Archive for the ‘moon’ Category

Credit: NASA


The idea is to validate Belgian astronomer Willy de Rop’s 1971 calculations, which can be found here.

From our 2016 post discussing his paper, De Rop’s long-term lunar cycle:

De Rop’s basic premise is that there’s a correlation between the so-called ‘lunar wobble’ period and the anomalistic year.
His paper contains a geometric proof, and the final numbers are:
300 lunar wobbles in 1799 anomalistic years (the lunar wobble is known to repeat in just under 6 years).

To see what the lunar wobble is, refer to the paper. Essentially it’s when the number of lunar apsidal and nodal cycles in the period sums to 1. For more information, please refer to that post.

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Image credit: naturalnavigator.com


We’re told: ‘They refer to what they’ve found as ANTS, for Active Nearside Tectonic System’, which is ‘a mysterious system of tectonic features (ridges and faults) on the lunar nearside, unrelated to both lava-filled basins and other young faults that crisscross the highlands.’ Tectonic activity on one side only sounds a bit unlikely somehow, but what about tidal disturbance from Earth? We know it works the other way round: the Moon causes tides on Earth. Of course the Moon is tidally locked to Earth, hence the term ‘nearside’.
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Researchers have discovered a system of ridges spread across the nearside of the Moon topped with freshly exposed boulders, reports Phys.org.

The ridges could be evidence of active lunar tectonic processes, the researchers say, possibly the echo of a long-ago impact that nearly tore the Moon apart.

“There’s this assumption that the Moon is long dead, but we keep finding that that’s not the case,” said Peter Schultz, a professor in Brown University’s Department of Earth, Environmental and Planetary Sciences and co-author of the research, which is published in the journal Geology.

“From this paper it appears that the Moon may still be creaking and cracking—potentially in the present day—and we can see the evidence on these ridges.”

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The Saros cycle by numbers

Posted: April 14, 2020 by oldbrew in Analysis, Cycles, data, moon


The basis for discussion is the abstract of the paper below. Instead of their ‘high-integer near commensurabilities among lunar months’ we’ll just say ‘numbers’ and try to make everything as straightforward as possible. This will expand on a previous Talkshop post on much the same topic.

Hunting for Periodic Orbits Close to that of the Moon in the Restricted Circular Three-Body Problem (1995)
Authors: G. B. Valsecchi, E. PerozziA, E. Roy, A. Steves

Abstract
The role of high-integer near commensurabilities among lunar months — like the long known Saros cycle — in the dynamics of the Moon has been examined in previous papers (Perozzi et al., 1991; Roy et al., 1991; Steves et al., 1993). A by-product of this study has been the discovery that the lunar orbit is very close to a set of 8 long-period periodic orbits of the restricted circular 3-dimensional Sun-Earth-Moon problem in which also the secular motion of the argument of perigee ω is involved (Valsecchi et al., 1993a). In each of these periodic orbits 223 synodic months are equal to 239 anomalistic and 242 nodical ones, a relationship that approximately holds in the case of the observed Saros cycle, and the various orbits differ from each other for the initial phases. Note that these integer ratios imply that, in one cycle of the periodic orbit, the argument of perigee ω makes exactly 3 revolutions, i.e. the difference between the 242 nodical and the 239 anomalistic months (these two months differ from each other just for the prograde rotation of ω).
[bold added]

To start with we can create a model that pretends the ‘high-integer near commensurabilities’ really are whole numbers, then break down the logic of the result to see what’s going in with the Moon at the period of one Saros cycle.

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Encylopaedia Britannica on the Metonic cycle:

Metonic cycle, in chronology, a period of 19 years in which there are 235 lunations, or synodic months, after which the Moon’s phases recur on the same days of the solar year, or year of the seasons. The cycle was discovered by Meton (fl. 432 bc), an Athenian astronomer.

Calendar Wiki’s opening paragraphs on the Metonic cycle say:

The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal i.e. tropical year) and the synodic month. Nineteen tropical years differ from 235 synodic months by about 2 hours. The Metonic cycle’s error is one full day every 219 years, or 12.4 parts per million.

19 tropical years = 6939.602 days
235 synodic months = 6939.688 days

It is helpful to recognize that this is an approximation of reality.

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Earth
New laser technology delves into Earth’s history.
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Earth turned faster at the end of the time of the dinosaurs than it does today, reports Phys.org, rotating 372 times a year compared to the current 365, according to a new study of fossil mollusk shells from the late Cretaceous.

This means a day lasted only 23 and a half hours, according to the new study in AGU’s journal Paleoceanography and Paleoclimatology.

The ancient mollusk, from an extinct and wildly diverse group known as rudist clams, grew fast, laying down daily growth rings. The new study used lasers to sample minute slices of shell and count the growth rings more accurately than human researchers with microscopes.

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Jupiter-Saturn-Earth orbits chart


This was just about to go live when a new idea involving the Sun cropped up, now added to the original. The source data is from NASA JPL as usual.

From our 2015 de Vries post we saw that the 2503 year period, which the numbers were based on, consisted of 85 Saturn and 211 Jupiter orbits [see chart on the right].

Taking Saturn’s orbit period, and using JPL’s planetary data we find:
10755.7 days * 85 = 914234.5 days

The lunar year is 13 lunar orbits of Earth:
27.321582 days * 13 = 355.18056 days

914234.5 / 355.18056 = 2573.9992 (2574) = 13 * 198 lunar years

Number of beats of Saturn and the lunar year = 2574 – 85 = 2489 in 2503 years.
2503 – 2489 = 14
Number of Jose cycles in 2503 years = 14 (= 126 Jupiter-Saturn conjunctions, i.e. 9 J-S * 14).

Therefore the difference per Jose cycle between ‘Saturn-lunar year’ beats and Earth years is exactly one.

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View from Titan [artist’s impression]


From the report: ‘the researchers said, learning more about the energy budget of Titan can add to the understanding of climate change on Earth.’ Indeed – and help could be at hand with that.

Researchers have found that Saturn’s largest moon Titan undergoes significant seasonal changes in its energy budget — the amount of solar energy it absorbs, and the heat it emits — an advance that may lead to new insights about climate fluctuations on the Earth, reports Financial Express.

The study, published in the journal Geophysical Research Letters, noted that Titan is the only body in the solar system, other than Earth, with a significant atmosphere and liquid surface lakes.

The researchers, including those from the University of Houston in the US, said Titan’s dynamically-varying energy budget has important impacts on its weather and climate systems.

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Neptune Moon Dance: This animation illustrates how the odd orbits of Neptune’s inner moons Naiad and Thalassa enable them to avoid each other as they race around the planet. (courtesy: JPL)

Well, this is fun. Need we say more?

Even by the wild standards of the outer solar system, the strange orbits that carry Neptune’s two innermost moons are unprecedented, according to newly published research.

Orbital dynamics experts are calling it a “dance of avoidance” performed by the tiny moons Naiad and Thalassa, says Space Newsfeed.

The two are true partners, orbiting only about 1,150 miles (1,850 kilometers) apart.

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Credit: reference.com


There are many reasons NASA is pursuing the Artemis mission to land astronauts on the moon by 2024: It’s a crucial way to study the moon itself and to pave a safe path to Mars, says Phys.org.

But it’s also a great place to learn more about protecting Earth, which is just one part of the larger Sun-Earth system.

Heliophysicists—scientists who study the Sun and its influence on Earth—will also be sending up their own NASA missions as part of Artemis. Their goal is to better understand the complex space environment surrounding our planet, much of which is driven by our Sun.

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Thanks to Ian Wilson for introducing us to his new paper, which is part three of the planned four-part series. The paper can be downloaded from The General Science Journal here. Abstract below.

Abstract

The best way to study the changes in the climate “forcings” that impact the Earth’s mean atmospheric temperature is to look at the first difference of the time series of the world-mean temperature, rather than the time series itself.

Therefore, if the Perigean New/Full Moon cycles were to act as a forcing upon the Earth’s atmospheric temperature, you would expect to see the natural periodicities of this tidal forcing clearly imprinted upon the time rate of change of the world’s mean temperature.

Using both the adopted mean orbital periods of the Moon, as well as calculated algorithms based upon published ephemerides, this paper shows that the Perigean New/Full moon tidal cycles exhibit two dominant periodicities on decadal time scales.

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Image credit: farmersalmanac.com


The Harvest Moon is the Full Moon nearest to the September equinox, which occurs around September 22.

The UK is set to be treated to a rare occurrence of a Harvest Moon tonight.

The Moon will be about 14 per cent smaller in the sky than an average full moon, making it an especially rare “micromoon”, says the London Evening Standard.

Maine Farmers’ Almanac astronomer Joe Rao said the time it peaks will depend on the position of the moon.

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Image credit: naturalnavigator.com


The contention here is that in the time taken for 14 lunar nodal cycles, the difference between the number of Saros eclipse cycles and lunar apsidal cycles (i.e the number of ‘beats’ of those two periods) is exactly 15.

Since 15-14 = 1, this period of 260.585 tropical years might itself be considered a cycle. It is just over 9 Inex eclipse cycles (260.5 years) of 358 synodic months each, by definition.

Although it’s hard to find references to ~260 years as a possible climate and/or planetary period, there are a few for the half period i.e. 130 years, for example here.

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The Kepler-42 system as compared to the Jovian system [credit: NASA/JPL-Caltech]

The headline was NASA’s joke about both the size and the short orbit periods (all less than two days) of the three planets in the Kepler-42 system.

The discovery of this system dates back to 2012, but there don’t seem to be any numbers on resonant periods, so we’ll supply some now.

Wikipedia says:
‘Kepler-42, formerly known as KOI-961, is a red dwarf located in the constellation Cygnus and approximately 131 light years from the Sun. It has three known extrasolar planets, all of which are smaller than Earth in radius, and likely also in mass.’

‘On 10 January 2012, using the Kepler Space Telescope three transiting planets were discovered in orbit around Kepler-42. These planets’ radii range from approximately those of Mars to Venus. The Kepler-42 system is only the second known system containing planets of Earth’s radius or smaller (the first was the Kepler-20 system). These planets’ orbits are also compact, making the system (whose host star itself has a radius comparable to those of some hot Jupiters) resemble the moon systems of giant planets such as Jupiter or Saturn more than it does the Solar System.’

The three planets in order of distance from their star (nearest first) are c,b and d. They all have very short orbit periods ranging from under half a day to less than two days, and the star has only 13% of the power of our Sun.

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Image credit: interactivestars.com


In 2015 this post discussed long-term lunar precession from an apsidal, or anomalistic, standpoint.

We saw that all the numbers related to an exact number (339) of Metonic cycles (19 tropical years each, as discussed below).

Here we show the equivalent from a nodal, or draconic, standpoint.

Again, all the numbers relate to an exact number (337 this time) of Metonic cycles.

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Plus: how big will the bite of the ongoing solar minimum be, compared to the last one? We’re due to find out sometime soon.

Spaceweather.com

July 16, 2019: Note to astronauts: 2019 is not a good year to fly into deep space. In fact, it’s shaping up to be one of the worst of the Space Age.

The reason is, the solar cycle. One of the deepest Solar Minima of the past century is underway now. As the sun’s magnetic field weakens, cosmic rays from deep space are flooding into the solar system, posing potential health risks to astronauts.

NASA is monitoring the situation with a radiation sensor in lunar orbit. The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) has been circling the Moon on NASA’s Lunar Reconnaissance Orbiter spacecraft since 2009. Researchers have just published a paper in the journal Space Weather describing CRaTER’s latest findings.

lroAbove: An artist’s concept of Lunar Reconnaissance Orbiter.

“The overall decrease in solar activity in this period has led to an increased flux of…

View original post 540 more words

Lift-off is scheduled for 2:51GMT on the 15th July 2019

Our friends Ned Nikolov and Karl Zeller will be keen to see the data from the Chandrayaan 2 lunar mission scheduled for take-off next week. Among many other experiments planned, the rover will be measuring surface thermal conductivity – a key factor in estimating the global lunar surface temperature.

The daily mail reports:

India’s space agency is preparing to launch its ambitious Chandrayaan-2 mission next week which is set to land near the currently unexplored south pole of the moon.

Chandrayaan-2 will blast off from the Satish Dhawan Space Center at Sriharikota on the country’s south west coast at 2.51am (10.21pm BST) on July 15.

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View from the Moon [credit: NASA]


Moons don’t generally ‘shrink’, so what’s going on here? The abstract of the research paper speaks of compressional stresses, but the only potential source of compression would seem to be the Earth. It’s known that ‘the crust on the far side is a lot thicker than it is on the near side’, as discussed here.

The moon is still tectonically active, like Earth, generating moonquakes as our planet creates earthquakes, a new study based on Apollo mission data found.

These moonquakes likely happen because the moon is quivering as it shrinks, researchers added.

On Earth, tectonic activity, such as earthquakes and volcanism, results from shuffling of the crust’s tectonic plates driven by the churning of the planet’s molten interior, says Charles Quoi at Space.com.

However, the moon is much smaller than Earth and therefore largely cooled off long ago, so one might not expect much, if any, tectonic activity.

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Lunar evections and the Saros cycle

Posted: May 7, 2019 by oldbrew in Maths, moon, solar system dynamics
Tags:

Credit: Matthew Zimmerman @ English Wikipedia


The Saros cycle can be used to predict eclipses of the Sun and Moon, and is usually defined as 223 lunar synodic months, or about 11 days over 18 years.

But there are a few other lunar-related periods which can used to arrive at 223.

One Saros cycle can be said to be the difference between the number of:
— anomalistic months and full moon cycles (239 – 16)
— draconic months and draconic years (242 – 19)
— tropical months and tropical years (241 – 18)

That may be fairly well known, but then there are the lunar evections.

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Earth from the Moon [image credit: NASA]


Part 3

To recap, the Lucas series starts: 2, 1, 3, 4, 7, 11, 18, 29 … (adding the last two numbers each time to find the next number in the series).

Note: for clarity, the three parts of this mini-series should be read in order (links below).

Since Part 1 showed that 7 Jupiter-Saturn conjunctions (J-S) = 11 * 13 lunar tropical years (LTY), and from Part 2 we know that 363 LTY = 353 Earth tropical years (TY), these numbers of occurrences can be integrated by applying another multiple of 13:
363 = 3*11*11 LTY
therefore
353 * 13 TY = 3*11*11*13 LTY = 3*7*11 J-S

7 and 11 are Lucas numbers.
13 is a Fibonacci number.
3 belongs to both series.

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The Lucas spiral, made with quarter-arcs, is a good approximation of the golden spiral when its terms are large [credit: Wikipedia]


Here we show numerical connections between the Moon, the Earth and Venus. These will be carried forward into part 2 of the post. The focus is on the smaller Lucas numbers (3-18).

Wikipedia says: The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values.

A look at the numbers:
19 Venus rotations = 169 (13²) lunar rotations
Lunar tropical year = 13 lunar rotations / orbits (1 rotation = 1 orbit)
So: 19 Venus rotations = 13 Lunar tropical years
(13 is a Fibonacci number. The Lunar tropical year is derived from the nearest whole number of lunar orbits to one Earth orbit.)

169 * 27.321582 = 4617.3473 days (Data source)
19 * 243.018 = 4617.342 days (Data source)

Now we bring in the Chandler wobble:
13*3 = 39
39 Lunar tropical years = 32 Chandler wobbles
19*3 = 57

Referring to the chart on the right:
7 and 18 are Lucas numbers.
This theme will continue in part 2 of the post.

(32 + 57 = 89 axial, and 89 is a Fibonacci number. In 1/89th of the period the sum of CW and Ve(r) occurrences is 1).

Re. the period of the Chandler wobble:
39 LTY / 32 CW = (169 * 3 * 27.321582) / 32 = 432.8763 days

Or, if we say 27 Chandler wobbles = 32 Earth tropical years:
(365.24219 * 32) / 27 = 432.8796 days

The two results are almost identical (Wikipedia rounds it to 433 days).

Note:
353 Earth tropical years (ETY) = 363 Lunar tropical years = 10 beats
1 beat = 35.3 ETY which is linked to the Chandler Wobble
See: Sidorenkov – THE CHANDLER WOBBLE OF THE POLES AND ITS AMPLITUDE MODULATION

These numbers also feed into part 2 of the post, with more planetary links.