Posts Tagged ‘resonance’

Neptune (top), Uranus, Saturn, Jupiter (bottom)

Neptune (top), Uranus, Saturn, Jupiter (bottom)


Continuing our long-term series researching Fibonacci and/or Phi based ratios in planetary conjunction periods, it’s time for a look at the inner- and outer-most gas giants of our solar system: Jupiter and Neptune.

Initial analysis shows the period of 14 Jupiter orbits is close to that of one Neptune orbit of the Sun, and even closer to the period of 13 (14 less 1) Jupiter-Neptune (J-N) conjunctions.

It also turns out that there’s a multiple of 13 J-N that equates to a whole number of Earth orbits:
Jupiter-Neptune(J-N) average conjunction period = 12.782793 years
221 J-N = ~2825 years (2824.9972y)
(221 = 13 x 17)

But this period is not a whole number of either Jupiter or Neptune orbits.
This is resolved by multiplying by a factor of 7.

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A simulation of a cross-section of a thread of solar material, called a filament, hovering in the sun's atmosphere [image credit: NAOJ/Patrick Antolin]

A simulation of a cross-section of a thread of solar material, called a filament, hovering in the sun’s atmosphere
[image credit: NAOJ/Patrick Antolin]


Researchers find this works in ‘the same way that a perfectly-timed repeated push on a swing can make it go higher’, as Phys.org reports:

Modern telescopes and satellites have helped us measure the blazing hot temperatures of the sun from afar. Mostly the temperatures follow a clear pattern: The sun produces energy by fusing hydrogen in its core, so the layers surrounding the core generally get cooler as you move outwards—with one exception.

Two NASA missions have just made a significant step towards understanding why the corona—the outermost, wispy layer of the sun’s atmosphere —is hundreds of times hotter than the lower photosphere, which is the sun’s visible surface [aka the coronal heating problem]

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[image credit: etsy.com]

[image credit: etsy.com]


Something a bit off-beat here: a paper entitled ‘The Multiperiodic Pulsating Star Y Cam A as a Musical Instrument’. A music extract can be played in the linked Phys.org report. It’s described as ‘a mixed bag of eerie pulsating sounds combined with a simple piano melody.’

Astronomer Burak Ulaş, with the Izmir Turk College Planetarium in Turkey has taken his work into a musical dimension, using star oscillations as a source for a musical composition. He has uploaded a paper describing what he has done along with sheet music and an audio recording of his work to the preprint server arXiv—along with a shout-out to other pioneers in the field, from Kepler to Pythagoras to modern composer scientists Jenő Keuler and Zoltán Kolláth.

Astronomers and other star-gazers have long associated celestial bodies with music, the twinkling of some stars offers a tempting back-beat and some stars in particular offer a variety of opportunities. One such star, Y Cam A, Ulaş noted, offered enough oscillation data for its use in creating chords.

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Perfect harmony? [image credit: homedit]

Perfect harmony? [image credit: homedit]

From the believe-it-or-not file, Phys.org reports a possible solution to an old puzzle:

Almost 350 years ago, Dutch inventor and scientist Christiaan Huygens observed that two pendulum clocks hanging from a wall would synchronise their swing over time.

What causes the phenomenon has led to much scientific head-scratching over the centuries, but no consensus to date.

‘But now’ – as Tomorrow’s World presenters used to say…

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Orcus in blue, Pluto in red, Neptune in grey [credit: Eurocommuter / Wikipedia]

Orcus in blue, Pluto in red, Neptune in grey
[credit: Eurocommuter / Wikipedia]

The ‘anti-Pluto’ label arose from the fact that the orbit of probable dwarf planet Orcus looks like a mirror-image of that of Pluto (as shown above), and is less than three years weeks shorter than Pluto’s 248 years. It also has its own relatively large moon – or binary neighbour – just like Pluto. [More details about the graphic here]

Wikipedia says: 90482 Orcus is a Kuiper belt object with a large moon, Vanth. It was discovered on February 17, 2004 by Michael Brown of Caltech, Chad Trujillo of the Gemini Observatory, and David Rabinowitz of Yale University. Precovery images as early as November 8, 1951 were later identified. It is probably a dwarf planet.

Orcus is a plutino, locked in a 2:3 resonance with Neptune, making two revolutions around the Sun to every three of Neptune’s. This is much like Pluto, except that it is constrained to always be in the opposite phase of its orbit from Pluto: Orcus is at aphelion when Pluto is at perihelion and vice versa.

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[image credit: imagineeringezine.com]

[image credit: imagineeringezine.com]

Only two questions are needed here:

(1) What is the period of a Jupiter(J)-Saturn(S)-Earth(E) (JSE) triple conjunction?
JSE = 21 J-S or 382 J-E or 403 S-E conjunctions (21+382 = 403) in 417.166 years (as an average or mean value).

(2) What is the period of a Jupiter(J)-Saturn(S)-Venus(V) (JSV) triple conjunction?
JSV = 13 J-S or 398 J-V or 411 S-V conjunctions (13+398 = 411) in 258.245 years (as an average or mean value).

Since JSV = 13 J-S and JSE = 21 J-S, the ratio of JSV:JSE is 13:21 exactly (in theory).

As these are consecutive Fibonacci numbers, the ratio is almost 1:Phi or the golden ratio.
Golden ratio: relationship to Fibonacci sequence

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Comparison of the eight brightest TNOs [credit: Wikipedia]

Comparison of the eight brightest TNOs [credit: Wikipedia]


As Pluto is getting some media attention due to the impending ‘fly-by’ of a NASA space probe, let’s take a look at its orbital relationship with its neighbours.

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Planetary conjunction [image credit: EPA / Daily Mail]

Planetary conjunction [image credit: EPA / Daily Mail]


For the Jupiter-Venus-Mercury (JVMe) model, we start with this basic synodic conjunction relationship:
61 Jupiter-Venus (J-V) = 100 Venus-Mercury (V-Me) = 161 Jupiter-Mercury (J-Me) conjunctions in 39.58 years.
Orbit numbers per 39.58y: 64.337~ Venus, 164.337~ Mercury, 3.3365~ Jupiter
Jupiter-Venus-Mercury chart

[3 x 39.58 years = 118.74 years]


Since the ratio 61:100:161 is only one conjunction different from 60:100:160 (= 3:5:8), there is a very close match to a Fibonacci-based ratio as 3,5 and 8 are all Fibonacci numbers.

In the model we convert the orbits to whole numbers using a multiple of 3, to obtain a triple conjunction period where there are (very close to) a whole number of orbits of the relevant planets, as per the chart [right].

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Click on image to enlarge

Click on image to enlarge

The Mars-Earth model is based on 34 Mars orbits. This equates to 64 years, which is 8². Since Venus makes 13 orbits of Earth in 8 years, we can easily add it to the model.
2,3,5,8,13 and 34 are Fibonacci numbers.

The story doesn’t end there, because as the diagram shows this results in a 3:4:7 relationship between the 3 sets of synodic periods. This was analysed in detail in a paper by astrophysicist Ian Wilson, featured at the Talkshop in 2013:

Ian Wilson: Connecting the Planetary Periodicities to Changes in the Earth’s Length of Day

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Exoplanet analysis is a growing field of scientific study as data pours in from the likes of NASA’s successful Kepler probe.

The abstract of a new paper explains its focus on this data:
‘Mean motion resonances and near-resonances up to the outer/inner orbital period ratio’s value of 5 and the denominator 4 are tested for all adjacent exoplanet orbits.’

Without delving into the nuts and bolts of the analysis here, let’s look at the list of results (click on image to view details):

By Marian C. Ghilea (2015)

By Marian C. Ghilea (2015)

The column ‘resonance type’ shows the planet:planet ratios we’re interested in.
Clearly there are many examples, although ‘near resonances’ are also included.

From the author’s concluding remarks:
‘Performing a simple analysis, the resonance or near-resonance states present in all the multiplanetary systems known to date can be found numerically using a computer analysis tool.’

‘The first results, presented in this paper, suggest different resonance or near-resonance distributions for different planet categories. The resonance/near resonance numbers of 2/1 and 3/2 appear to be dominant for the planets with larger masses while the 5/3 resonance seems to be the most common for terrestrial planets and mini neptunes. For giant planets, the 2/1 resonances are dominating at larger distances from the host star while the 3/2 resonance is more common at close distances from it. Resonances for values higher than 5/2 are encountered
only for planets with masses larger than 10 (ME*)’ [*Earth masses].

We can see from this that these ‘near resonances’ crop up regularly in exoplanet systems just as they do in our solar system e.g. Jupiter-Saturn 5:2, Neptune-Pluto 3:2.

Whatever the mechanism(s) involved, the frequency of their appearance can’t be regarded as accidental.

***
See also the Wikipedia page on orbital resonance

H/T Oldbrew.

Golden rings of star formation

NGC 3081 is seen here nearly face-on. Compared to other spiral galaxies, it looks a little different. The galaxy’s barred spiral centre is surrounded by a bright loop known as a resonance ring. This ring is full of bright clusters and bursts of new star formation.

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After last week’s symbolic collapse of a wind turbine in Kyoto province, here’s news of another downed bird mincer in Donegal, Ireland. From the Donegal Daily:

NowindDD EXCLUSIVE: An investigation is underway after a 80 ft wind turbine came crashing to the ground in strong winds near Ardara.

The windmill is one of nine located at Maas on the backroad near Ardara.

It is believed the wind turbine came down overnight when winds were gusting in the area to 80km/hr (50mph).

However the fact the turbine crashed in conditions it should otherwise have easily coped with has puzzled experts.

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