Archive for the ‘moon’ Category


This was a surprise, but whatever the interpretation, the numbers speak for themselves.

‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured relative to the stars, but because the Earth is orbiting the Sun, we see this period as 27.2753 days.’ – Wikipedia.

What happens if we relate this period to the lunar draconic year?

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Image credit: interactivestars.com


It turns out that the previous post was only one half of the lunar evection story, so this post is the other half.

There are two variations to lunar evection, namely evection in longitude (the subject of the previous post) and evection in latitude, which ‘generates a perturbation in the lunar ecliptic latitude’ (source).

It’s found that the first is tied to the full moon cycle and the second to the draconic year.

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Why Phi? – a lunar evection model

Posted: November 16, 2018 by oldbrew in Fibonacci, moon, Phi, solar system dynamics
Tags: ,

Apogee = position furthest away from Earth. Earth. Perihelion = position closest to the sun. Moon. Perigee = position closest to Earth. Sun. Aphelion = position furthest away from the sun. (Eccentricities greatly exaggerated!)

Lunar evection has been described as the solar perturbation of the lunar orbit.

One lunar evection is the beat period of the synodic month and the full moon cycle. The result is that it should average about 31.811938 days (45809.19 minutes).

Comparing synodic months (SM), anomalistic months (AM), and lunar evections (LE) with the full moon cycle (FMC) we find:
1 FMC = 13.944335 SM
1 FMC = 13.944335 + 1 = 14.944335 AM
1 FMC = 13.944335 – 1 = 12.944335 LE

Since 0.944335 * 18 = 16.9983 = 99.99% of 17, and 18 – 17 = 1, we can say for our model:
18 FMC = 233 LE (18*13, -1) = 251 SM (18*14, -1) = 269 AM (18*15, -1)
See: 3 – Matching synodic and anomalistic months.
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Why Phi: is the Moon a phi balloon? – part 2

Posted: November 9, 2018 by oldbrew in Astrophysics, moon, Phi
Tags: ,

Credit: universetoday.com


Picking up from where we left off here

Three well-known aspects of lunar motion are:
Lunar declination – minimum and maximum degrees
Orbital parameters – perigee and apogee distances (from Earth)
Anomalistic month – minimum and maximum days

Standstill limits due to the lunar nodal cycle

‘The major standstill limit of the moon can be reached if the lunar node is near the vernal (or autumnal) point, and with the moon at its max. distance from the equator, equal to a declination at present days of 23.44° + 5.1454°= 28.59°.

The minor standstill limit of the moon can be reached if the lunar node is near the vernal (or autumnal) point, and with the moon at its min. distance from the equator, equal to a declination at present days of 23.44°- 5.1454° = 18.29°.’
http://iol.ie/~geniet/eng/moonperb.htm#nodes

28.59 / 18.29 = 1.5631492
4th root of 1.5631492 = 1.11815
This number leads to the key to the puzzle.

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Ian Robert George Wilson and Nikolay S Sidorenkov

Wilson and Sidorenkov, J Earth Sci Clim Change 2018, 9:1, p. 446

https://www.omicsonline.org/open-access/a-lunisolar-connection-to-weather-and-climate-i-centennial-times-scales-2157-7617-1000446.pdf

Abstract

Lunar ephemeris data is used to find the times when the Perigee of the lunar orbit points directly toward or away from the Sun, at times when the Earth is located at one of its solstices or equinoxes, for the period from 1993 to 2528 A.D. The precision of these lunar alignments is expressed in the form of a lunar alignment index (ϕ). When a plot is made of ϕ, in a frame-of-reference that is fixed with respect to the Perihelion of the Earth’s orbit, distinct periodicities are seen at 28.75, 31.0, 88.5 (Gleissberg Cycle), 148.25, and 208.0 years (de Vries Cycle). The full significance of the 208.0-year repetition pattern in ϕ only becomes apparent when these periodicities are compared to those observed in the spectra for two proxy time series. The first is the amplitude spectrum of the maximum daytime temperatures (Tm ) on the Southern Colorado Plateau for the period from 266 BC to 1997 AD. The second is the Fourier spectrum of the solar modulation potential (ϕm) over the last 9400 years. A comparison between these three spectra shows that of the nine most prominent periods seen in ϕ, eight have matching peaks in the spectrum of ϕm, and seven have matching peaks in the spectrum of Tm. This strongly supports the contention that all three of these phenomena are related to one another. A heuristic Luni-Solar climate model is developed in order to explain the connections between ϕ, Tm and ϕm.

Wilson_Sidorenkov_Fig_04

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Credit: NASA


Researchers say: ‘Study of wave characteristics reveals complex interconnections between the Sun, Moon, and Earth’s neutral atmosphere and ionosphere.’

The waves in the upper atmosphere are similar to the V-shaped waves left behind by a ship moving through water, reports The IB Times.

The 21 August total solar eclipse that overshadowed the entire stretch from Oregon to South Carolina, not only offered some mind-boggling views, but also left a weird effect on Earth’s atmosphere.

The event created heat-energy ripples or “bow waves”, something akin to the V-shaped waves left behind by a ship moving through water, in Earth’s upper atmosphere, Gizmodo reports.

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This started as a search for a period when the Sun and the Moon would both complete a whole number of rotations.
The result was:
Solar: 25.38 days * 197 = 4999.860 d
Lunar: 27.321662 * 183 = 4999.864 d
(data sources: see reference notes at end)

Taking these as equivalent, we have 197-183 = 14 ‘beats’.
197 = 14*14, +1
183 = 13*14, +1
4999.864 / 14 = 357.13314 days
357.13314 days * 45/44 = 365.2498 days
45 * 14 (630) beats = 44 * 14 (616) calendar years, difference = 0.022 day

So the beat period of the two rotations is 44/45ths of a year, i.e. the difference in number of rotations is exactly 1 in that length of time.
630 beats = 616 years (630 – 616 = 14)
616/45 = 13.68888 calendar years = 4999.8663 days
184 lunar sidereal months (rotations) = 4999.864 days

Then something else popped up…

The Phi factor:
‘We recover a 22.14-year cycle of the solar dynamo.’ (2016 paper)
See: Why Phi? – modelling the solar cycle

Solar Hale cycle = ~22.14 years (est. mean)
13.68888 * Phi = 22.149~ years
22.14 / 13.68888 = 1.61737 (99.96% of Phi)
(55/34 = 1.617647)

From the same post:
Jupiter-Saturn axial period (J+S) is 8.456146 years.
That’s when the sum of J and S orbital movement in the conjunction period = 1

13.68888 / 8.456146 = 1.618808
Phi = 1.618034

Conclusion:
This cycle of solar and lunar sidereal rotation (SRC) sits at the mid-point of the Phi²:1 ratio between the J+S axial period and the mean solar Hale cycle, i.e. with a Phi ratio to one and inverse Phi to the other.
SRC = (J+S) * Phi
SRC = Hale / Phi
SRC = Hale – (J+S)
(Mean Hale value is assumed)

In a period of 616 years there are 45 SRC.
The period is 44 * 14 years = 45 SRC = 45 * 14 beats.
SRC * (45/44) = 14 years.

Cross-checks:
Carrington rotations per 616 y = 8249
8249 CR / 45 = 4999.865 days

Synodic months per 616 y = 7619
7619 SM / 45 = 4999.856 days
8249 – 7619 = 630 = 45 * 14

45*183 sidereal months = 8235
8235 – 7619 = 616
8249 CR – 8235 Sid.M = 14
Beat period of CR and Sid.M = 616/14 = 44 years = 45 * (13.6888 / 14)
Every 44 years there will be exactly one less lunar rotation (sidereal month) than the number of Carrington rotations.

8249 CR – 7619 synodic months = 630 = 45 * 14
630 – 616 = 14
– – –
The anomalistic year

The beat period of the tropical month and solar sidereal rotation * 45/44 = the anomalistic year.
(27.321582 * 25.38) / (27.321582 – 25.38) = 357.14265 days
45 * 357.14265 = 16071.419 days
44 * 365.259636 = 16071.423 days

The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 3 in 2011), and the aphelion, where the Earth is farthest from the Sun (July 4 in 2011). The anomalistic year is usually defined as the time between perihelion passages. Its average duration is 365.259636 days (365 d 6 h 13 min 52.6 s) (at the epoch J2011.0).
http://en.wikipedia.org/wiki/Year#Sidereal.2C_tropical.2C_and_anomalistic_years
– – –
Data sources

— Carrington Solar Coordinates:
Richard C. Carrington determined the solar rotation rate by watching low-latitude sunspots in the 1850s. He defined a fixed solar coordinate system that rotates in a sidereal frame exactly once every 25.38 days (Carrington, Observations of the Spots on the Sun, 1863, p 221, 244). The synodic rotation rate varies a little during the year because of the eccentricity of the Earth’s orbit; the mean synodic value is about 27.2753 days.
http://wso.stanford.edu/words/Coordinates.html

— The standard meridian on the sun is defined to be the meridian that passed through the ascending node of the sun’s equator on 1 January 1854 at 1200 UTC and is calculated for the present day by assuming a uniform sidereal period of rotation of 25.38 days (synodic rotation period of 27.2753 days, Carrington rotation).
http://jgiesen.de/sunrot/index.html

The sidereal month is the time between maximum elevations of a fixed star as seen from the Moon. In 1994-1998, it was 27.321662 days.
http://scienceworld.wolfram.com/astronomy/SiderealMonth.html

Saturn’s moon Janus


Cassini maintains its reputation for surprises right to the end. It’s the ‘moon resonances’ that maintain ring stability, but with a new twist.

For three decades, astronomers thought that only Saturn’s moon Janus confined the planet’s A ring – the largest and farthest of the visible rings.

But after poring over NASA’s Cassini mission data, Cornell astronomers now conclude that the teamwork of seven moons keeps this ring corralled, as Phys.org explains.

Without forces to hold the A ring in check, the ring would keep spreading out and ultimately disappear.

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How bright is the moon, really?

Posted: October 17, 2017 by oldbrew in moon, research, solar system dynamics
Tags:


Researchers aim to find out. It’s an interesting question as ‘our Moon’s average visual albedo is 0.12’, similar to soil or asphalt, and yet songwriters can describe ‘the light of the silvery Moon’.

The “inconstant moon,” as Shakespeare called it in Romeo and Juliet, is more reliable than his pair of star-crossed lovers might have thought, says Phys.org.

Now researchers at the National Institute of Standards and Technology (NIST) plan to make the moon even more reliable with a new project to measure its brightness.

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Lunar precession update

Posted: October 15, 2017 by oldbrew in Fibonacci, Maths, moon, Phi, solar system dynamics
Tags: ,

Credit: NASA


I found out there’s an easy way to simplify one of the lunar charts published on the Talkshop in 2015 on this post:
Why Phi? – some Moon-Earth interactions


In the chart, synodic months (SM) and apsidal cycles (LAC) are multiples of 104:
79664 / 104 = 766
728/104 = 7

The other numbers are not multiples of 104, but if 7 is added to each we get this:
86105 + 7 = 86112 = 828 * 104 (TM)
85377 + 7 = 85384 = 821 * 104 (AM)
5713 + 7 = 5720 = 55 * 104 (FMC)
6441 + 7 = 6448 = 62 * 104 (TY)

TM = tropical months
AM = anomalistic months
SM = synodic months
LAC = lunar apsidal cycles
FMC = full moon cycles
TY = tropical years


Here’s an imaginary alternative chart based on these multiples of
104. [Cross-check: 828 – 766 = 62]

In reality, 55 FMC = just over 62 TY and 7 LAC = just short of 62 TY.
For every 7 apsidal cycles (LAC), there are 766 synodic months (both chart versions).

In the real chart:
For every 104 apsidal cycles, all numbers except SM slip by -1 from being multiples of 104. So after 7*104 LAC all the other totals except SM are ‘reduced’ by 7 each.

In the case of tropical years, 6448 – 7 = 6441 = 19 * 339
19 tropical years = 1 Metonic cycle

If the period had been 6448 TY it would not have been a whole number of Metonic cycles.
Also 6441 * 4 TY (25764) is exactly one year more than 25763 synodic years i.e. the precession cycle, by definition.

Fibonacci: 104 is 13*8, and the modified FMC number is 55 (all Fibonacci numbers).

Phi: we’ve explained elsewhere that the number of full moon cycles in one lunar apsidal cycle is very close to 3*Phi².
We can see from the modified chart that the FMC:LAC ratio of 55:7 is 3 times greater than 55:21 (55/21 = ~Phi²)
– – –
Note – for more discussion of the ~62 year period, try this search:
site:tallbloke.wordpress.com 62 year
[see Google site search box in grey zone on left of this web page]

Also eclipsing internet records


Only to be be expected, but the great American eclipse was a massive internet hit, as the daily sun [sic] reports.

The total solar eclipse of August 21 attracted more traffic to NASA websites than any other event on record, according to data revealed by the US space agency, reports Ians. 

“With more than 90 million page views on nasa.gov and eclipse2017.nasa.gov, we topped our previous web traffic record about seven times over,” NASA officials wrote. 

It was one of the biggest internet events in recent history and by far the biggest online event NASA has ever measured. “We estimate more than 40 million views of our live broadcast on nasa.gov and multiple social platforms,” NASA said. 

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They admit that “The exact origin of water in the lunar interior is still a big question”, as Phys.org reports. The article also points out that ‘The idea that the interior of the Moon is water-rich raises interesting questions about the Moon’s formation.’ Perhaps they are suggesting that some prevailing theories might no longer…er…hold water.

A new study of satellite data finds that numerous volcanic deposits distributed across the surface of the Moon contain unusually high amounts of trapped water compared with surrounding terrains.

The finding of water in these ancient deposits, which are believed to consist of glass beads formed by the explosive eruption of magma coming from the deep lunar interior, bolsters the idea that the lunar mantle is surprisingly water-rich.

Scientists had assumed for years that the interior of the Moon had been largely depleted of water and other volatile compounds.

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sun-earth-moon

Overview

More than a year after “Part II” of a guest post from Talkshop contributor ‘Galloping Camel’ on the Moon’s equatorial temperature here is “Part III”.  Peter actually sent this to Tim Channon last year, but Tim became to ill to deal with it and forgot to throw it my way. In current discussion of Ned and Karl’s new paper, the issue of planetary surface temperature variation due to speed of rotation arose. Ned thinks it makes no difference. Peter’s model says it does, so now is a good time for discussion, as this impacts theoretical estimates for the temperature of ‘Earth with no atmosphere’.

Modeling the Moon

It has been claimed that the GHE (Greenhouse Effect) is 33 Kelvin because the Earth’s average temperature is 288 K compared to a temperature of 255 K assumed for an “Airless Earth”.  The Diviner LRO showed that the Moon’s average temperature is 197.3 K which makes one wonder how an estimate based on impeccable mathematics could be so wrong?   Vasavada et al. published a paper in 2012 that mentioned a one-dimensional model of the Moon’s regolith.  As I was unable to obtain details of this model I attempted to replicate it using Quickfield, a powerful FEA (Finite Element Analysis) program.  Results obtained using my model were published here.

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Astrophysicist Ian Wilson has emailed me to ask for a brainstorming session at the talkshop to assist him. Ian writes:

“I was wondering if you or your colleagues (e.g. oldbrew) could help me work out the solution to the following lunar puzzle”

Drift_01

The Conundrum

The diagram below shows the Perigee of the lunar orbit pointing at the Sun at 0.0 days. In addition, the diagram shows the Perigee of the lunar orbit once again pointing at the Sun after one Full Moon Cycle (FMC) = 411.78443025 days. It takes more than 1.0 sidereal year (= 365.256363004 days) for the Perigee to realign with the Sun because of the slow pro-grade (clockwise) precession of the lunar line-of-apse once every 8.85023717 sidereal years.

1.0 FMC falls short of 15 anomalistic months (= 413.31824817 days) by 1.53381792 days (= 1.5117449198O). During these 1.5117449198 days the Perigee end of the lunar line-of-apse rotates by 0.17081406in a prograde direction, producing an overall movement of the line-of-apse (red line) of 1.34093086O (= 1.5117449198O – 0.17081406O) with respect to the Earth-Sun line (blue line).

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The largest ‘TNOs’

This is about the ‘no-name’ dwarf planet 2007 OR10, which has the unusual property of being 3 times further from the Sun at aphelion (furthest) than at perihelion (nearest).

Everybody gets a moon! With the discovery of a small moon orbiting the third-largest dwarf planet, all the large objects that orbit beyond Neptune now have satellites, reports New Scientist.

Trans-Neptunian objects (TNOs) spend most or all of their orbits beyond Neptune. Last April, the dwarf planet Makemake became the ninth of the ten TNOs with diameters near or above 1,000 kilometres known to have a moon.

So when dwarf planet 2007 OR10 was found to be rotating more slowly than expected, it was suspected that a moon might be the culprit.
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Image credit: NASA

Image credit: NASA


From the research paper: ‘We suggest the possibility that the Earth’s atmosphere of billions of years ago may be preserved on the present-day lunar surface.’

A team of researchers affiliated with several institutions in Japan, examining data from that country’s moon-orbiting Kaguya spacecraft, has found evidence of oxygen from Earth’s atmosphere making its way to the surface of the moon for a few days every month, reports Phys.org.

In their paper published in the journal Nature Astronomy, the researchers describe what data from the spacecraft revealed.
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Take that [credit: universetoday.com]

Take that [credit: universetoday.com]


It seems that there’s always another Moon theory, or variation of an existing one, in the pipeline and here’s one of the newest contenders. Each seems to have its own issues though.

The most widely accepted theory about how the Moon formed has been challenged, with scientists saying a series of large impacts – rather than one giant collision – created our natural satellite, reports the IB Times.

By running numerical simulations, researchers say the Earth being hit by several large planetary bodies would help explain why our planet and the Moon are largely composed of the same material – a problem that has plagued scientists for decades.

The giant impact Moon formation theory was first proposed in the mid-1970s. It says a Mars-sized protoplanet called Theia smashed into Earth around 4.5 billion years ago. The ejected material created a disk of debris, molten rock and gas that eventually condensed to form the Moon.

However, there is a big problem with this theory. If it was correct, the Moon’s composition should be a mix of both Earth and Theia. For this to happen, Theia would have had to be almost identical to Earth in terms of its composition, which is highly unlikely.
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Why Phi? – a lunar ratios model

Posted: January 8, 2017 by oldbrew in Cycles, modelling, moon, Phi
Tags: ,
Lunar ratios diagram

Lunar ratios diagram

The idea of this post is to try and show that the lunar apsidal and nodal cycles contain similar frequencies, one with the full moon cycle and the other with the quasi-biennial oscillation.

There are four periods in the diagram, one in each corner of the rectangle. For this model their values will be:

FMC = 411.78443 days
LAC = 3231.5 days
LNC = 6798.38 days
QBO = 866 days (derived from 2 Chandler wobbles @ 433 days each)
The QBO period is an assumption (see Footnote below) but the others can be calculated.
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Some stones of Rego Grande, known as the 'Amazon Stonehenge'

Some stones of Rego Grande, known as the ‘Amazon Stonehenge’


As soon as the Mail Online report of this historic site said there were 127 stones, an idea occurred. In the lunar Metonic cycle of ~19 years there are 254 lunar orbits (= sidereal months) of the Earth, which is 127 x 2. If this has already been suggested somewhere, I’m not aware of it!

Wikipedia says: ‘the Metonic cycle…is a period of very close to 19 years that is remarkable for being nearly a common multiple of the solar year and the synodic (lunar) month.’

A megalithic stone circle in Brazil hints that the indigenous people of the Amazon may have been more sophisticated than archaeologists first thought.

Rego Grande, known as the ‘Amazon Stonehenge’ after the famous prehistoric monument in Wiltshire, is located in Amapá state, near the city of Calçoene. Experts say the unusual stone arrangement may have been used as a place of worship as well as for astronomical observations related to crop cycles.

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Sidorenkov and the lunar or tidal year

Posted: November 27, 2016 by oldbrew in climate, Cycles, Maths, moon
Tags: ,

Credit: reference.com

Credit: reference.com


This is an attempt to understand via the numbers the concept proposed by Russian researcher Sidorenkov of a lunar year interacting with the terrestrial year to produce an effect of a ‘quasi-35 year’ climate cycle.

Sidorenkov in his paper ON THE SEPARATION OF SOLAR AND LUNAR CYCLES says:

The lunisolar tides repeat with a period of 355 days,
which is known as the tidal year. This period is also
manifested as a cycle of repeated eclipses. Meteorological
characteristics (pressure, temperature, cloudiness, etc.)
vary with a period of 355 days. The interference of these
tidal oscillations and the usual annual 365-day oscillations
generates beats in the annual amplitude of meteorological
characteristics with a period of about 35 years (Sidorenkov
and Sumerova, 2012b). The quasi 35-year variations in
cloudiness lead to oscillations of the radiation balance
over terrestrial regions. As a result of these quasi-
35-year beats, the climate, for example, over European
Russia alternates between “continental” with dominant
cold winters and hot summers (such as from 1963 to 1975
and from 1995 to 2014) and “maritime” with frequent
warm winters and cool summers (such as from 1956 to
1962 and from 1976 to 1994)

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