Thanks to the Earth’s gravitational pull, the Moon is slightly egg shaped. The closest part bulges out by 51cm towards the Earth, and here’s the weirdest thing, the bulge moves. The same side of the Moon always faces Earth, but if you stood on the Moon, the Earth would appear to wobble around a particular patch of “moon-sky”. And like a tide of rock, the bulge in the surface, slowly rolls around on the Moon — following the pull from the Earth.
The ball of rock called the Moon is 3,474 km in diameter. I’m guessing the Man-on-the-Moon would not notice the tide much.
Though I imagine it will be a right headache for future Moonville Skyscrapers.
Despite the force required to deform a ball of rock that large, and from such a distance, climate models in their infinite wisdom know that the science is settled and the Moon has no significant effect on Earth.
You might recall that Ian Wilson has other ideas, and suggests lunar cycles set up atmospheric standing waves which may seed ENSO patterns.
And we wonder why those models don’t work?
NASA missions let scientists see moon’s dancing tide from orbit
Scientists combined observations from two NASA missions to check out the moon’s lopsided shape and how it changes under Earth’s sway — a response not seen from orbit before.
The team drew on studies by NASA’s Lunar Reconnaissance Orbiter, which has been investigating the moon since 2009, and by NASA’s Gravity Recovery and Interior Laboratory, or GRAIL, mission. Because orbiting spacecraft gathered the data, the scientists were able to take the entire moon into account, not just the side that can be observed from Earth.
“The deformation of the moon due to Earth’s pull is very challenging to measure, but learning more about it gives us clues about the interior of the moon,” said Erwan Mazarico, a scientist with the Massachusetts Institute of Technology in Cambridge, Mass., who works at NASA’s Goddard Space Flight Center in Greenbelt, Md.
The lopsided shape of the moon is one result of its gravitational tug-of-war with Earth. The mutual pulling of the two bodies is powerful enough to stretch them both, so they wind up shaped a little like two eggs with their ends pointing toward one another. On Earth, the tension has an especially strong effect on the oceans, because water moves so freely, and is the driving force behind tides.
Earth’s distorting effect on the moon, called the lunar body tide, is more difficult to detect, because the moon is solid except for its small core. Even so, there is enough force to raise a bulge about 20 inches (51 centimeters) high on the near side of the moon and similar one on the far side.
The position of the bulge actually shifts a few inches over time. Although the same side of the moon constantly faces Earth, because of the tilt and shape of the moon’s orbit, the side facing Earth appears to wobble. From the moon’s viewpoint, Earth doesn’t sit motionless but moves around within a small patch of sky. The bulge responds to Earth’s movements like a dance partner, following wherever the lead goes.
“If nothing changed on the moon — if there were no lunar body tide or if its tide were completely static — then every time scientists measured the surface height at a particular location, they would get the same value,” said Mike Barker, a Sigma Space Corporation scientist based at Goddard and co-author of the new study, which is available online in Geophysical Research Letters.
A few studies of these subtle changes were conducted previously from Earth. But not until LRO and GRAIL did satellites provide enough resolution to see the lunar tide from orbit.
To search for the tide’s signature, the scientists turned to data taken by LRO’s Lunar Orbiter Laser Altimeter, or LOLA, which is mapping the height of features on the moon’s surface. The team chose spots that the spacecraft has passed over more than once, each time approaching along a different flight path. More than 350,000 locations were selected, covering areas on the near and far sides of the moon.
The researchers precisely matched measurements taken at the same spot and calculated whether the height had risen or fallen from one satellite pass to the next; a change indicated a shift in the location of the bulge.
A crucial step in the process was to pinpoint exactly how far above the surface LRO was located for each measurement. To reconstruct the spacecraft’s orbit with sufficient accuracy, the researchers needed the detailed map of the moon’s gravity field provided by the GRAIL mission.
“This study provides a more direct measurement of the lunar body tide and much more comprehensive coverage than has been achieved before,” said John Keller, LRO project scientist at Goddard.
The good news for lunar scientists is that the new results are consistent with earlier findings. The estimated size of the tide confirmed the previous measurement of the bulge. The other value of great interest to researchers is the overall stiffness of the moon, known as the Love number h2, and this was also similar to prior results.
Having confirmation of the previous values — with significantly smaller errors than before — will make the lunar body tide a more useful piece of information for scientists.
“This research shows the power of bringing together the capabilities of two missions. The extraction of the tide from the LOLA data would have been impossible without the gravity model of the moon provided by the GRAIL mission,” said David Smith, the principal investigator for LRO’s LOLA instrument and the deputy principal investigator for the GRAIL mission. Smith is affiliated with Goddard and the Massachusetts Institute of Technology.
Fascinating! But it also brings up an issue of any base on the moon. Since 51cm is significant when designing most any structures, air tight ones are even more critical.
I guess “Balloon Boy” might be the way to go.
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You are joking aren’t you?
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You are joking aren’t you?”
Well that was a particularly stupid comment.
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Only to the totally ignorant
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It depends on where you place the emphasis in what the Griss wrote.
Well that was a
Well that was a
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I’m sure you mean BY the totally ignorant.
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Building tolerances. About 1% of this.
Fault lines move at less than 1% of 51 cm per year (although all in one go after many decades).
PJ said its significant when designing rather than it was impossible, so Brian is a troll?
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51 cm would be a big problem as Phil said, if the structure had to be — and stay — air tight. If you start leaking you’ve nowhere to get a refill like you can for a tire at the nearest gas station. Assuming of course that gas stations still supply air for your tires, which some do not do these days.
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Phil, I don’t think the article is suggesting that the surface of the moon is heaving up and down half a metre a day, it would have expended a huge amount of energy internally by now at that rate and would have left us. Because the spin of the moon about its axis matches its orbit rate around the earth (more or less), then that ‘bulge’ is a bit of a permanent fixture. If you re-read you will see that the article says that the bulge moves a few inches, that is laterally, not up and down. The lateral shift would only result in a miniscule up and down movement. So in short, no worries about your moon base cracking up and leaking, although I do wonder why on
earthmoon you would want to build one out there, although a ‘speccie’ might pay out while the real estate prices are still low out there.I think that is what Brian was hinting at with his comment when he got slammed.
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… that is ‘per day’ or per month or per year to be more correct.
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If the Moon has a moving distortion of its shape by about 51 cm by the proximity and movement of the earth, then surely this must cause some thermal effects both on and within the moon itself?
Is this thermal effect measureable, and if so does it taint the lunar temperature record? This lunar temperature record is used as a reference for assesing the earth’s energy balance is it not?
Enquiring minds need to know!
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Tomo, this inquiring mind wants to know how much the Earths crust deforms from the same process. Could it be affecting satellite sea level measurements?
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Mark D.
Interesting question.
The Moon is exceptionally large satellite for a planet the Earth’s size. Relative to Earth: equatorial radius 0.273 of Earths (nearly a quarter the diameter of the Earth) and 1/81 its mass.
I would have thought that it was very low as the these distortions are the result of proximity and the gravitational pull of the bodies.
IMO the Earth being the larger should have a large effect on the moon than vise versa. But I await correction on this matter.
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This may answer your question.
http://www.youtube.com/watch?v=q65O3qA0-n4
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For a moment there, I thought you had caught the dreaded U-toobs virus from BA4.
But that video was very instructive – gotta love the way it is done.
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Did you notice the word Metre at the end,and NOT millimetre.Funny how some Clim-astrologists brag about measurements to the Millimetre.
Impossible In reality.
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Actually, the numbers look even scarier when expressed in microns.
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Try it in Ångstrom! 😉
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I would have done, but I don’t know how to get the accented characters on my Mac.
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I had the use of millimeters drummed into me from day one in my trade only for accuracy in fabrication and building, you actually got into trouble for saying centimeters, once during a trade test for a job I converted an answer from cms to mills and had to point out why I was correct relating to trade accuracy.
51cm or 510mm could be roughly called half a metre. 🙂
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What worries me about this video is that it says the earth is not flat. I’ve been told that as I’m a “denier”, then I must believe the earth is flat. Who am I to argue with the 97%? I must believe it’s flat…
Is the moon flat too?
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About 25cm and no.
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Land tides are estimated to be up to 64cm.
The sea level rise over the whole period that satellites have been used is about 2 cm and even with your 25 cm estimate, you couldn’t be certain that the 10% of that was permanent distortion.
Or are you pointing out that it is irrelevant because each satellite altimetry measurement could be 2.5cm off, or that the waves are usually much bigger than this?
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certain it wasn’t permanent distortion and the link to the data.
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Excellent link Vic. Thanks!
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Mark,
I suspect not. At least not for any useful purpose. But see comment #17.
On the other hand, when they’re trying to measure to millimeter accuracy, maybe so.
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I’m wondering what is a centimeter, or 51 cm? Is that tall for a man?
Hypothetical question. Suppose at the primordial time the moon has a rotation. How long would a gravity drag that can deform solid rock take to stop that spin?
FYI the effect of the moon’s gravity will be smaller but more apparent because the lower mass of water and continents floating on a ball of magma are easier to deform.
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Two rungs on the lander ladder, laddie.
Try saying that fast!
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papertiger May 31, 2014 at 4:56 am · Reply
I’m wondering what is a centimeter, or 51 cm? Is that tall for a man?
A centimeter is an interval or distance, 1/100 of a meter, about the width if your fingernail. or the distance that light travels in 1/3×10^-10 seconds.
Hypothetical question. Suppose at the primordial time the moon has a rotation. How long would a gravity drag that can deform solid rock take to stop that spin?
Please define “primordial”. Currently the Moon is tidelocked to the Earth, and rotates at the same rate as its orbital period. +/- 3 minutes of angle. Wiggling because of all other planets and some noise. That noise angle the Climate Clowns can statistically modify from the book of creative statistics Vol 2 page 241.
Now that we all know which way the Moon is pointing (statistically), can we please get on with whatever lives we have left?
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The moon is a complete mystery to me.
Why do we only ever see one side? The earth spins relative to the sun so why not the noon relative to the earth?
Why is the moon exactly the same size (visually) as the sun? What is the probability of that?
How did the moon form?
I can hear the rush of computer keys ready to pounce with the “textbook science” solution.
Guess what, nobody knows, nobody will ever know.
[There are 5 key theories on the creation of the moon. Perhaps other readers will share their favorite one and why? To say we will never know is a little pessimistic Sonny. – Mod]
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A few years ago, I went to a lecture by Dr Andrew Prentice at Monash Uni.
He speculated about the formation of the Moon and thought that his Modern Lapacian Theory might explain it. His theory is that the Earth and the Moon both formed at the same time from the same ring of dust and gas.
MLP say that the solar system formed from a rotating ball or disc of gas/dust. As the disc contracts rings of dust are shed from the outer edge to preserve angular momentum. Hence the outer planets form first.
He did prove using a computer graphic ( model), that the Giant Collider theory could not be correct. All the debris from the collision would fly off and not coalesce into the moon!
Unfortunately the Modern Laplacian theory does not explain the tilt of the Earth.
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When I was a school, we had lessons in Religious Instruction*
The teacher was talking about creation, and how God made heaven and the earth. One kid asked why the earth had a tilt, rather than being perfect, if God made it.
While the teacher was thinking about this, another kid piped up, “Perhaps God knocked it, on his way to lunch”.
* “Instruction”, not “Education” you might note – the Belief was settled.
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They tried the religious instruction thing on us in year 7,8 high school.
I dutifully went to the first one, then told my dear Mum that I would rather be doing extra maths of science (yes please) or even (shudder) English
Mum went straight up to the headmaster, and told him that was what was happening 🙂 End of story.
So, here I am….. heathen…. and proud of it. 🙂
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The only benefit of RI in schools is to educate the student as to the nature of RI so that they can recognize it in future. Especially in politics and non-science preaching.
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Bernd, I think you are being generous to RI. Another way to look at it is that RI over the thousands of years in all it’s various flavours, has really conditioned man into being open to believing lots of things that arguably might not be ‘truths’ from a scientific viewpoint. We often joke about the ‘global warming religion’ but I fear there is a dangerous similarity there with religion and how they are both propagated and promoted. The religious texts of not so long ago aim to make us fearful and tell us that it is angry gods bringing us bad weather, floods, droughts and even boils and that we had to make sacrifices to these gods and follow certain practices to avoid these calamities. Now we are told to fear the CO2 and that we all need to make sacrifices and give a good sum to those who would fight off this CO2 menace and save us all so that order is restored. When they say that global warming is the biggest con in history, I think that there are many that have been made in the name of RI that are far far greater and are probably still being perpetuated. I don’t think that we ever had scientific closure on that whole RI thing, we simply defined a different class of gnosis that somehow did not need to be reconciled with other knowledge. In a way the proponents of global warming might have been more successful if they just stuck with the old angry gods story and just said that the gods now required 10% of your wages because we had been bad with the CO2 and that the UN had been appointed or is that anointed by the gods, as the collectors on earth.
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Nice!!
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CAGW is not a substitute for religion. Religion is a substitute for things like CAGW.
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Just timing. It use to appear larger than the Sun, and eventually it will appear smaller because it is moving away from the Earth at a rate of aboit 3.8cm per year.
It’s had enough, it’s out of here.
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Is nothing constant anymore? Pretty soon C will be a variable too I suppose.
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Ah, so we can look forward to a C-change ?
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I’m reporting your comment!
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C if I care.
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You’re just makingitworse.
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C is a programming language. 😉
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I give that a C++.
Get with the program, Phil, and be more object oriented.
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Damn! You dropped my GPA! 😉
Actually I got out of programming around the time C++ gained in popularity (turn of the century). So I know about it, just never used it.
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Not on the theory of the moon creation, but on the rotation. E.M.Smith had a great article on the Moon not too long ago (chiefio.wordpress.com). The size of the moon relative to the earth means it is not really a host/slave system like the earth and sun, but rather a binary planet system. It is very unique within this solar system as no other planet has a moon quite like ours in both size and behavior.
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Once they all get up there and start mining for stuff which will be brought back to earth, there will be an imbalance which will knock the earth out of orbital kilter.
We’ll all die. Mark my words, the Earth will become an uninhabitable hulk hurtling randomly through space for eternity.
There.
That’s my post-CAGW scary story. Can I have my grant to study this please?
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Sorry mate,
The one thing the Moon has not got and that is any minerals worth mining, unless there is sufficient debris from an ancient iron/nickel/PGM rich asteroid impact.
The Earth is a very unique planet, much denser than all the other planets and moons in our solar system. If you want mineable minerals, you will need to go out to the Asteroid Belt between Mars and Jupiter and even there you are going to have to be quite picky.
Somehow, I don’t think we will be doing that anytime soon. Anyhow, you can rely on the greenies to oppose mining there by spuriously – is there any other type of greenie claim? – claiming they want to protect the environment in the Asteroid Belt.
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from http://www.space.com/17138-helium-moon-atmosphere-lunar-discovery.html
And many people think that this substance could be the fuel of the future in fusion reactor.
http://www.asi.org/adb/02/09/he3-intro.html
I am as alway skeptical.
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Sorry Peter, there’s no such thing as “very unique”. ‘Unique’ is an absolute, and can’t have a qualifier. Something or someone is either unique, or not.
Cheers!
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C500,
“…post-CAGW scary story.”
Look up IPCC Policy and Procedures Manual Sec 17.5.1 Climate Agenda > Key Performance Indicators > Preferred Outcomes.
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Could you give us a link, James?
I am under the impression that the UNEP Policies and Procedures also apply to the IPCC. Perhaps I am mistaken?
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Probably should have added sarc…
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Actually Carbon500, I read somewhere that earth collects space debris (meteorites) to the tune of 100 tons (I’m not sure if it was per day, week, month or year). When you calculate the tonnage over the eons this adds up to lotsa stuff being collected by the earth. So, your theory isn’t wrong. At what point will we reach the tipping point (earth gets too heavy)
“there will be an imbalance which will knock the earth out of orbital kilter. We’ll all die. Mark my words, the Earth will become an uninhabitable hulk hurtling randomly through space for eternity.”
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Well, at least we will get a change of scenery.
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No, No. All this added space debris tonnage will increase the gravitational pull of the earth eventually pulling the moon down on top of our heads.
We are doomed I tell you doomed.
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“An uninhabitabl hulk hurtling randomly through space… ”
Already been there, done that, got the t shirt and just look where it is now.
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Here is a link to a good post from E.M> Smith bearing on possible Lunar effects.
http://chiefio.wordpress.com/2014/02/16/tides-vectors-scalars-arctic-flushing-and-resonance/
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This has been known for years. You can see more clearly in the moons of saturn and jupiter because they greater mass than Earth.
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Slightly off topic but IMO without a moon similar to the one we have life on other planets is very difficult to start and maintain.
How could life in the early oceans and seas differntiate and evolve without the tidal mixing? How could those early fish get stranded on the beaches to later evolve to lungfish? Why are so many plant affect by lunar cycles?
( http://www.howplantswork.com/2009/07/25/does-the-moon-affect-plants-part-2-moonlight-and-biorhythms/ )
As are many animals mass migration timings.
Why is the urge to procrate in nature liked to phases of the moon, especially in the spring or fall.
Just about all life on our planet has some kind cyclic behavior that is linked to the moon and its regular cycles.
We are all in some way lunar affected, some more than others.
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The biggest issue is that the earths rotation wouldn’t be stable, so the position of the poles and the equator would differ by thousands of kilometers every year, making it difficult for life as we know it to survive, however life is surprisingly resiliant and despite being in the tropics one year and the arctic the next I suspect some form of life would still have evolved, but clearly wouldn’t be as wimpish as humans.
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Yes. A point I keep trying to make. The moon was much closer and really whizzed around when life was first forming on this planet. A real super kitchen mixer. And then all those chemicals plopping down at super high heat levels. Positively glowing, a lot of them. Luckily things are much quieter now. But we still get 7 metre plus spring tides here at Milford Haven. Can you imagine a 7 metre tsunami? Of course most people wouldn’t notice if it happened at low tide. 🙂
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tom0mason,
You left out the obvious linkage, the seasons, which have nothing to do with the moon as far as I know. But the question about the influence of the tides, well, you may be onto something there.
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Only slightly off topic. Larry Niven , the science fiction writer, was aware of these permanent lunar tides, and has several stories with the planet “Jinx” for a background.
Jinx is a small, partially habitable, planet orbiting a Jupiter size planet in the habitable zone of a nearby star. Jinx, like the moon, has permanent tides- with one side always facing the Jovian planet. Thanks to those permanent tides, the air is too dense for humans near the equator, also where most of the seas are, is inhabited by humans in the two temperate bands where there is a breathable atmosphere, and at the poles, with no atmosphere, the humans have set up astronomical observatories.
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They might not have seen the distortions, but …
“After more than 85 years of study and speculation, recent digs have confirmed the presence of a ceremonial road running through the heart of Cahokia, the largest prehistoric city north of Mexico, archaeologists report.
“Why would Cahokians have built this 1 kilometer-long earthen feature after they constructed everything else?
Adding to the evidence that the road may have been a literal and symbolic centerpiece of the city, Baires noted that it is aligned 5 degrees east of north, forming a central “axis” around which the community seems to have been built.
Previous research has suggested that Cahokia’s buildings align with a celestial event known as the lunar standstill, when the moon rises at its southernmost point in the sky.
The event occurs once every 18.6 years, and, as seen from Cahokia’s Grand Plaza, it is visible over the bluffs south of Rattlesnake Mound, where the causeway ends.”
~ ~ ~
The Lunar Standstill explained
. . .
Much to learn, and, it seems much to re-learn.
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Bl…y interesting Hj. Science never bores me.
R-Coo- K+
Potassium salt of an aliphatic carboxylic acid – named to be a chemist
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As this sis the result of gravity and relative motion there must be an almost imperceptible loss of kinetic energy (moon’s rotation) resulting in a loss of rotational speed, and lunar orbital decay.
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“Yes the moon is slowly moving farther away and slowing the Earth’s rotation in the process.
This was first discovered following the Apollo moon landings by bouncing laser off reflectors left behind by astronauts. The reflectors were designed to accurately measure the Earth-Moon distance. The measurements showed that the moon is getting further away at a rate of 1.5 inches or 3.82 cm per year. Furthermore a day is getting longer by 1.7 milliseconds per day per century. Both affects are a result of tidal forces between them these same forces are responsible for the high and low tides experienced trice a day.
There’s lots more at
http://genesismission.4t.com/Physics/Geophysics/lunar_recession.html
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There are more things in heaven and earth, Horatio
R-COO- K+
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As far back as the Neolithic, the lunar standstill was apparently associated with disturbances in weather affecting crop yields. You mentioned the 18.6 year cycle, but the effect is probably more complex as the effect on the earth’s oceans appears to depend on the time of year that standstill occurs- in cyclic patterns of up to 465 years.
I will be interested to see if next year’s lunar standstill coincides with any unusual ENSO variation.
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apologies o/t but:
31 May: Australian: Sid Maher: Solar bonus to swamp carbon tax savings
QUEENSLAND’S solar rooftop feed-in tariff scheme will swallow half the expected 8.5 per cent cut in electricity prices from the repeal of the carbon tax for average residential users.
The cost of the Solar Bonus scheme will rise from $53 in 2013-14 to $106 in 2014-15, swallowing half the $107 reduction in electricity prices if the carbon tax is abolished by the Senate after July.
The scheme, which no longer allows new entrants, is predicted to double in cost again the following year…
The 8.5 per cent cut from abolition is less than the 10 per cent rise in electricity prices when the carbon tax was introduced in 2011. The QCA said a typical customer’s annual bill would rise from $1407 to $1599, up 13.6 per cent, if the carbon tax remained in place. If the carbon tax was repealed, it would rise to $1480, up 5.1 per cent…
http://www.theaustralian.com.au/national-affairs/policy/solar-bonus-to-swamp-carbon-tax-savings/story-e6frg6xf-1226937799914#mm-premium
30 May: Brisbane Times: Amy Remeikis: Electricity bills set to rise about $200 a year
Chief Executive Officer of the Queensland Council of Social Service, Mark Henley, said the increase fixed costs would be felt the most “by those who can afford it the least”.
“People are making tough decisions and they are making decisions about turning off the power at times when they actually really need it,” he said.
“..Sometimes it is a choice between actually living in the dark and actually putting a meal on the table or being able to afford to go to the doctor.”
Mr Henley said he had spoken to energy minister Mark McArdle about lowering prices or establishing a concession for low income earners.
“The solution is to look at what concessions are available to people on low income, who can no longer afford things such as energy and I think government is looking at that and we welcome that, but this increases the urgency,” he said.
Mr McArdle said state Labor’s “legacy” from the Solar Bonus Scheme and the carbon tax were to blame.
He said the easiest way to lower electricity prices would be for Labor to support the carbon tax repeal bill…
“Whether by political design – or incompetence – past and present Labor MPs booby-trapped Queensland’s path to more affordable electricity prices.”…
“There is some very low hanging fruit here – carbon tax and the RET – very low hanging fruit that can have an impact [on power prices] now,” he said.
“All you have to do is to get Labor to vote for Queensland, not for themselves.”
http://www.brisbanetimes.com.au/queensland/electricity-bills-set-to-rise-about-200-a-year-20140530-zrjlc.html
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Pat,it is not looking rosy for grid electricity users in Qld. I believe that Qld also has a mandatory gas generation target of something like 15% and a very cosy relationship between the private gas generators and the Gov. Did they quote the cost of gas generation in the QCA final report? I think it currently adds something like $74 to the average consumers bill and will increase next year. The solar base definitely cuts into the gas market and it would be interesting to see how the costs would look if there was only the gas and not the solar. Altho the Fed Gov does not have an excise on the photons yet, they do have an excise on gas which is waived as a subsidy for gas used to generate power, just as is the case for diesel fuel used in smaller generators.
I think to really appreciate the background to the whole pricing debate you should be quoting not only from the body of the QCA report but also the public submissions considered in the process. There are many public concerns that are totally overlooked by the findings of the report. I think it is worth being a little cynical and remembering that the QCA was a ‘handpicked’ body set up by the Qld Government, the same Government that owns all the coal stations and the distribution network in Qld. Critics of the QCA point out that these Gov owned entities have guaranteed returns for the Gov which are commercially unreasonable. While the QCA was instructed to focus on the Carbon Tax costs there was no quantification of all the other Gov charges that make up our electricity bill. No mention of the affect of increased royalties on coal by the Qld State Gov, no mention of the profit guarantee of the State owned generators and distribution entities, no mention of excise concessions granted by the Fed Gov, no mention of the GST which the Fed Gov chooses to apply to the provision of electricity, not regarding it as an essential service like health, no mention of the proposed company tax levy based on the size of the company which could affect the electricity supply chain, no mention of the MRRT which might affect the coal prices, no mention of the effect of possible GST rises.
While the Qld Premier operates both solar electric and solar hot water at his residence, he does claim that this does not impose any cost on others (somehow). Nobody seems to have found out how he manages this. Solar electric users seem to be the scapegoat for the decreased electricity usage which has upset the balance of the fixed costs but in reality ANYONE with reduced electricity usage, whether they have solar hot water installed (hw is a big part of most domestic bills), are simply poor, have energy efficient homes, or are just frugal, they have a similar effect. So the QCA wants to increase the fixed costs for all those who use less. The network costs which are at the basis of this are determined largely by the peak demands. The universal notion that all low energy users (in particular solar users) are somehow just using peak hour electricity is a poor assumption. Better time of use tariffs with lower fixed costs would be a more equitable solution. As for the costs of the RECs and newer STCs, there is controversy about how the QCA treats those costs. The nominal value of $40 for a REC is unrealistically high and the market rate for these is more like $26 (thanks to that free market). RECs were issued for a whole range of energy saving devices including solar hot water but the QCA lumps this all onto solar electricity costs, way skewing the figures. I am not certain of the exact numbers but I think there were more solar contracts for the higher 44 cent FIT under the current Qld Gov than the previous because they gave and extraordinarily long notice for the closure of the scheme instead of turning it off overnight. As for the whole renewable energy target, I think we are still chasing the current Gov’s target set by Howard. If we have indeed managed to surpass that it is probably more due to our reduced consumption overall than any great achievements by the Oppn or of the solar base.
Might end up cheaper buying a Chinese made diesel generator from Bunnings (gotta respect that Chinese Gov controlled market they have for keeping us supplied with cheap stuff hey. So when we talk about the free market, we really just mean free of our own Gov I guess, perhaps an extension lead from up there to Oz might be the way to go too)
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so how does ABC report the rise in electricity prices?
***the one & only mention of the carbon tax in Melinda’s lengthy piece, which allows Labor to go on the attack.
30 May: ABC: Electricity price hike: Queensland regulator announces 13.6 per cent rise from July
By Melinda Howells
***But the QCA, the body that regulates the state’s power prices, says prices will only go up by 5.1 per cent if the Federal Government’s carbon tax is repealed…
Mr Roberts (QCA Chairman) says there may be some relief next financial year.
“The price increases we’ve seen in recent years have been exceptional,” he said.
“Some of the factors that have pushed those prices up – there’s good grounds to hope or expect that they’ll abate in 2015-16, but again there’s no guarantee about future prices.”…
Labor says the Newman Government is failing in its promise to lower the cost of living.
Opposition treasury spokesman Curtis Pitt says another massive power price hike is the last thing Queenslanders need.
“Campbell Newman promised that he had all the answers when it came to electricity prices,” he said.
“He promised that he would lower the price of electricity – prices have gone up when the LNP said they would go down at some stage.
“On the eve of the LNP’s third budget, the Newman Government is going to have to take responsibility for the decisions that they are making.”…
But Queensland Energy Minister Mark McArdle says Labor’s criticism is a cheap shot.
“The Labor party cannot say anything about their own record – their record is appalling,” he said.
“It is simply unbelievable they can try and claim a moral high ground when they left this state in a power situation that was critical.
“Power prices were rising because of their own actions and they did not take any action to drive prices down.”…
http://www.abc.net.au/news/2014-05-30/electricity-price-hike-queensland-regulator-announces-rise/5489722
Craig & Andy more interested in discussing further subsidies, but briefly mentions the carbon tax twice without quoting anyone!
30 May: ABC: Irrigators hit hard by power increase
QLD Country Hour / Craig Zonca and Andy Toulson
The Queensland Competition Authority points to increases in generation and network costs as the key reasons for the price jump in its latest determination.
“We’re seeing a tightening of supply in the market, driven partly by the expected increase in demand from the LNG industry…
The price rise would be limited to 10 per cent if the Federal Parliament repeals the carbon tax.
Rural lobby group Canegrowers had appealed to the Queensland Premier for a 33 per cent reduction in electricity costs, arguing it would be cost neutral due to the resulting higher demand.
But that’s been rejected by Mr Roberts, who says the 18,000 irrigators on transitional tariffs are already subsidised and currently pay less than the cost of supply.
“If you reduced the price and demand increased, you would be making a greater loss that would ultimately have to be paid for by the taxpayer.
“On one calculation, if you followed the Canegrowers scenario through, we’d be looking at that $32 million subsidy going to about $80 million more.
“When people say, ‘I can’t pass these costs on’, I completely understand that, but I also know that’s true for small businesses in town and pensioners who don’t suddenly have an increase in their pension because the power price has gone up.”
The average Queensland household power bill will rise by 13.6 per cent, or about $190 per year.
Cane farmer Alan Parker says another price rise will bring about a new species, the ‘dinosaur grower’, because many will be extinct.
His power bill has increased by 70 per cent in the past 12 months alone…
(FINAL LINE) Mr McArdle says the quickest way to achieve price relief would be for the federal Labor Party to support the Abbott Government in repealing the carbon tax.
http://www.abc.net.au/news/2014-05-30/irrigators-hit-hard-by-power-increase/5489650
10
When I was a teenager I thought the Moon might influence weather via tidal action. Never thought anyone would ever seriously study it. But if the Earth’s crust rises and falls very slightly and water more so it stands to intuitive reasoning the more lighter, fluid air should be affected gravitationally.
20
There is an old Greek proverb. If the crescent shaped moon looks like it will hold water, it will not rain. If it is upside down and looks like its emptying its water, it will rain. I suppose it came from an area where it happened often enough to become a proverb so the moon might have an effect on local weather patterns.
00
Like Tomo, I am curious about the thermal effects of the tidal distortion, both on the moon and on the Earth’s crust.
We all know (from first principles) that man-made CO2 is making those effects more extreme. Does anyone have a sciencey sounding explanation of how CO2 does this?
10
On this Earth the tidal effects on temperature,locally are huge, affecting local “climate”. That effect, smoothed by Global 30 year Gaussian weighted, average global temperature is totally devoid of any information of what “is” right here!
The process that the Climate Clowns use is total BS. Some of the measurements may give a clue of what “is” here!
00
Huh?
00
He’s asking for an explanation, Roy. Good luck.
00
Yes he is, Vic. His ignorance of the matter begs to be explained. Now how do I explain the obvious to someone who apparently doesn’t understand obvious, who apparently doesn’t understand chemistry, who…?
But while my fingers are moving: There is no difference between “man made” CO2 and naturally occurring CO2. The implication that the CO2 from burning fossil fuels may have a different isotope of carbon and that this makes some difference is plain old nonsense. Regardless of the isotope of carbon the molecules behave exactly the same way in the air and they have no effect whatsoever that anyone has ever shown evidence of.
10
Preaching to the converted, including RoHa. I think that he was being sarcastic.
10
“I think that he was being sarcastic”
Nah, I’ve never know RoHa to be sarcastic 😉
01
known
01
This is important information for Richard Branson and his followers who want to become disenfranchised for Earth. 😉
10
“from Earth” … thick head.
00
I had not heard of the moon body tides before. But it makes sense, there are even larger earth tides and this has been known for some time. And, yes, the earth tides are used to correct GPS location/elevation data. There is even a site where one can calculate the earth tides at any location. Please copy the link and past in your browser.
http://www.taygeta.com/etides/index.jsp
Wonderful world we live in.
30
Leonard Lane May 31, 2014 at 3:26 pm ·
On this Earth Lunar ocean tides are important and measurable. Lunar and Solar atmospheric tides are very large or huge, but never considered by the Climate Clowns with their Academic “knowledge”!`
10
Leonard,
I ran the calculator. The result is measured in Microgals. I’ve never heard of that unit before. You learn something new every day.
I see from a Google search that the Gal is not part of any international standard units of measurement. Interesting!
10
The Gal comes from the CGS unit system proposed by James Clerk Maxwell:
http://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units
The MKS system never bothered to find a name for the units of acceleration.
00
Roy, please run the program and click the displacement box. That should give heights.
00
Leonard,
Thanks!
The numbers are a lot larger than I thought they would be.
00
Oh Yes, I put in several geographic coordinates and several lengths of computations and the results are actually quite surprising. Much larger than I ever suspected also. The graphics on the Wikipedia for earth tides are also surprising in how large the areas are that move.
Fascinating material isn’t it? Thanks to Jo for the moon body tides post.
00
Thank you for that link Leonard, one has to wonder if this effect influences earthquakes?
Roy, thanks for pointing me to this post!
00
Leonard Lane, has there been any computation of the energy induced by these Earth tides? It seems to me that friction alone would produce a tremendous heat component in the Earth.
00
tidal flex causing heating is not uncommon. have a look at the ‘tiger stripes’ on Saturn’s moon Enceladus, as well as other evidence for cryovolcanism on other moons like Ganymede, Titan, and Europa.
00
Mark D.
I seem to remember something but cannot recall when or where.
A quick look at Wikipedia produced the following interesting observations. Alas, they mention everything but heat, but since crustal movement and magnetic fields are involved it seem reasonable, as you suggest, then significant heat must be involved.
“Earth tide effects[edit]
Volcanologists use the regular, predictable Earth tide movements to calibrate and test sensitive volcano deformation monitoring instruments. The tides may also trigger volcanic events. [5] [6] Seismologists have determined that microseismic events are correlated to tidal variations in Central Asia (north of the Himalayas).[citation needed] The semidiurnal amplitude of terrestrial tides can reach about 55 cm at the equator which is important in GPS calibration and VLBI measurements. Also to make precise astronomical angular measurements requires knowledge of the Earth’s rate of rotation and nutation, both of which are influenced by earth tides. Terrestrial tides also need to be taken in account in the case of some particle physics experiments. [7] For instance, at the CERN or SLAC, the very large particle accelerators were designed while taking terrestrial tides into account for proper operation. Among the effects that need to be taken into account are circumference deformation for circular accelerators and particle beam energy. [8]
Since tidal forces generate currents of conducting fluids within the interior of the Earth, they affect in turn the Earth’s magnetic field itself.”
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For the Aussies, I remember our not so lamented and departed Climate Commissioner W. Stefffens once commented that “we no longer debate gravity or the tides”,Steffens could think again,but then again thinking was never his strong point.
20
“Steffens could think again,”
Surely once is enough !!
11
Minds like that I class as Think to Yield.
After one stupid application you retract and throw the nut out.
00
It’s far more interesting to me that the moon does similar things to the Earth. The Moon doesn’t move in an orbit around the Earth. The Earth and moon orbit as a system around their common center of mass. But with the moon so much smaller than the Earth that common center of mass is inside the Earth. Only it’s not at the Earth’s geometric center. As a result, the direction we call down, the one that gravity determines, is constantly changing as the Earth rotates because down is always toward that moving point, the common center of mass.
It’s hard to detect but anything free to move under the influence of a change in the direction, down, will move. Hence the tide that comes in and goes out twice a day. But this change in where down is puts changing stresses on what we think of as solid, the ground under our feet. And no one knows for sure what all the consequences of this really are.
Never mind the moon, the same force of gravity is right here at home. Is the “continental drift” caused by or influenced by changes in where down is? Are earthquakes caused or influenced by it? Is volcanic activity influenced by it?
We don’t know. But the moon definitely influences things here on Earth.
10
The prevalent explanation for the tides that the moon’s gravity pulls on the water, causing it to move toward the moon always bothered me. If that were so then how could there be high tide twice a day. How could there be a high tide on the side facing the moon and on the far side of the Earth where the moon’s gravity would have to be pushing the water away from the moon in order to have a high tide? It didn’t make sense.
I had to sit down and do a little analysis of the problem. And the binary star, which has the two massive bodies orbiting around a point in space somewhere between them was the example I needed to figure it out. The high tide on the opposite side of the Earth is accounted for by the direction down being directly toward the center of the Earth, just as it is on the near side.
Close to either the Earth or the moon, their gravity will be dominant. But the gravity of the other body will still have it’s effect.
00
The great lakes in America have a small tide, they are higher up the world than where the moon gets to. The tides run away from the moon in these lakes, explain that using gravity.
00
Wayne,
I don’t know if you expected a reply or not. But I’m a long way from the Great Lakes and I’m not at all familiar with them. All I know about them is that Lake Superior in particular is subject to sometimes quite violent storms and probably the others as well. So I would need some detailed information about what you describe before I could say anything about it.
But water moves to keep its surface orthogonal to the direction, down, even in the Great Lakes. And gravity is the only force available to cause tides. There is no tide fairy nor is there any nefarious force unique to the Great Lakes. 😉
Something I’d never considered before is that centripetal force resulting from the Earth/moon system orbiting around their common center of mass might contribute to the high tide on the side of the Earth facing away from the moon.
00
Extract from Alex S Gaddes’ work ‘Tomorrow’s Weather’ (1990.)
“The Moon I now accept as being a satellite of the Earth, responsible for exerting great influence on all life thereon.
Though the Moon is bound to Earth by gravitation and so must, as part of a binary system, not only orbit Earth, but also (with Earth,) orbit the Sun once a year, the lunar year differs in length slightly, to Earth’s tropical year.
The lunar year is defined as having a duration encompassing 12 new moons. Its length is approximately 11 days shorter than Earth’s tropical year of 365.25 days.
No doubt the fact that Earth’s rotation rate has slowed down (and continues to do so) over geological time, and conversely, the moon has speeded up in its orbit, would account for the 11 day discrepancy, by virtue of the transfer of angular momentum over the same period of time.
The Law of the Conservation of Angular Momentum states that two separate bodies, spinning in the same plane around a common axis, are subject to the above law, so that any loss of angular momentum by the one, must, by law be transferred to the other.
Thus the Moon is gaining angular momentum at the expense of the Earth’s, while at the same time moving farther away from the Earth.
Once Much Closer?
If this process is reversed, the conclusion is reached that the Earth and moon were once much closer neighbours. George Darwin (son of Charles Darwin) postulated that the Moon came into existence as a result of a great rupture in the Earth’s crust, caused, in turn, by centrifugal force, set up by a much faster spinning Earth at some earlier stage in its evolution, and the great scar it left became the Pacific Ocean basin.
It follows, that if the Moon came really close to the Earth, gigantic tides would be raised in the oceans, evidence of which ought to be plainly displayed. This has not, so far, been discovered.
Sister Planet?
Later studies, and the analyses of Moon-rocks brought back by the astronauts, have demonstrated the probability that the Moon is more likely to be a sister planet than the daughter that George Darwin suggested.
The study of the annular growth rings of Devonian corals (400 mill. Yrs. BP (before the present) indicates that Earth had a 375 day year at that time.
Thus, the Moon would have been somewhat closer to Earth, and orbiting more slowly, while Earth’ rotation would have been correspondingly speeded up, if not precisely conforming to the ideal 12 orbits of Earth each tropical year, the coming close to 12 lunar months of a similar duration to the Earth month of the times.
Solar System Running Down
This indicates that the Solar System’s ‘clock-works’ is slowly running down, along with that of the rest of the Universe. According to scientists, the rate at which the Earth’s day is lengthening, is one second in every 1000 years.
Newton’s Law of Gravitation states that two (or more) bodies will attract each other in proportion to their respective masses and inversely proportional to the square of the distance between them.
It is the gravitational effect of the Moon and, to a lesser degree, the Sun and planets, that produces the reaction in the Earth which we call tides.
Not only does the ocean react by the well known ebb and flow of the tides, but at the same time there are tides raised in the solid Earth and the atmosphere too. These tides are in fact a never-ending train of cycles, wrought mainly by the influence of the Moon on land, sea and air.
By virtue of the Moon’s decree that on Earth there will always be two high tides and two low tides daily, it becomes evident that the Moon, by directly controlling these cycles, simultaneously exerts complete control over countless cycles of life on Earth.
Patterns of Cycles
Nature’s great and fundamental law of conservation, acting through its agent, gravity, has set the patterns of the cycles, which are repeated over and again.
The simplest and most widely accepted is the Earth’s year(or period) cycle, which itself is made up of varied and manifold cycles, such as days, weeks, months etc, as well as the seasons (not to mention the countless cycles of life.)
I have listed but a few of the cyclic patterns in Nature which, while the Solar System continues to exist, will go on being repeated.
Why then, should our climate/weather patterns be exempted from a cyclic system, when all else appears locked into it?
We have seen that amongst the numerous cyclic phenomena directly affecting the earth and all life on it, is the Moon. Apart from the Moon’s cyclic effects on Earth’s tides and marine life, it also controls Mean Sea Level.
While to find Mean Sea Level might appear to be merely a matter of ascertaining the median between high and low water, it turns out that such is not so. The method employed by scientists requires the recording of water levels every hour, over the full 18.61 Yr metonic cycle of the Moon’s nodes, then striking the average.
The metonic cycle of the Moon turns out to be an all-important factor in the overall pattern of our climate/weather; the more so when it happens to coincide with one or more of the unknown (to me) number of cycles which control the Solar System.
Find and Correlate the Cycles
It has been my in concern to find these multi-various cycles and endeavour to correlate them with the evidence recorded, in the short term, by man on one hand, and in the longer term, tree-rings, deep-sea sedimentary drill cores, ice, cores etc. on the other. The story they record is an epic one of climate/weather patterns, which have an historical graph resembling that of the stock exchange.
Let us now take a closer look at the various ways in which the metonic cycle of the Moon might affect Earth’s climate/weather patterns.
Fig.7: The Earth’s precession results from tidal attraction applied to the equatorial bulge.
Precession of the Equinoxes
To explain the metonic cycle of the Moon’s nodes clearly, it becomes necessary to describe another phenomenon, the precession of the equinoxes.
The earth, spinning on its axis, has a definite wobble, like a spinning top which has been nudged.
It requires about 22,000 years to complete one ‘wobble’, or cycle.
The phenomenon of Earth’s precession is caused by intermittent gravitational forces, brought to bear by the Sun and Moon.
The variation in G forces is a result of the fact, that due to the inclination of the Earth’s axis to the plane of the ecliptic, the Sun crosses the Earth’s equator twice and the Moon, 24-25 times a year.
Relax Their Influence
Because the Sun and the Moon, at the time of crossing the equator, relax their gravitational influence, (the cause of the earth’s precession) the Earth tends to ‘straighten up’ its axis; however, this is only a temporary reaction because soon the Sun and the Moon wander off the equator and once again Earth is subjected to a repeat of the afore-mentioned G forces.
The effect of all that pulling and relaxing is to cause what is known as nutation, (from the Latin ‘to nod’.)
Moreover, due to the inclination of the Moon’s orbit with relation to the plane of the ecliptic, there is a Moon cycle of 18.61 years regarding its effectiveness in abetting the cause of the Earth’s precession.
Moon’s Metonic Cycle
Over this 18.61 year cycle, the Moon also nutates, (nods.) This cycle is known as the regressional period of the Moon’s nodes, or the Metonic Cycle of the Moon.
A metonic cycle is said to be completed when a full moon, after leaving a specific position in space, relative to the observer on Earth and the fixed stars, returns to the original bearing or point of starting.
It can be seen the Moon possesses a mighty potential for influencing Earth’s climate/weather patterns. I think the main part of the problem of the lunar influence is that of clarification. I suspect the Moon’s incessant, varying tidal influence on the ocean, must have a significant effect on its circulation.
At least one scientist (Dr Bowen,) has claimed a correlation with cooler ocean surface temperatures off Eastern Australia and mainland droughts.
Could tidal action by the Moon, over time, have any influence on the upwelling of cold ocean-bottom waters? Scientific papers written on the subject of the periodicity of cold and warm ocean surface temperatures and their distribution in time and space are noteworthy by their absence, at least in the literature to which I’ve had access.
Oceans have to be considered as an important variable in the quest for answers. The very obvious gravitational link between the oceans and the Moon makes the latter a prime suspect.
As we shall see, the metonic cycle of the Moon keeps ‘bobbing up’ in connection with a whole range of cycles, as defined throughout this study.” (pp27-32}
A complete updated version of this work,(including ‘Dry’Cycle forecasts to 2055)is available as a free pdf from [email protected]
00
All very interesting just as long as it’s not my taxes being spent on such ventures.
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Don Gaddes
You are on the ball with your understanding and transcript to Joe’s letter of information from NASA is very well given.
May I give you my understanding of the Moon’s orientation and why it has this Bulge affect of the claimed 51cm’s.
It is my understanding that the Moon’s face is towards the Earth’s and its Magnetic emission is Positive. It is this energy that is being reactive to the South central pole is within, one third portion of the central face of the Moon. As you rightly point out, the circumference at this point is at its greatest and as you also indicate, the Moon wobbles during its oscillating cycle of Earth and again you point out that the cycle of the Moon varies constantly until it again resumes its averaged processional cycle of 18.6 Years.
Where I differ from you is the understanding of this cycle, is that I do not accept the term “Gravity.” I prefer to the term Magnetism is the controlling factor and as mentioned by others, the variable bodge is in fact that wobbly portion of the South Pole of the Moon’s face.
For one to understand where this has an affect to the Earth is the variable tidal effects every 29 odd days and when applying magnetism, it sits well with this understanding of why there is such a grand variation between the Northern and Southern Hemispheres tidal’s of Earth.
When one understands this magnetic approach of mine, it offers a greater understanding of the reason why its Orbital Height, within the Northern Hemisphere (356,000kms) is when there is always a Full Moon Characteristic and this event is never within the Southern Hemisphere, where it averages 406,000kms. The Southern Hemisphere, with a Positive Earth emission, pushes the Moon away and always experiences the New Moon cycle, and again, this is never repeated within the Northern Hemisphere.
To answer why we are experiencing the seasonal changes, the Sun’s Processional Cycle of 120,000 years completed this cycle on or near the 22 December 2012 and in so doing, entered again a Negative sector of the Milky Way and it is this influence that is changing our seasons.
Clouds have a magnetic involvement here, as the upper surface of Cumulus Clouds have a Negative Magnetic involvement when the Earth is also orbiting with the Sun, and during their respective seasonal exchanges. It is this combined Magnetic involvement that is generating a Push and Pull affect, like it is in the Southern Hemisphere of the tilt of Earth being tilted towards the sun, BUT is experiencing its winter cycle with the Sun’s Positive emission sector, making these clouds go to a higher altitude, which is also changing the Barometric Pressure systems.
Here in Geelong, Victoria, Australia, these Barometric Pressure cycles are averaging during this Winter cycle, as being 1028mb. The one passing over us today is 1031mb.(Summer Cycle values) It is this element that has determined the drizzle, instead of heavy rain. The weather patterns also show that the Lows over Australia are indeed very scares.
I trust that my latest book: “Formula Used to Determine Gravity Waves “gw” within Atoms” is at $40.00AU and has a CD(pdf) attached of my second book: Climate Change-Explained by Magnetism?
Thank you Joe for your contribution. I sincerely hope that your paper above stirs the possums.
00
I do not know the ‘Joe’of whom you speak, or his ‘paper.’
The Moon ‘nods’ on it’s axis (nutates) once every 18.61 years. This means the whole Moon is affected.
Earth’s ‘Dry’ Cycles are initiated in the Sun,(the 27 day rotation rate ‘Sunspot’ Latitude) and orbit the Earth West to East (thirty degrees of longitude/Month)with the Solar Orbit of Earth’s Magnetic Field. (360 degrees/Year.) The major influence in this ‘mechanism’ is Gravitation between Sun, Moon and Earth.
I offer you the following partial description of the Gaddes Dry Cycle Hierarchy, as fully set out in the aforementioned work ‘Tomorrow’s Weather’. (see post #20)
Fig. 3:
Earth’s Period (No. 1 Constant)
Divided by 4
(Obliquity, No. 2 Constant) = Quarter Year
Multiplied by 27
(Ratio, No. 3 Constant) = 6.75 Years
(Regional Drought Cycle)
Multiplied by 11.028148 Yrs
(Sunspot Wave Frequency,
No. 4 Constant) = 74.44 Years
(Quarterly Sub-cycle of a
Full 297.76 year Sunspot
Cycle)
Divided by 4
(Obliquity,No. 2 Constant) = 18.61 Years
(Metonic Cycle of
Moon’s Nodes)
Multiplied by 27
(Ratio, No. 3 Constant) = 502.47 Years
(Full Tree-ring Cycle;
3 x 167.49 Year Tree-ring
Sub-cycles. The 167.49 Year
Sub-cycle is in turn made up
of 9 x 18.61 Year Metonic
Cycles of the Moon.)
Fig. 3: cont,
Multiplied by 11.028148 Yrs
(Sunspot Wave Frequency,
No. 4 Constant) = 5,541.3135 Years
(Which equals 2 x 2,770.6567
Year Glacial Cycles,
See J. Bray, Ref. No. (?)
Multiplied by 27
(Ratio, No. 3 Constant) = 37,403.864 Years (The Cycle
Obliquity of the Earth’s Axis.)
Multiplied by 11.028148 Yrs
(Sunspot Wave frequency,
No. 4 Constant) = 412,495.34 Years (=?)
Divided by 4
(Obliquity, No. 2 Constant) = 103,123.83 Years (Precession
Of *Perihelion and Aphelion)
*Perihelion: When the Earth is nearest the Sun.
*Aphelion: When the Earth is furthest from the Sun.
Revised Solar rotation Rate = 27d
Fig. 3.
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