54/89 = 0.60674
55/89 = 0.618 (= 1/phi)
http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
The Mathis paper cites NASA saying the Moon is shrinking, meaning it has to become a bit more dense as it’s not losing any material. So the density must be gradually approaching the 1/phi ratio with Earth.
ob: I had another look. It looks much better now – my apologies!
I had missed the fact that the numbers in the squares related to their areas and not side length.
[reply] no worries, thanks for taking an interest.
Assuming that particles are spheres, the most efficient “packaging” is a pyramid shaped container.
Perhaps related: I believe that it is impossible to visualize a particle that does not contain TIME.
Does that mean that it is possible that TIME represents the “God” “particle” – and how would that affect our theory (s) of TIME
OB
NASA uses kg and wikopedia used by Mathis use gram
Moon / earth mean density
5.515 and 3.3464. g/cm3 The ratio there is 1.648 (wikopedia)
Mean density (kg/m3) 3344 : 5514 = 0.606 ( NASA facts)\
BTW the
moon
surface gravity 1.622 m/s2 (0.1654 g)
.001622km/s2
Earth
surface gravity 9.780327 m/s2[16]
0.99732 g (Earth gravity)
.00978km/s2
from wiki
Ratio
1.622 : 9.780327 = 0.166
no surprise here as gravity related to density
—————————————————————————
after the units revelation..which made me realise l was barking up the wrong tree with the 216000 value in miles when it is better converted to metric KM
Had a bit of a play with some figures from the notes above
I found this interesting (see my paint diagram)
but not sure if the result is a coincidence
https://picasaweb.google.com/110600540172511797362/SOLARSYSTEMAndClimate#6006184675445905762
@ weathercycles
As your link shows, Ian Wilson says (link below):
‘Now, it seems quite remarkable that:
a) The position of the Earth in its orbit, as seen once every half precession cycle of the Lunar line-of-apse (= 4.42558131 sidereal years for 2000.0), resets itself with respect to the stars once every 208.0 sidereal years.’
4.42558131 x 47 = 208.00232
So 23.5 (47/2) precession cycles of the Lunar line-of-apse = one de Vries cycle
Note also that 235 (47 x 5) Earth-Moon conjunctions = one Metonic cycle (19 years)
http://en.wikipedia.org/wiki/Metonic_cycle
(47 x any Fibonacci number returns a number very close to another Fibonacci number.
In the case of 47 x 21, it is a Fibonacci number i.e. 987).
@oldbrew: the 208 years spacing (as Ian calls it in his lunar wave diagram, your link) has a bit more Fibonacci — with planets:
at 1/3 de Vries are pairs of Lunar/Solar eclipses (you’d say 857.5 Earth-Moon conjunctions 😉
and 1/3 de Vries fits into 69/2 = (13 * 3) / 2 Mars-Saturn conjunctions.
B.t.w. in my spreadsheet there are 733.836 days for Mars-Saturn conjunctions, looking for a relation with 236.992 days for Venus-Jupiter conjunctions.
[reply] 31 V-J = 9 J-Mars and 80 J-Mars = 89 S-Mars
@mod: thank you, the relations work perfect here (Solex & heliocentric). Now the search for disobedient (naughty) Luna begins 😉
Hi Chaeremon: 34 J-Mars = 4 Metonic cycles (76 years)
Considering that the distance to the moon is constantly changing, how does that work?
It’s all based on the mean periods, data from:
http://nssdc.gsfc.nasa.gov/planetary/planetfact.html
E.g. the Moon fact sheet says:
‘These represent mean apogee and perigee for the lunar orbit.
The orbit changes over the course of the year so the distance
from the Moon to Earth roughly ranges from 357,000 km to 407,000 km.’
Hi oldbrew, yes Metonic is always nice but (unfortunately) also short of eclipses (1 x syzygy too short per 3 x Metonic — as you proposed in another thread). You may recall that I investigate eclipse distances because then Lunar line-of-apse and line-of-nodes are balanced as well (more interrelation with physical cause, not just numerical).
But, look at this: (1 x Mars-Jupiter) – (1 x Mars-Saturn) = (3 x Lunar line-of-apse) up-to-the-point 😎 direct result from our discussion above 🙂 and I think that time has come to drop the “pet-” prefix from my model … have I ever mentioned: very good blog here 😎
So, with Fibonacci: (13 x Mars-Jupiter) almost perfect (1 x Inex [358 syzygy] + 1 + 1/2), and 3 consecutive Inex eclipses have peculiar line-of-apse relation (line-of-nodes still under investigation — Venus seems waiting — may change 13 to another Fibonacci);
also: (8 x Mars-Jupiter + r) = (9 x Mars-Saturn – r) almost perfect (1 x Saros = 223 syzygy) with r small (direct result from your 80:89 relation & Saros cycle series is very long, it easily fits 80:89 with r = 0).
Too much correlation for just coincident cyclomania.
[reply] Yes, and the 80:89 period is also 9 Jupiter-Saturn = 1 Jose cycle = just over 89*2 years (178.73y)
@oldbrew: my recent post does not appear (retried 2 times), no message from wordpress 😦
[reply] Sorry, went in the spam bin for some reason – retrieved now (above).
@oldbrew: almost every lunar/solar eclipse of the NASA canon pairs at 2212.5 syzygy = 65336.41 days = 9 x Jupiter-Saturn (~178.88 years, checked within 7 kyears as usual). No wonder in light of the above.
My focus goes now to something for the line-of-nodes, similar to what we’ve seen above for (1 x Mars-Jupiter) – (1 x Mars-Saturn) = (3 x line-of-apse) — still looking at the Venus girl.
Some ‘lunar node’ links at the end of the post below.
‘Naturally the IPCC takes no notice of solar cycles, planetary cycles or lunar cycles and all these are lumped into what could be considered “natural variability”.’
http://ktwop.wordpress.com/2013/07/27/the-lunar-nodal-cycle-and-its-effects-on-climate/
LNC / Jupiter orbit is close to phi² (99.98% +)
@oldbrew: thanks for the link (it mentions the usual suspect 65 years to which you made a proposal in another thread); checked the last paper: a corrected model on basis of [yes:] another corrected model and to see a fit the tidal gauge data was corrected; is IPCC dog food [/shudder].
But, look at (3 x Jupiter) = eclipses at (441 syzygy also at +/- 1/2 syzygy) = (2 Saros – 5 syzygy) = (19 x Mars) = (2*29 x Venus) = (4*37 x Mercury); around 35+2/3 year.
Lady Luna dancing with the members of her orchestra.
[reply] 8 Jupiter = 5 Metonic (Fibonacci numbers)
@oldbrew Re: 8 Jupiter = 5 Metonic (Fibonacci numbers)
Yes 🙂 1 x syzygy before that interval ends are eclipses en masse 😎 someone’s put on the brakes (rule of negative feedback/friction we are looking for). Very good one.
Hi oldbrew, the Jupiter-Saturn great conjunction has the following lunar interrelation, suppose we start at around equinox with an eclipse then:
after 2 x Saturn & 5 x Jupiter is again eclipse season, in year 59+1/3
after another equinox is final eclipse season (final in J-S interval)
thereafter is the J-S conjunction at around equinox 60th year
Around the 2 initial and around the 2 final equinoces [Miles’ spelling] both line-of-nodes and line-of-apse are aligned, perigee to perigee and ascending node to ascending node.
Lady Luna dancing with her jovian cavaliers.
@ Chaeremon: some bigger numbers…
25 x 19 x 18.6y = 8835y (475 lunar node cycles, 465 Metonic cycles)
300 Saturn = 8837y (60 x 5)
745 Jupiter = 8837y (149 x 5)
445 J-S = 8837y (89 x 5)
Two years in 8837 = less than 1 in 4000 variation.
Impressive 😎 yet, a pity that a mere 1/5 of the time-frame is based on (sort of) trustworthy observations (and the rest on mathematical fiction and sourced in poetic mystery).
From this discussion I take (475 gcd 465) = 5 and 465/5 = 3 x 31 (Metonic) and 475/5 = 5 x 19 (LNC), and that 3:5 are Fibonacci (well, 31 and 19 are prime and their ratio close to phi 🙂
All the numbers I used are multiples of 5 except 8837, so the fundamental cycle is 89 J-S.
18.6 : 31 = 3:5
http://en.wikipedia.org/wiki/Lunar_standstill#Direction_of_moonrise_and_moonset_and_altitude_of_moon_at_culmination
Some interesting numbers/ratios in the ‘Azimuth of full moon on horizon’ table 😉
@oldbrew: sure & appreciated (times 5 🙂 have you seen that my shortcut is 1767 years and that is 3 x 19 x 31 🙂
[reply] yes I was already aware of that one, now try 1618 Jupiter-Earth 😉
Sorry 😉 have no data points for a 1618×pJupiter = 19196.6 years (237440.5 syzygy) time-frame. I have “just” about 7 kyears, double checked by experts of numerical integration.
But mathematical astronomy says: there be lunar/solar eclipse pairs on both interval ends 🙂
Sorry, I meant the Jupiter-Earth conjunction period 1.092~ years.
1767 Earth – 149 Jupiter = 1618 J-E
(1618 = phi x 1000)
Congratulations! to 3 x 5 x 31 x 47 syzygy (contains Metonic factors) and almost integer 60 x Saturn and 149 x Jupiter 😎
Example equinoctial lunar eclipses @ 3764/03/31 05:07 (not in canon) at 191° longitude and @ 1997/03/24 04:46 at 183° longitude, but: at the other node & apsides not commensurate.
Note on such long distance we have already significant precession of equinox.
Thanks C – may have said this before but:
3 x 5 x 31 x 47 = 21855 Moon-Earth = 1767y (93 Metonic cycles)
98 Saros cycles = 21854 Moon-Earth
There may be more but I need to run it past TB first.
Yes, mathematically 😉 but at around 72 to 77 cycles the Saros series runs out of steam (therefor I “only” compare all possible eclipses by interval and not by series). Hit the +1 Saros (button) at
http://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm#calculator
and also compare the 2000 epoch to -3000 (this all academically [poetically] correct).
B.t.w. I’ve made this observation for Saros series: the next after last Saros eclipse goes north of north (resp. south of south, the shadow is meant) but in the same month an eclipse happens +/- 1 syzygy earlier/later at the other pole and begins (at the same node) a new series (the overlap already began some Saros earlier); it’s like relay race but apparently never ending.
I’ve made a (big) .svg graph diagram which connects Saros series to Saros series (and therefore: physically pole-to-pole), with labels for year/month and connecting edges. There seems no gap nor outlier, but this can be due to academically smoothed ephemeris data — dunno.
The .svg diagram can be sent in email.
[reply] it’s OK thanks, I can do it just on the numbers and throw in the Inex cycle and phi too 😉
I’m sure one of the reasons the orbital movements may have seemed baffling in the past is that the phi factor has been overlooked. With that in the toolbox it’s like having a torch instead of stumbling around in the dark.
Sometimes the batteries need a recharge though 🙂
Torches? they used concealed candle light and tilley lamps when searching for precious metal and artwork for antiques trade, and also while they hacked out “burial” chamber walls for museums and private collections:
This girl measured lunar eclipse to lunar eclipse (the 2 baskets at her hands) and the 3 setting tools above the baskets (same as the 2 tools in her hands) mark pivotal points in the interval where adjacent quadratures reflect the inclination and apsides of the whole interval’s ends. The 3 setting tools are mirrored in her hands (arms are bodily quadratures) and the middle setting tool is reflected (in function, like algebra) on her head (and her headband).
Now, what is the whole measured temporal distance? what equidistant subinterval have the 4 signs before and after the 3 setting tools over the baskets (maybe minus above mentioned quadrature subintervals)? Hint: note her thumbs, they show opposite inclination 😉
@oldbrew, coming back to Venus: the most stable of her periods is 243 (3^5) years (base of transit recurrence); Earth-Venus ratios are 8:13 and 243:395.
And indeed, at 3005.5 syzygy are solar/lunar eclipse pairs & alignment is perigee to perigee and node to opposite node 😎 note that the bulk of eclipses happens 1/2 syzygy earlier (with perfectly opposited apsides and nodes).
Lady Luna dancing with Lady Venus.
[reply] 155 Earth-Venus (31×5) = 28 x 8.85y lunar perigee cycles
@oldbrew, I have only 154.75~ , is your Earth-Venus 585.063 or is it 1 day off? also how many revolutions of apsidal line have you, integer 3286? (I have a small but notable fraction less).
Chaeremon: the NASA Venus fact sheet says ‘Synodic period (days) 583.92’
http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html
Extending the numbers by a factor of 3:
465 E-V (233 x 2, -1) = 21 x 4 x 8.85y
Another one:
21 x 8 x 5 x 3 x 2 [= 5040] Moon orbits = 377 years — all Fibonacci numbers.
5040 is also 144 x 35, and 35 Moon orbits = phi² years
144 x phi² = 377
There’s that phi balloon again 🙂
Hi oldbrew, I can see where your figure comes from, seemingly 2 x 291.95789 days from the conjunction period Earth-Venus but, which attempts to hide Venus behind the sun? if so, why not the same with exterior planets? why is 2014/10/25 07:31:55 not Earth-Venus conjunction?
For data points I always ask numerical integration for 600 years up to 2100 CE (just checked again and found my typo). Thanks for making me aware of my typo here. And b.t.w. I love the phi balloon 🙂
I stick to the average numbers in order to work out ratios, so don’t look at specific orbits.
FWIW some lunar intervals in comparison to planet orbits (always on eclipse distance, details omitted: sidereal month and nodical and apsidal month in sync for quite some time):
300 years = 159½ Mars = 3710½ syzygy and 50.0 times was the line-of-apse overtaken by the line-of-nodes.
558 years = 47 Jupiter = 6902½ syzygy and 30.0> times was the line-of-nodes overtaken by the (analog) line-of-sideral-position.
P.S. the Ark of Noah measured 300 x 50 x 30, what a coincidence …
Longitude of ascending node = 18.6y
18.6 x 75 = 101 Jupiter-Uranus conjunctions (1395 years)
(75:100 = 3:4)
Some Saros cycle links to Fibonacci & phi:
1 Saros = 223 synodic months (Earth-Moon conjunctions)
34 x 223 (=7582) synodic months = 55 x 149 (=8195) Moon orbits/rotations = 613 years
(8195 – 7582 = 613)
55 / 34 = phi (both Fibonacci numbers)
(613 = 34 x 18,-1)
223 / 149 = 1.4966442
1.4966442 x 446 = 445 x 1.5
446 = 223 x 2
445 = 89 x 5 (both Fibonacci numbers)
242 draconic months = 223 synodic months
242 / 149 = 1.624161 (1.625 = 13/8 — 13 and 8 are both Fibonacci numbers)
1.624161 x 1937 = 1936 x 1.625
1937 = 13 x 149
1936 = 8 x 242
http://en.wikipedia.org/wiki/Saros_(astronomy)
21 Metonic cycles = 987 x 5 lunations
http://en.wikipedia.org/wiki/Metonic_cycle
http://en.wikipedia.org/wiki/Lunation
5, 21 and 987 are all Fibonacci numbers
@oldbrew compare Metonic to:
21 years = 2 x 2 x 5 x 13 = 260 lunations, all factors Fibonacci (Metonic 19 years is not 😉
For 260 we have, in addition: (nodical – apsidal) revolutions = 3.50~ (very well aligned orbit), but Metonic doesn’t have anything near. So what’s the secret of accuracy?
B.t.w. the Mayan 260 interval and the Metonic 235 interval both have good accuracy for: lunar phase int, sidereal int, solar day int, stellar day int. Of course, both run out of stellar accuracy due to precession after ~72 years.
Chaeremon says: ‘So what’s the secret of accuracy?’
Note that 929 Metonic @ 19y = 949 lunar node cycles @ 18.5996y = 979 Saros @ 18.02933y
(929 is a prime number, 949 = 13 x 73, 979 = 89 x 11) – Fibonacci numbers in bold
Any Fibonacci number multiplied by 20 lunations (e.g. 260 = 13 x 20 in your example) will give that type of result because 20 lunations = 1.617 years, just short of phi which is 1.618
Something else: the period of 929/949/979 above is 17651 years.
17651 x 93 = 929 x 1767 years (see Chaeremon comment: April 28, 2014 at 12:30 pm)