*This is an open thread for Eclipses, Moon cycles and Inner solar system Observations to run in parallel with Ian Wilson and Paul Vaughan’s technical discussion.*

## Eclipses, Moon cycles and Inner solar system Observations – open thread

Posted: December 12, 2014 by**tallbloke**in moon, solar system dynamics

Comments

Sorry we’ve had to corral the discussion over on the technical workshop, but on the bright side, anything goes here. 🙂

NASA: “Earth’s magnetotail extends well beyond the orbit of the moon and, once a month, the moon orbits through it,” says Tim Stubbs, a University of Maryland scientist working at the Goddard Space Flight Center. “This can have consequences ranging from lunar ‘dust storms’ to electrostatic discharges.”

Every time of ‘new moon’, moon finds itself sheltered from solar wind and the CMEs proton storms. Although the effect small, over period of 3-4 billion of years it is sufficiently large to synchronise lunar orbit time with rotation of the sun’s magnetic bulge, longitudinal source of the enhanced solar activity.

http://www.vukcevic.talktalk.net/LFC7.htm

A note for Paul in his and Ian’s private thread.

It’s 31 + 31 + 44 + 31 + 31 + 44 + 27 = 239 (tropical years)

https://tallbloke.wordpress.com/2014/12/06/ian-wilson-are-the-strongest-lunar-perigean-spring-tides-commensurate-with-the-transit-cycle-of-venus/comment-page-1/#comment-94499

The Lunar perigee-syzygy solar year series doesn’t repeat well with Venus Transit cycle intervals. Perigee and syzygy fall out of sync with each other, and both fall out of sync with the Venus Transit cycles.

Vuk – I know that you know that you meant “full moon”… I’ve made the same mistake before…

Any speculations as to the source of the solar “magnetic” bulge?

Hi Bob

Thanks. That is funny indeed, I was thinking about not making a mistake, having in mind fully lit moon, and as you noted, despit of it I wrote wrong term. (btw) in my native language they are: new moon= mlad mjesec (young moon or sometimes mlad = new) and full moon = ? (ustap); and since there is no English translation brain went to the Freudian fail-safe.

I read post twice and never realised the error.

Bob Weber says:

Any speculations as to the source of the solar “magnetic” bulge?Dr. Svalgaard (in his early days) noticed repeating pattern and wrote a paper (1975)

I think he called it ‘rigid structure’. In the early 2000s NASA-JPL’s Dr. J. Feynman (sister of Richard) did some further research, she called it magnetic memory.

Polar graph I constructed clearly shows anomaly and AFAIK is unique, I called it ‘magnetic bulge’.

I have no clear idea where cause might come from, but clearly must be some reason for it.

Abstract: ‘On January 4, 1912 – almost exactly 100 years ago – both a full Moon and a lunar perigee occurred, with these two events separated by only a few minutes of time and with the Earth near perihelion. The resulting lunar distance (356,375 km) on that date stands as the closest approach of the Moon to the Earth in an interval of more than 1400 years.

The centennial of this extreme lunar perigeeis an appropriate time to consider the effect of lunar distance on the range of ocean tides.’‘http://adsabs.harvard.edu/abs/2012AAS…21911503O’

Link via: http://en.wikipedia.org/wiki/Perigean_spring_tide#cite_note-3

Venus was nowhere near conjunction with Earth on that date according to the solar simulator.

[re: Ian Wilson: Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?]

This graphic shows how the clouds together with the polar vortex works.

There is another cooling mechanism. If the polar vortex in the winter is not symmetrically above the polar circle, the exchange of air in the troposphere and the heat is dissipated into space. When the vortex is strong air exchange is small.

Let’s see how the temperature is distributed in the South Pacific. Permanent circulation is able to locally change the temperature. And surfaced ocean currents.

If the greenhouse effect works, how to explain that in America in November, the temperature was like in January? Should fall gradually. I wanted to show that the satellites demonstrate that the greenhouse effect does not work.

It works just the sun and the albedo. Sorry.

The current position of the polar vortex.

High solar activity clearly changes the pressure above the polar circle.

Plotted a range of Perigee/Syzygy data points 1599-2076 (.csv file available by email):

[hope the URL works]

Wikipedia: ‘On March 6, 1962, the Ash Wednesday Storm surge coincided with perigean spring tide, and for the following 65 hours inundated the entire Atlantic coastline of the United States from the Carolinas to Cape Cod. This disastrous event resulted in a loss of 40 lives and over 500 million dollars of property damage’

No correlation with Venus-Earth positions on the solar simulator.

[re: Ian Wilson: Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?]

Bit of layman waffle; I read the sun and the moon can draw a tidal bulge over the equator. The coriolis effect moves surface water in an easterly direction. This sun warmed water ends up on the coast of Peru around Christmas time, hence El Nino. This effect has been observed long before so called man made CO2 was being produced. Anything in this theory?

Richard 111: Yes, Ian Wilson has been working on this stuff. Have a poke around on the site with the search function.

Ah! Got it. Post dated November 15th. Much reading to do. Thanks.

The 243 year Venus-Earth period ‘drifts’ at least partly because:

9883 Venus = 6080 years = 3803 conjunctions

but

243y x 25 = 6075 years (6080 / 25 = 243.2y)

Not quite sychronized, but:

6080 = 320 x 19y so very close to the 19 year lunar Metonic cycle (itself about 1.5 hours less than 19 years, or 2 hours more than 19 tropical years)

oldbrew

As previously shown, 243yr transit cycles don’t repeat that many times in a row, some are at 235yr.

events

event series

event clusters

conceptually (philosophically) different

different math

ongoing misunderstanding / misinterpretation / misrepresentation

assuredin the absence of conscious distinctionno point in arguing the length of cats with someone who’s measuring dogs and calling them cats

hoping the community will evolve past this definitions (aggregation criteria) impasse eventually (no progress notable so far, unfortunately)

this note offered to help clarify the root of philosophically fundamental divisions within the community, divisions which will hopefully be transcended sooner rather than later

– –

ren (December 14, 2014 at 9:51 am ) wrote & linked:

“This graphic shows how the clouds together with the polar vortex works.“That’s an effective way to get the point across succinctly.

(1 image showing a ring of clouds around the polar night + 1 simple, clear sentence)

Paul V: this note offered to help clarifyFeedback: It doesn’t.

Suggestion: Try giving specific examples to illustrate your definitions of:

events

event series

event clusters

oldbrew said:

December 14, 2014 at 11:37 am

Unfortunately, oldbrew, all this tells me is that you have not understood the key result of my paper.

My paper shows that the ~ 243 year drift of the pattern of Perigean spring tides with respect to the tropical year is synchronized with the ~ 243 year drift of the (pentagonal) pattern of the Venus with respect to nodes of Venus orbit.

The paper says absolutely NOTHING about individual Perigean Spring tidal events and the specific

alignments of Venus and the Earth.

oldbrew said:

December 14, 2014 at 2:15 pm

oldbrew, Now this is much more constructive comment – further investigation would be helpful in the underlying physical reasons for this slow drift.

Ulric said:

“The Lunar perigee-syzygy solar year series doesn’t repeat well with Venus Transit cycle intervals. Perigee and syzygy fall out of sync with each other, and both fall out of sync with the Venus Transit cycles.”

If Paul and I had to repeatedly stop and explain the basics to you Ulric, we would not be able to achieve anything over at the workshop. We included you in the workshop because we value your knowledge and input, however, you just used the opportunity you were given to repeatedly post vacuous statements like those above.

e.g.

1. “Perigee and syzygy fall out of sync with each other”

Yes we have repeatedly said that the 31 year Perigee-Syzygy cycle is based upon

9 + 9 + 9 =27 years pattern that slips by 4 years to re-establish synchronization.

Hence, you are just repeating an obvious point that has little or no bearing upon the final outcome.

What could we have done to stop you from doing this? We were left with little alternative other than to create an alternative forum were you would not cloud the Workshop discussion.

2. “…both fall out of sync with the Venus Transit cycles.”

My paper shows that the 31 year Perigean/Syzygy spring tidal cycle slowly drifts with respect to the tropical year in such a way that it repeats itself roughly once every 243 years.

My Paper also shows that whenever there was transit of Venus, the 31 year Perigean/Syzygy spring tidal cycle would drift through almost precisely the same date and time in the Gregorian calendar. This indicated that the ~ 243 year cycles were very nearly synchronized.

The key words here are “..very nearly synchronized” – the conclusions and the abstract of the paper both highlight that ~ 243 year drift of the pattern of Perigean spring tides with respect to the tropical year slowly slides with respect to the ~ 243 year transit cycle of Venus.

Again, you keep stating an obvious point that has little or no bearing upon the final outcome. And again, We were left with little alternative other than to create an alternative forum were you would not cloud the Workshop discussion.

Believe me, this the last thing that we wanted to do but you left us with no choice.

Paul Vaughan says on the workshop thread:

Submitted on 2014/12/14 at 5:39 pm

I’m becoming increasingly convinced that 243 / 34 is the root of WWI & WWII excursions from RI & SCD. This is passing the diagnostics I’m throwing at it.

During 2030-2070 (a) 34 aligns differently with 243, (b) the polarity reversal is in the opposite direction, and (c) RI & SCD will be different, so without good historical proxies, we have no analogs. Since there’s no available avenue by which to cheat with analog odds, the only available option is deeper exploration of fundamentals (via iterative refinement) to the point of geometric lockdown. This appears feasible.

However, there are ethical issues. If we could know, would we want to?

I would definitely not trust politicians, the government, and the general public to understand (without potentially severe misinterpretation) and respond appropriately. There would just be floods of misunderstanding & propagandistic distortion artistry, especially if financial & military (& perhaps healthcare) strategists perceived a security risk.

We have to be satisfied with exploring for entertainment purposes & no credit in such a context. I absolutely would not trust politicians, the government, and the general public to understand (without potentially severe misinterpretation whether deliberate or accidental) and respond appropriately even if a perfect forecast was given. The darker side of human nature won’t be overwritten by any forecast no matter how perfect.

On the brighter side: Nature’s still beautiful to simply explore.

[Moderation note] we’ll discuss this one here pleaseIW: OK, my reading of ‘commensurate’ wasn’t what you intended.

Ian:

Example; at 3 Venus transit cycles (3*152*583.922d), it’s 5.8 days past 9016.5 lunations, and 8.8 days past 9663 anomalistic months. I don’t see how you can claim that to be very nearly synchronized.

And exactly what use is something that drifts in respect to the solar year?

Ian said:

“Yes we have repeatedly said that the 31 year Perigee-Syzygy cycle is based upon

9 + 9 + 9 =27 years pattern that slips by 4 years to re-establish synchronization.”

There’s nothing at 9. It goes in 8’s then drops back a year at 4*8 to re-establish synchronization at 31 years.

“My paper shows that the 31 year Perigean/Syzygy spring tidal cycle slowly drifts with respect to the tropical year in such a way that it repeats itself roughly once every 243 years.”

Which is essentially gobbledegook as the 31yr cycle breaks down after two steps and requires a 44yr step to reach 106 years. The 106 repeats to 212, and then it takes a further 27 to reach 239.

(or +31 to reach 243)

It seems that I am the one that has to repeatedly explain the basics to you.

Paul, the only ethical issue is ones responsibility to share a forecast for the benefit of all, keeping quite about it would be a travesty. Though it would certainly have to be fully deterministic for that to be valid.

The general public would understand readily and it would make good sense to them. The IPCC et al will just remain ignorant until climatic circumstances force them. While professional conflicts are guaranteed in the associated fields of solar physics, astronomy, climatology, and meteorology because of the scale of paradigm shift. Conflict is also guaranteed in this forum, as our individual research paths will inevitably challenge the validity of others.

Gents: am I right in thinking that the lines of nodes and line of apse contra-rotate and cross each other every 4 years? If so, then would that mean Ulric’s 8yr scheme makes some practical sense?

UL: ‘it’s 5.8 days past 9016.5 lunations, and 8.8 days past 9663 anomalistic months. I don’t see how you can claim that to be very nearly synchronized’

In 729 years a slip of a few days falls within the term ‘very nearly’ doesn’t it?

Btw I find 7 perigee cycles = 766 synodic months = 61.931364y i.e. just under 2 x 31y.

oldbrew said:

“Btw I find 7 perigee cycles = 766 synodic months = 61.931364y i.e. just under 2 x 31y.”

You mean 7*8.85yr the apse cycle. That’s one lunation short of the full moon cycle:

http://en.wikipedia.org/wiki/Full_moon_cycle#Matching_synodic_and_anomalistic_months

8.8 days is several and not “a few”.

UL: ‘one lunation short of the full moon cycle’

Good point, thanks.

Also: 223 apse cycles = 1973 tropical years, so as 223 synodic months = 1 Saros:

766 x 223 SM = 766 Saros = 7 x 223 apse cycles = 7 x 1973 TY

There are various other numbers arising from this.

Ulric: You mean 7*8.85yr the apse cycle. That’s one lunation short of the full moon cycle:During the year we only see 12 full moons from Earth, even though the Moon has gone round the Earth 13 times.

Could it be that the ‘slippage’ of one lunation between the multiple of the apse cycle and the full moon cycle happens for a similar reason?

8.8 days is several and not “a few”.8.8 days in 729 years is 0.003%

@tallbloke says (December 14, 2014 at 7:50 pm): “Gents: am I right in thinking that the lines of nodes and line of apse contra-rotate and cross each other every 4 years?”

Contra-rotate: yes; cross each other: yes; 4 years: no, it happens (if both nodes treated equal) every

3years (almost exact) and otherwise 6 years.In the other thread Oldbrew posted a nice link for “6 years relative to the wobbling plane”

http://www.cyclesresearchinstitute.org/cycles-astronomy/lunar.shtml

Chaeremon, thanks, my bad memory. i remember now you and I went through this on an earlier thread. It is pretty much exactly 3 years as I remember, which is remarkable in itself. What I can’t remember is how many degrees round the circle the crossover occurs after the previous one. Any idea before I bend my head round working it out?

TB: ‘During the year we only see 12 full moons from Earth, even though the Moon has gone round the Earth 13 times.’

Depends which year. In every 19 years there will be 7 with 13 full moons (19 x 12,+ 7 = 235)

Tallbloke,

Put it this way, 3005.5 lunations is very close to 243 solar years, but several days away from the Venus transit cycle, so they are not in close sync.

And the lunar perigee and syzygy are ~1 day apart at 243yrs, while they are much closer together at 239 years, so the idea of 243 perigee syzygy cycles repeating, is illusory, The numbers are wrong.

Or rather, 9016.5 lunations is very close to 729 solar years, but several days away from the Venus transit cycle, so they are not in close sync.

TB: ‘It is pretty much exactly 3 years as I remember, which is remarkable in itself. ‘

I make the 6-year period one tropical year short of 329 x 6, i.e. 1973 TY / 329 = 5.9969604 TY.

(see your lunar chart)

@tallbloke says (December 14, 2014 at 10:02 pm) “how many degrees round the circle the crossover occurs after the previous one.”

I’m using Solex but it reports the Earth ecliptic° for apsidal and the Moon ecliptic° for nodical, so: sorry I can’t compare here.

But in terms of syzygy (3 years are 37.0~ synodic) that’s about -4° to -3°.

And for 6 years (74.17~ synodic), mathematically, that’s about ~16.88% of 360° (~61°).

Ulric: And the lunar perigee and syzygy are ~1 day apart at 243yrs, while they are much closer together at 239 years, so the idea of 243 perigee syzygy cycles repeating, is illusory, The numbers are wrong.Yeah, I asked on the workshop thread if it might be the case that over the long term, the Transit cycle might turn out to be coincident with the 1/5 precession of the V-E conjunction cycle at 239.8yr (or 243yr if looking at it another way). Librations can be over long periods.

150 Ea-Ve synods has nothing to do with the transit cycle.

What does have a slow precession against the solar year is the transit cycle itself. Here’s a geocentric plot of Venus every 583.922d at ~235yrs (147 Ea-Ve synods):

and at ~243yrs (152 Ea-Ve synods):

Ulric Lyons said:

December 14, 2014 at 7:39 pm

Please read pages 85 and 86 of my paper and look at table 1. It discusses both the 239 lunar cycle and the 243 lunar cycle. It raises many of the points that you have put forward with regards to the lunar cycle. Then please go and look a 243 year [and NOT 238 year) envelop in the lunar distance when aliased at one (tropical year cycles).

Then go back to figure 4 and draw a horizontal line across the diagram at 119.5 years (=239.0/2 years). If what you are saying about the relative orbits of Venus and the Earth is correct then this line should evenly split the sinusoidal curve, with 50 % above the line and 50 % below. Even a novice can see that it clearly is not split in half.

The sinusoidal curve in figure 4 of my paper is almost perfectly split in half (in a vertical direction) by the curve I have drawn in the diagram at 121.5 years (=243.0/2 years).

This means that, if we observe at the times when Venus, the Earth and the Sun align at inferior conjunction, and we note the slow (primarily north-south or south-north) passage of the closest position of Venus to the centre of the Sun (as seen from the Earth), then the times at which the drifting position of Venus (with respect to the Sun) appears to cross the Sun’s equator are separated by 121.5 +/- 8 years (i.e. 129.5 years and 113.5 years). To confirm that this is indeed the case over a 700 year period between 1600 and 2300 A.D., look at figure 2 in my paper. Last I heard, 129.5 + 113.5 = 243.0 years and NOT 239.0 YEARS!

I am claiming, with the use of direct observational data, that this 243 year cycle applies between 1 and 3000 A.D., no more and no less. I make no claim as to what happens outside this particular epoch, although I do not expect things to change by that much for a thousand years or so before and after the epoch that I have been studying.

Note: Venus’s orbit is inclined by roughly 3.39 degrees with respect to the ecliptic. This means that Venus does not necessarily lie in front of the Sun when it passes between the Sun and the Earth roughly every 8 years. The inclination of Venus’s orbit means that location of Venus when it is nearest to the centre of the solar disk (as seen from the Earth) will slowly drift north-south and then south-north, passing across the Sun’s equator roughly every 121.5 +/- 8 years. It is important to realize that at the precise time that this north-south drift of Venus crosses the Sun’s equator, Venus may not be anywhere near the Sun (as seen from the Earth), since it the drift that sets the 243 year

cycle and not necessarily the 7.9933 year penta-VE cycle.

Ulric Lyons said:

December 14, 2014 at 11:46 pm

150 Ea-Ve synods has nothing to do with the transit cycle.

I have been saying this since I have been blue in the face. Thank God you have finally realized this.

Ulric Lyons said:

December 15, 2014 at 1:08 am

“What does have a slow precession against the solar year is the transit cycle itself. Here’s a geocentric plot of Venus every 583.922d at ~235yrs (147 Ea-Ve synods) and at ~243yrs (152 Ea-Ve synods).”

Again you have finally stumbled upon the obvious. Please read my post above at December 15, 2014 at 4:05 am.

Ulric Lyons said:

December 15, 2014 at 1:08 am

Those images show that you are still fixated with the east-west movement of Venus and totally ignoring the equally important north-south movement of Venus with respect to the Sun (as seen from Earth).

Ian Wilson says: December 15, 2014 at 4:30 am

“Those images show that you are still fixated with the east-west movement of Venus and totally ignoring the equally important north-south movement of Venus with respect to the Sun (as seen from Earth).”

Does this mean we have a 3-4D Solar system, rather than a 2D surface? No wonder that all is non- commensurate in time, and in its conjugate. Is this a requirement?

Ulric Lyons says (December 14, 2014 at 10:10 pm) wrote:

“[…] the idea of 243 perigee syzygy cycles repeating, is illusory, The numbers are wrong.”Again:

You’re using different aggregation criteria.

You can’t refute a statement about the average length of cats by measuring the length of a single dog.

Envelopes (comprised of

groupsof events) differ conceptually from single events.Lunar range is a

continuousvariable.The degree of fullness &/or newness of the moon is also a

continuousvariable.Similarly the Venus variable Ian explored is continuous.

The lunar range

envelopeis 243.1 and this isgeometrically proven. There’s nothing to debate there. Either you acknowledge a valid proof or you expose your ignorance.Maybe you can find a way to point to astronomical events you find interesting

withoutmisrepresenting Ian’s work.TB: I outlined the calculation for the ~4 year cycle in the workshop thread. It matches Horizons lunar range exactly (because it’s a geometric proof). I’ve been communicating on the assumption that everyone already graphed range independently and realized this ….but reading most of the commentary in this thread I’m left wondering if anyone looked at any of the Horizons output — it looks more like the discussion is about some twisted (for what purpose?) misrepresentation of what Ian actually wrote in his paper.

Ian Wilson says, in reverse order:

“Those images show that you are still fixated with the east-west movement of Venus and totally ignoring the equally important north-south movement of Venus with respect to the Sun (as seen from Earth).”

As if the north-south movement was equally important to the precession! Not.

“Again you have finally stumbled upon the obvious.”

Oh please Ian, I’ve known it for many many years. And your comment at December 15, 2014 at 4:05 am doesn’t even address the precession.

“I have been saying this since I have been blue in the face. Thank God you have finally realized this.”

Finally realised? Very funny, it was immediately apparent without any help from God. Who raised such a figure in the first place?

“Last I heard, 129.5 + 113.5 = 243.0 years and NOT 239.0 YEARS! ”

I never said the Venus transit was 239yrs. As if I need an explanation of the transit cycle!

The conclusion is that the lunar syzygy-perigee cycles are NOT in close sync with the Venus transit cycle, because they repeat best at 239 and not 243 years.

Ulric: As if the north-south movement was equally important to the precession!The precession and N-S motion are both functions of the changing orientation of the relative inclinations of Ea and Ve orbits with respect to time. You don’t get one without the other. And you don’t see a transit unless the intersection of Venus’ orbital plane with Earth’s orbital plane lines up between Earth and Sun as Venus itself crosses Earth’s orbital plane. So the notion that the Z component is ‘less important’ than the X-Y components is just… not even wrong.

lunar syzygy-perigee cycles are NOT in close sync with the Venus transit cycle, because they repeat best at 239Ian doesn’t make this claim. Ian states that: “An analysis of the 31/62 lunar peak tidal cycle shows that the sample tidal events reoccur on almost the same day of Gregorian (seasonal) calendar after 106 years, and then they reoccur on almost the same day after another 137 years. This produces a two-stage long-term repetition cycle with a total length of (106 + 137 years =) 243 years.”

Conclusion: Read the paper.

Paul Vaughan,

I have evidenced not one dog, but the ratio of 2956 dogs to 3168 cats. While your dog-cat cross breed doesn’t seem to know when perigee-syzygy actually occur. Your envelopes misrepresent the real events.

And I have already shown that perigee-syzygy is not in close sync with Venus transits, which you are exposing your ignorance of.

Tallbloke,

By definition, from transit to transit as they precess, there is no north-south change BECAUSE THEY ARE TRANSITS. Not even wrong my foot!

Tallbloke said:

“Conclusion: Read the paper.”

Done, and fully commented on above. Lunar perigee-syzygy sync with the solar year is poor at 243yrs and slips considerably when repeated. While Lunar perigee-syzygy sync with the solar year at 239yrs is far tighter and can be repeated several times. The 243 is a fudge.

Ulric: there is no north-south change BECAUSE THEY ARE TRANSITS.Yes there is. It’s the reason why Venus crosses the Sun at different solar latitudes as seen from Earth on successive transits. Sometimes it misses altogether and no transit is seen

Ulric: Lunar perigee-syzygy sync with the solar year at 239yrs is far tighter and can be repeated several times.So what? That has nothing to do with what Ian is setting out to prove. Read what I wrote:

Ian states that: “An analysis of the 31/62 lunar peak tidal cycle shows that the sample tidal events reoccur on almost the same day of Gregorian (seasonal) calendar after 106 years, and then they reoccur on almost the same day after another 137 years. This produces a two-stage long-term repetition cycle with a total length of (106 + 137 years =) 243 years.”

I don’t need to read it again, the 243 is a fudge. The long term repetition cycle is 239 years.

[Reply] I don’t like people’s work being deliberately misrepresented on the talkshop. You came back here uninvited, and now you can sod off again.‘the sample tidal events reoccur on almost the same day of Gregorian (seasonal) calendar after 106 years, and then they reoccur on almost the same day after another 137 years’

Presumably not a coincidence that 137 – 106 = 31 years?

Just to remind people who will be continuing to take part in this discussion:

Transits of Venus are among the rarest of predictable astronomical phenomena.[1] They occur in a pattern that generally repeats every

243 years, with pairs of transitseight years apartseparated by long gaps of121.5 yearsand105.5 years. – WikipediaNote that this means one of the transits will occur at

.~~135~~137.5 yearsIan Wilson has discovered something very interesting, which is that our Moon has a similar length cycle composed of similar length sub-periods at

137 yearsand106 yearswhen the strongest perigean tides occur on the same calendar day of Earth’s year, which also add up to243 years, the same Venus transit cycle period.Note these periods are in an approximate 9:7 ratio (0.5%).

Note also that the

Eight years apartis the same period as the conjunction cycle of Earth and Venus. This 5-legged conjunction cycle completes 1/5 of it’s precession in 239.8 years.There is also a lunar cycle at 239 years, which Ulric was crapping on about when I booted him for his shitty attitude. This period is also of interest, but it is not the principle focus of discussion regarding Ian’s paper, which finds the strongest perigean tides happening on the same Gregorian Calendar day at the

106 and 137 yearperiods.TB: ‘Note that this means one of the transits will occur at 135 years.’

Shouldn’t that be 137.5 years = 243 – 105.5 ?

OB: 0(+8)=8(+121.5)=129.5(+8)=137.5(+105.5)=243 so yes, thanks.

Waves in the stratosphere at high latitudes are visible in the winter, is missing UV. Thus, other factor must be cause of their formation, especially since involve a with a sudden rise in temperature in the stratosphere. It can be seen that the waves are formed in the upper stratosphere. It has to therefore be other factor sunny.

So now you’ve got:

Venus transits: 137.5y + 105.5y (difference = 32y)

Lunar tidal cycle: 137y + 106y (difference = 31y)

As a model that is – exact numbers may or may not line up 100%.

‘Note also that the Eight years apart is the same period as the conjunction cycle of Earth and Venus.’

So in a model of 105.5+32+105.5 the middle 32 years is 4 V-E cycles (in fact just short of 32y).

And in a model of 106+31+106 the middle 31 years is 3.5 apse cycles (in fact just over 31y).

In that way both 137:106 and 106:137 are possible in theory, as are 137.5:105.5 and 105.5:137.5

Two lunar tidal cycles = 55 apse cycles = 486.61~y.

Ulric Lyons (December 15, 2014 at 12:03 pm) misrepresented:

“Your envelopes misrepresent the real events.”Again: They’re not “mine”.

We’re discussing

“RG Range; distance from coordinate center (AU)”from NASA Horizons.

That’s a

continuous(not binary) variable.The moon doesn’t suddenly teleport to perigee and then suddenly teleport away from it.

Ulric is saying

NASA’s “RG Range; distance from coordinate center (AU)”

“[…] misrepresent the real events.”As with agents LS, WE, PG, MM, WHT, & SM, sensible discussion with UL is impossible by design.

[Reply] I’ve relieved you from the burden of attempting it.tallbloke said:

December 15, 2014 at 1:57 pm

Tallboke,

Care needs to be taken when determining the cycle length for the transits of Venus.

There are two primary alignments needed to produce a transit of Venus across the Sun:

1. In the plane of the ecliptic: Venus and Earth must be at inferior conjunction i.e. Venus, the Earth and the Sun must be aligned in the orbital plane.

2. Perpendicular to the plane of the ecliptic: Venus must be located at or near one of the two nodes of its orbit. [Note: The ascending node of Venus’ orbit is where Venus crosses the Earth-Sun plane (i.e. the ecliptic) from below to above, while the descending node is where Venus crosses the plane from above to below.]

Hence, Venus and the Earth must be aligned at a time where Venus is located near one of the nodes of its orbit for a transit to occur.

Because the Sun subtends and angular size of ~ 32 arc minutes, the geometry of the alignments mean that it is possible for Venus to transit the Sun twice during the period where Venus lies near one of its nodes. The pairs of transits are separated by almost exactly 8 years. This pairing of transit events often confused people who are trying understand the pattern of spacing.

The current spacing, over a seven hundred year period centred upon the present, is:

121.5 +/- 8 years i.e. if you consider the first of each of the 8 year pairs, then the first of these particular transits are separated from the second by 129.5 years and then second from the third by 113.5 years, leading to a total cycle length = 129.5 + 113.5 years = 243.0 years.

Please see figures 2 and 3 of the following paper to confirm that this is the case:

“Transits” are fleeting events. They’re temporary symptoms of an underlying

continuousphysical process. Those attempting to straight-jacket the discussion into a narrow focus onmomentary fleeting symptomsof the underlying continuous physical process are misrepresenting continuous variables as binary variables. This is an effective way to sabotage the discussion.tallbloke says: December 15, 2014 at 1:23 pm

…………

106 years periods (see the link) are strongly associated with low solar activity (possibly just a coincidence).

PV: as it says at the top – ‘This is an open thread for Eclipses, Moon cycles and Inner solar system Observations’. The restrictions that apply to the technical thread are not in place here.

Ian, thanks for your explanation. Have you calculated the maxima and minima for the periods over the long term?

Paul Vaughan said:

December 15, 2014 at 5:20 pm

““Transits” are fleeting events. They’re temporary symptoms of an underlying continuous physical process.”

Paul,

I know that you understand but for the sake of the others here, I will try to elaborate.

In my paper, I only use the transit dates of Venus to locate the times at which the slow continuous north-south (or south-north) movement of Venus crosses the Sun’s equator. Paul has implicitly understood that I am only using the transits to assist me in tracking an underlying continuous process.

This has been a source of confusion for some. I wish to apologize for not explaining this particular aspect well enough so that others could appreciate the subtlety of this phenomenon.

oldbrew,

I am very sorry that you, Chaeremon, others have been moved off the Workshop thread to this open thread. Unfortunately Ulric was using the posts of others to flood the workshop with his own misunderstandings and confused thinking. Hopefully, you and Chaeremon will be able to bring your expertise to bear in this open thread. I know that I will be tracking what you are saying as the debate evolves.

Ulric is a brilliant man who has a lot to contribute to this topic. Unfortunately, he has the diplomatic skills of a wooden post. He doesn’t seem to appreciate that there are times where he has misunderstood the problem he is criticizing. In these circumstances, no amount of explanation seems to mollify him.

Ulric is correct in saying that a 239 year pattern is a marginally better fit to the long-term changes of the 31 year perigee/syzygy cycle. I actually show this in my paper. However, he misses the point that this is not what I am claiming in my paper.

[Note: A basic underlying assumption in my paper is that tidal forces that peak at the same point in the seasonal calendar are more effective at influencing the climate than peak tides that drift through the tropical year.]

What I find is that the 31 year perigee/syzygy peak tidal cycle slowly drifts through the seasonal calendar. The only reason that I mention the 239/243 year lunar cycle is the fact that it suggested that I investigate the following:

I noticed that every time the north-south drift of Venus (at the times of inferior conjunctions of Venus and the Earth) crossed the Sun’s equator, the slow drift of the 239/243 year lunar through the seasonal calendar passed through roughly the same day of the year. Indeed, this commensurability was so good that it only drifted by -7 +/- 11 hrs over a period of 3,000 years.

Paul has subsequently shown that there is a natural ~ 34/243 envelope in the lunar distance when it is annually aliased. This discovery has come out of Paul’s discussions of the results of my paper and its importance will be clearer as Paul’s investigation unfolds.

@oldbrew (December 15, 2014 at 6:39 pm) speaking of

restrictions not in place here:1] we’ve already recognized (somewhere?) that 18.6 and 8.85 have common divisor 3. Now that allows to eye 10/3 of LNC and 20/3 of LAC. The difference between these intervals is 62 – 59 = 3 years (the 3 year wobbling plane for both nodes).

2] so we can take the wobbling plane for completing Ian’s 2 x 31 years 😎 and base the time-frame on observable occurrences — for which we attempt ~same calendar date (62 + 3 years).

3] this gives the following: 804 synodic = 65.00~ years perfect eclipse cycle [1, eclipses align syzygy with draconic], minus 3 years (1 x wobbling plane) = 822.0~ apsidal.

4] since the Unidos series (1 x Inex + 2 x Saros) has ~39 members, a triple of its eclipses aligns perigee at syzygy with the ~same calendar date, at 2585.0~ apsidal 🙂 can I say q.e.d.

5] shifting the phase of LNC and LAC cannot change much (except that we may not observe eclipses at syzygy), so I think we have a general schema here.

[1] Unidos, H. v. Gent writes: nearly same date in Julian/Gregorian calendar.

Chaeremon, forgive me, what time period is “2585.0~ apsidal” referring to? Anomalistic months? = 195.01 years = 3 x 65 years ??

No restrictions on this thread, and your observations are very welcome.

@tallbloke: yes (I used the monthly apsides for anomalistic month). No confusion intended.

B.t.w. the 195.01 years you calculated looks “mathematical” only; I’ll launch Solex (later in the day) and check the almanacs for what drift we can expect, also in ecliptic longitude°. I somehow think that the wobbling plane contributes to balancing the whole scenario.

IW says: ‘What I find is that the 31 year perigee/syzygy peak tidal cycle slowly drifts through the seasonal calendar’

Looking for a match between ‘apse cycles’ (8.847345 years) and whole years I found:

452 apse = 3999 years = 31 years x 129 (= 93y x 43)

452 x 2 = 904, 43 x 21 = 903 i.e. one less.

Is that related to the ‘drift’ e.g. if 21 apse cycles were exactly equal to 186 years would there be no drift? (21 a.c. = 185.79424y)

43 x (186 – 185.79424) = one apse cycle.

88 apse cycles = 487 V-E conjunctions.

Chaeremon says: ‘this gives the following: 804 synodic = 65.00~ years perfect eclipse cycle [1, eclipses align syzygy with draconic], minus 3 years (1 x wobbling plane) = 822.0~ apsidal.’

As UL pointed out earlier (quoting Wikipedia here):

767×SM = 822×AM = 22650 days = 55×FC + 2 days = 62 years + 4 days‘Matching synodic and anomalistic months’

http://en.wikipedia.org/wiki/Full_moon_cycle#Matching_synodic_and_anomalistic_months

Also 37 SM = 2.9915~y and 767 + 37 gives 804 SM = 62 + 3 = 65 years

Note: 2 Inex = 716 SM = 777 draconic months = 61 draconic years (777 – 716)

oldbrew (December 15, 2014 at 6:39 pm) wrote:

“PV: as it says at the top – ‘This is an open thread for Eclipses, Moon cycles and Inner solar system Observations’. The restrictions that apply to the technical thread are not in place here.”OB unfortunately you’ve misinterpreted my comment, which was:

Paul Vaughan (December 15, 2014 at 5:20 pm ) wrote:

““Transits” are fleeting events. They’re temporary symptoms of an underlying continuous physical process. Those attempting to straight-jacket the discussion into a narrow focus on momentary fleeting symptoms of the underlying continuous physical process are misrepresenting continuous variables as binary variables. This is an effective way to sabotage the discussion.”I didn’t object to the exploration of binary aggregation.

I objected to egregiously psychologically manipulative attempts to LIMIT discussion to

ONLYbinary aggregations.More generally I’m objecting to the propaganda tactic of deliberately

narrowing(the polar opposite of opening) the terms of discussion to an infinitesimal subspace specifically engineered to facilitate thought policing (as is done 24/7 at wuwt and as 2 commentators have recently tried to import to the talkshop).It’s an artificial (political) world in which

ONLYbinary aggregations are allowed as components in the construction of meaning.Regards

From the technical thread – TB says:

‘Maybe it’s time to take a look at Mars and its moons too. Oldbrew might like to tell us about some of his discoveries on that front on the open thread.’

A correlation can be proposed between the rotation and orbit periods of the Earth and Mars:

356 (89 x 4) Mars rotations = 8765.7524 hours

365.25 days = 8766 hours

Mars orbit = 686.98 days, obviously close to 687 x 24 hours.

(8766 / 8765.7524) x 686.98 = 686.99937

OB: Have you looked at Mars moons at all? I thought you might have.

TB: yes, their orbit ratio is 25:99 i.e. almost 1:4 (= 25:100).

13 Deimos = 16 Mars rotations (99.977% true)

Best for Phobos was: 29 P = 9 Mars rotations (99.84%)

Both are synchronous (orbit time = rotation time) as are most solar system moons.

Some say Phobos is approaching the Roche limit where the gravitational force of Mars overwhelms it, or so the theory goes. Don’t hold your breath though.

Chaeremon says: ‘3] this gives the following: 804 synodic = 65.00~ years perfect eclipse cycle [1, eclipses align syzygy with draconic], minus 3 years (1 x wobbling plane) = 822.0~ apsidal.’

To get the ‘65.00~’ to a whole number, multiply everything by 272 (

34x 8):272 x 804 synodic months = 17681 years = 272 x 65, +1 (or

34x 13 x 8 x 5, +1 as Fibonacci)Since 12 lunar months = 1 lunar year:

272 x 804 SM =

34x 536 lunar years = 18224 LY = 17681 Y18224 – 17681 = 543 =

34x 16, -1Note also: 17681 = 1768 x 10, +1

Re 1768y, see: https://tallbloke.wordpress.com/2014/10/26/why-phi-giant-planets-update/

@oldbrew: thanks for the connection to 1768y and why phi 🙂

Into another direction, you may be interested in the following observation Re anomalistic month over longer time-frames:

Look at Saros series 117 and 155 they produce duo eclipses (same month begin+end) from 1928 to 2054. The pair in 2054 has virtually the same apsidal distance, but the pair in 1928 diverged by 0.00376~ Gm (!) despite the members being in

parallelSaros series. This divergence appears to develop gradually over 2054 – 1928 = 126 years (haven’t yet checked other possible cases).If ever I was critical to averaging innocent numbers until they accumulate meaninglessness, this is one of the cases.

More Mars: there’s a 521-year lunar period that lines up with it, plus a lot of other stuff ‘nearby’.

If we put 18 Inex into the lunar Eclipse Cycle Calculator:

(http://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm#calculator)

521 years = 537 lunar years = 549 draconic years [DY] (= 1098/2 ‘eclipse seasons’)

= 18 Inex (18 x 358 synodic months = 537 SM x 12 = 716 SM x 9)

and

521 years = 277 Mars orbits = 244 Mars-Earth conjunctions

If 549 draconic years = 244 Mars-Earth conjunctions

then (divide by 61)

9 draconic years = 4 Mars-Earth conjunctions (ratio = 3² : 2²)

Note also:

2 Inex = 61 DY = 716 SM = 777 DM (draconic months)

times 9 gives

18 Inex = 521 years = [etc. – see above]

233 Jupiter-Mars = 520.814y

477 Jupiter-Earth = 520.912y

(477 – 233 = 244 Mars-Earth: see above)

803 Jupiter-Venus = 521.025y

326 Venus-Earth = 521.176y

(803 – 326 = 477 Jupiter-Earth)

847 Venus = 521.072y

2163 Mercury = 520.95y

44 Jupiter = 521.955y

1316 V-Me = 520.873y

2119 J-Me = 520.9286y

1642 E-Me = 520.934y

So all the inner planets and the Moon ‘line up’ around 521 years.

Note for Chaeremon: it’s also 65 years x 8, +1 .

Footnote – the Catalogue of Eclipse Cycles says:

‘Basic Period (Pingr� Cycle, Hyper Saros)

‘Achieves a nearly integer number of calendar years (521 years + 4 days) and anomalistic years (521 years + 5 days). According to Lalande (Astronomie, 3rd ed., vol. II, 195) this cycle was first discovered by A.G. Pingr�. It was rediscovered by Monck (1902) and named Hyper Saros by Alexander Pogo (1935). Also mentioned by Torroja Menéndez (1941) and in Barlow et al. (1944). Van den Bergh lists it as

the Basic Period.’‘http://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm#Basic Period (Hyper Saros)’

@oldbrew yes, 6444 (~Hyper ~Saros) is well known and Prof. George van den Bergh (amateur astronomer) wrote many things about Inex also in his seminal “Periodicity and Variation of Solar (and Lunar) Eclipses, 2 vols.” 1955; a good man and very good work!

@oldbrew 125 full-moon “cycle” periods are commensurate with 141 years, found it by eyeing both ends of duo eclipse intervals 😎

a) 174

3synodic complete 125.0~ full-moon cycles.b) 174

4synodic complete 141.0~ years.Reminds me of the

Ksaya monthin the India system …Oldbrew, what did you name the result of 141 – 125, in general ? couldn’t find it presto with Ctrl-F, but was certain you already had labeled this difference. TIA.

This might be it? 125 FMC x 14 = 1750 FMC:

https://tallbloke.wordpress.com/2014/12/06/ian-wilson-are-the-strongest-lunar-perigean-spring-tides-commensurate-with-the-transit-cycle-of-venus/comment-page-1/#comment-94562

also

https://tallbloke.wordpress.com/2014/12/06/ian-wilson-are-the-strongest-lunar-perigean-spring-tides-commensurate-with-the-transit-cycle-of-venus/comment-page-1/#comment-94582

@oldbrew, yeah that is it (and x 14 looks ever more intriguing). Thanks.

The 125 FMC / 141 years appear to squeeze and release the “torsion” imposed by the 3/6 years wobbling plane; and if so we might find the next “orbital” level (where things somehow turn around for balancing, this I think is probable).

Chaeremon says: ‘we might find the next “orbital” level’

At the 1750 FMC level you have 2079 draconic years.

2079 DY – 1750 FMC = 329

It’s also 1973 tropical years.

1973 TY / 329 = 5.99696 TY = the ‘wobble cycle’

@oldbrew: thanks for the suggestion, but I’m reluctant because with 1973 TY there are pairs with perigee

andapogee each at interval end, and other pairs with ~same apse; this seems already overshoot. Also my spreadsheet shows 106.08LNC.Will have to work harder or have more coffee (compatible both 😉

OK, I use the numbers as a model so reality might differ slightly – but not much, because in the end the Moon can’t be out of sync with itself.

If we accept that 2079 draconic years = 1973 tropical years, the numeric difference is 106.

2079 * 346.62008 = 720623.14 days

1973 * 365.24219 = 720622.84 days

Marginal difference.

2079 / 106 = 19.613207 DY

1973 / 106 = 18.613207 TY (DY – 1)

Paul Vaughan quotes these figures:

Nodal period = 6798.38 days

Apsidal period = 3231.50 days

https://tallbloke.wordpress.com/2014/12/06/ian-wilson-are-the-strongest-lunar-perigean-spring-tides-commensurate-with-the-transit-cycle-of-venus/comment-page-1/#comment-94393

1973 / 106 = 18.613207 TY = 6798.3284 days

1973 / 223 = 8.8475336 TY = 3231.4925 days

Both figures well within 1/10th of a day of the above data.

Then 106 + 223 = 329

(see – oldbrew says: December 18, 2014 at 11:17 am )

Also: (1973 + 1) / 329 = 6

Number of full moon cycles = 1973 – 223 = 1750.

1750 / 223 = 7.8475336 TY i.e. one less than the apsidal period (8.8475336 TY).

@oldbrew (December 18, 2014 at 8:50 pm) it appears we compare apples and oranges, sort of.

The average of your draconic distance, over a 7ka time-frame, is 72062

0.0~ days and that is3days ‘un’marginal difference, sort of.On a sideline you appear to compare, at one interval end the ascending/node, apogee and new-moon, with the other interval end the descending/node, perigee and full-moon. Comparing this all at one of the sides is already very complex and time-consuming for me, and I’m often too impatient to also compare the (2^3) – 1 = 7 additional combinations for each and every opposite case.

For comparison of the years I suggest the 2015 autumnal equinox and same equinox 720620~ days earlier, in astronomical dates that is (courtesy to Solex/11.x)

Both have an eclipse close after (in eg. NASA almanac) for comparison with the draconic year.

@ Chaeremon

If we multiply all the numbers quoted (December 18, 2014 at 8:50 pm) by 7, the results show 766 x 223 synodic months = 766 Saros. That means 766 SM = 7 apsidal cycles.

Also 766 x 239, -6 anomalistic months and 766 x 242, -1 draconic months in the same period.

Which all looks a lot like this Wikipedia entry:

‘The saros is an eclipse cycle of 223 synodic months = 239 anomalistic months = 242 draconic months. This is also equal to 16 full moon cycles [FMC].’

http://en.wikipedia.org/wiki/Full_moon_cycle#Full_moon_cycle_and_the_saros_-_using_the_FMC_for_predicting_eclipses

Wiki numbers are approximate, of course, e.g. with my figures the FMC number is:

12250 / 766 = 15.992167 whereas Wiki just says 16 (= 239 AM – 223 SM)

(7 x 1750 = 12250 FMC but 16 x 766 = 12256)

Since 329 is 987/3 and 1973 TY is 987 x 2, -1 logic tells me to multiply the numbers by 7 x 3 i.e. 21 rather than just 7. This logic: 21 x 47 = 987, and both 21 and 987 are Fibonacci numbers.

Note that none of the numbers for SM, AM or DM above is divisible by 7, but they are found following multiplication by 7 (or 3 x 7 = 21).

[Cross-check: 170818 SM (766 x 223) = 183068 AM and 183068 – 170818 = 12250]

@oldbrew (December 19, 2014 at 9:52 am): I understand most of your figures, you derive them by multiplication (extrapolation of non-linear connections), and I derive mine by division (particularization of non-linear connections).

NP. I’ll proceed with my thing (search for the other “turning” point of the wobbling plane).But I do not understand 766 SM, this distance is not draconic ‘anything’ (yet near 828 sidereal and near 821 anomalistic).

B.t.w. big shock for cycle deniers: 887 SM / (½ x Inex) + 3 = 887 SM / (½ x Saros), the factors as Fibonacci: 5.xyz + 2.9999~ = 8.xyz with .xyz same~ decimals 🙂 and 887 is producing eclipses 😎 (more than 25% of all pairs over 7ka).

Thanks for discussing all these connections, very good blog here 🙂

C: ‘I do not understand 766 SM, this distance is not draconic ‘anything’ ‘

It is if you look a bit closer…

766 SM = 7 apsidal cycles, and 223 apsidal = 2079 draconic years.

So 223 x 7 apsidal = 766 x 223 SM = 766 Saros = 2079 x 7 DY.

Also: (2079 x 7) / 766 = 18.998694 DY

2079 x 7 = 14553 (21 x 693)

766 x 19 = 14554 i.e. one more

Recall that 766 x 223 SM = 766 x 242, -1 DM

Numeric difference = 185371 – 170818 = 14553

@oldbrew (December 19, 2014 at 12:51 pm): expressing it as 18.99~ DY is a good idea (this your case is expression for Saros).

Using same factor for FMC this gives 265 synodic (284.0 anomalistic) and interesting pairs of eclipses: duo-to-duo is

½day longer (avg) in synodic than sandwich-to-sandwich (inside of duo). Makes me curious since these eclipses don’t come in triples. Now, we have this pattern:Saros:

19draconic years with 223 synodic.Metonic:

19equinoctial years with 235 synodic.284.0 anomalistic:

19FMC with 265 synodic.Not at all that bad prey for a day 🙂

More re Saros:

34 Saros = 613 years = 223 x 34 SM (7582)

55 x 149 sidereal months (8195) = 613 years (8195 – 7582)

1 Saros = 55/34 (~phi) x 149 sidereal = about 11+1/3rd days over 18 years

613 = 34 x 18, +1

Note: 241 / 149 is almost the same as 55 / 34, and 241 sidereal = ~223 synodic

Just for the record, as quoted by Chaeremon:

Saros: 19 draconic years with 223 synodic. = 242 draconic months (223 + 19)

Metonic: 19 equinoctial years with 235 synodic = 254 sidereal (235 + 19)

284.0 anomalistic: 19 FMC with 265 synodic. (265 + 19 = 284 anom.)

Just for the record, the continued fractions for the above, using Dr Ron Knott’s

I sent a ‘bug’ report to Dr Ron Knott for drawing his attention to the unequalness of the last two lines 😉

But what says this ‘bug’: even if you use professional mathematics, extrapolation with ‘real’ truncated numbers is a method for the creation of freaking esoteric unknowingness …

Re the Inex series, Wikipedia says: ‘Their appearance and longitude are irregular due to

a lack of synchronizationwith the anomalistic month (period of perigee).’Wiki: ‘The inex is an eclipse cycle of 10,571.95 days (about 29 years minus 20 days).

Here’s the missing

synchronization:49 x 10571.95 = 518025.55 days, divided by 27.55455 (AM) = 18800 exactly.

1 Inex = 358 synodic months so 49 Inex = 17542 SM

18800 AM – 17542 SM = 1258 Full Moon Cycles (1258 = 34 x 37)

(2 Inex = 61 draconic years so 2 x 49 Inex = 2989 DY)

http://en.wikipedia.org/wiki/Full_moon_cycle

The link says: ‘The equivalence of 14 synodic months is an approximation that will accumulate an error of one synodic month after 18 cycles:

18×FC = 251×SM = 269×AM

whereas 18×14 = 252’

17542 SM x 9 = 157878 (= 441 x 358 — see below)

251SM x 629 = 157879 (one more)18800 AM x 9 = 169200

269AM x 629 = 169201 (one more)18800 – 17542 = 1258 FMC (as stated earlier)

1258 FMC x 9 = 11322 =

18x 629 =49 x 9 Inex = 441 = 21²

157878 SM = 14 SM x 11277 = 21² x 358

(re: ‘The equivalence of 14 synodic months is an approximation’)

Fibonacci footnote:

21² Inex =34x 333 full moon cycles@oldbrew: Re

Inex lack of synchronizationpropaganda by wiki-Pravda.The Inex is so precise *) that Saros eclipses have an Inex eclipse 358 synodic later (ignoring a few exceptions for simplification). It is the ‘fault’ of Saros series to not have a constant members size (which is also shorter than that of Inex series). But the decades long wrong impression is propagated by wiki-Pravda.

Instead, decades and centuries ago, when eclipse almanacs were incompetently academicised by the anointed, everybody (and their dog) made eclipse series too short (and/or had no idea of series existence). In particular, the anointed never traveled to the two polar regions or outside of western-ideology colonies, for collecting observational data (oh my oh my, where have we seen this rent-seeking before, recently and presently).

The gaps were only corrected after *) had published rational details (beginning 1950~). The Saros-Inex Panorama of Luca Quaglia and John Tilley added even more missing eclipses (which certainly do not appear in every almanac). I asked these authors for .csv files, for lunar

andsolar eclipses, and they sent copies for use in my work (I mapped this to Solex output for adopting to lastest and greatest numerical integration results).*) actually, the Inex is an order of magnitude (IIRC) more precise than Saros (amateur astronomer Prof. George van den Bergh published the details, referenced earlier).

In the example: 49 x 9 Inex = 441 = 21²

– times 2 is a multiple of 18 Inex.

See earlier notes re: 18 Inex = 521 years. So yes, Inex is precise (also 2 Inex = 61 Draconic years).

Correction of the continued fractions (December 20, 2014 at 9:03 am above):

I just received email from Dr Ron Knott and it works.

As to : “Correction of the continued fractions”, don’t know if this might help but from my continued fraction calculator:

223/19 = 11.736842105263157894736842105 = 11;1,2,1,4

235/19 = 12.368421052631578947368421053 = 12;2,1,2,2

265/19 = 13.947368421052631578947368421 = 13;1,18

284/19 = 14.947368421052631578947368421 = 14;1,18

One base is:

0;1,2,2 = 5/7 = 0.714285714285714285714285…

Like 285/0.7142857142857142857142857143 = 399;

And 265/0.7142857142857142857142857143 = 371;

And 223/0.7142857142857142857142857143 = 312;5 = 1561 / 5

And 242/0.7142857142857142857142857143 = 338;1,4 = 1694 / 5

Other is half of that base:

0;2,1,4 = 5/14 = 0.35714285714285714285714285…

Gives same as above but doubled as:

Like 285/0.3571428571428571428571428571 = 798;

And 265/0.3571428571428571428571428571 = 742;

But 223/0.3571428571428571428571428571 = 624;2,2 = 3122 / 5

And 242/0.3571428571428571428571428571 = 677;1,1,2 = 3388 / 5

I search in this thread for 399, 371, 1561, 1694 and the fractional of 5 and find no mention so maybe this will be helpful.

I still can’t figure out what you all are searching for in the numbers. Integer fractions? If so continued fractions can be a huge help.

Wayne – I recognise this one: ‘And 223/0.7142857142857142857142857143 = 312;5 = 1561 / 5’

What it says to me is simply: 223 x 7 = 1561

1561 apse cycles = 13811 tropical years = 766 x 223 synodic months = 766 Saros cycles

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