Posts Tagged ‘resonance’

From left, Mercury, Venus, Earth and Mars. [Credit: Lunar and Planetary Institute]

The planetary theory aspect appears a bit later, but first a brief review of some relevant details.

In this Talkshop post: Why Phi? – a triple conjunction comparison we said:
(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.
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London’s Millennium Bridge [image credit: Alison Wheeler / Wikipedia]


Researchers now believe ‘that the synchrony of the crowd might not be a root cause but instead acts as a feedback effect that amplifies pre-existing small-scale wobbles’, but leave open the question of how or why the swaying starts. So to date any such resonance seems to be largely a matter of luck – or bad luck, which ideally is where testing comes in.

Some bridges could really put a swing in your step, says Science News.

Crowds walking on a bridge can cause it to sway — sometimes dangerously. Using improved simulations to represent how people walk, scientists have now devised a better way to calculate under what conditions this swaying may arise, researchers report November 10 online in Science Advances.

When a bridge — typically a suspension bridge — is loaded with strolling pedestrians, their gaits can sync, causing the structure to shimmy from side to side.

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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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Credit: NASA


This is from a Q&A on a website linked with Sydney Observatory. We add brief notes at the end.

Lionel asks: Congratulations on your Venus book.

Excellent. I notice that there is a 243 year cycle for Transits of Venus
243 x 365.242 = 224.7 x 395
So far so good. The axial rotation period for Venus is 243.1 days.
Is this a coincidence or is there some underlying geometrical fact that I cannot see?
well-done,

Answer: An interesting and complex question that I address below.

Patterns in the transits of Venus
Let us first look at the patterns in the transits of Venus. We need to note that Venus and the Earth line up with the Sun every 583.92 days or 1.59872 years. This is called the synodic period.

If there was a transit, say the one in June 2004, for another transit to occur, the two planets must not only line up with each other and the Sun, but do so after an integer number of years so that they are back in the right places on each of their orbits.

Venus and Earth fulfil these requirements after five synodic periods = 7.9936 years as this is almost, though not quite, equal to the integer eight. Thus transits of Venus generally occur in pairs eight years apart. However, because of the slight inequality there is no third transit after another eight years.

A more accurate relationship occurs after 152 synodic periods = 243.00544 years or ~395 Venus years. The pattern of Venus transits thus repeats at 243 year intervals (This is the cycle quoted by Lionel in his question above). For example, the first pair of June transits after 8 June 2004 begins on 11 June 2247. Of course, in the meantime there is also a pair of December transits beginning in 2117.

The rotation of Venus
Scientists using radar observations from the 1960s onwards discovered that Venus spins backwards, that is in the opposite direction to its motion around the Sun, at the slow rate of 243.02 days.

They soon realised that means that Venus, almost but not quite, shows the same face towards the Earth each time the planets are lined up with each other and the Sun. Somehow there is a resonance between the motion of the Earth around the Sun and Venus’ spin around its axis. Scientists are unsure why this is the case, but one suggestion is that Venus is more massive on the face turned towards the Earth at those times and consequently it was gravitationally captured by the Earth.

How is it worked out that Venus shows the same face towards the Earth each time they line up? The quoted value of 243.02 days is with respect to distant stars. With a little arithmetic (taking inverses) we can easily convert that value to the rotation period with respect to the Sun or, in other words, to the day on Venus. It is 116.75 (Earth) days. Five of those periods equal 583.75 days, which is almost the same as the 583.92 day synodic period. So each time the planets line up Venus shows almost the same face to the Sun and hence the same face to the Earth, which is always on those occasions on the opposite side of Venus.

Coincidence or not
As Lionel points out it is interesting that transits of Venus repeat in a cycle of 243 years while the rotation period of Venus with respect to the stars is 243 days, The above detailed discussion indicates that there is no obvious connection that gives rise to the same number in each case. However, the calculations all depend on many of the same factors such as the orbital periods of Venus and the Earth so maybe there was a chance that the same number should recur.

Note the values quoted above are from the NASA Venus Fact Sheet.

Source: Are transits and the rotation of Venus linked? – Observations
– – –
Talkshop notes

Re: ‘Five of those periods equal 583.75 days, which is almost the same as the 583.92 day synodic period.’ [‘Venus and the Earth line up with the Sun every 583.92 days or 1.59872 years’]

Note 1: 23 solar rotations @ 25.38 days = 583.74 days
This also looks like a resonance, this time between the Sun and the Venus day.
. . .
Re: Venus and Earth fulfil these requirements after five synodic periods = 7.9936 years
A more accurate relationship occurs after 152 synodic periods = 243.00544 years or ~395 Venus years.

Note 2: using their own data, 157 synodic periods is more accurate, i.e. closer to a whole number of Earth orbits.
1.59872 * 152 = 243.00534 years (as stated in their notes)
1.59872 * 157 = 250.99904 years (~408 Venus years)
Of course that would be an ‘extra’ five synodic periods = 7.9936 years.

That may contradict the official ‘wisdom’ but there it is. It was discussed in some detail in this 2015 Talkshop post (some readers may find the comments to be of interest):
Why Phi? – a Venus transit cycle model

Image credit: NASA


We now know that Saturn’s rings share a process with spiral galaxies, and the unique co-orbital pattern of two of its moons get some attention.

This view from NASA’s Cassini spacecraft shows a wave structure in Saturn’s rings known as the Janus 2:1 spiral density wave, reports Phys.org.

Resulting from the same process that creates spiral galaxies, spiral density waves in Saturn’s rings are much more tightly wound.

In this case, every second wave crest is actually the same spiral arm which has encircled the entire planet multiple times. This is the only major density wave visible in Saturn’s B ring.

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Exoplanets up to 90 times closer to their star than Earth is to the Sun.

Excellent – we outlined this ‘resonance chain’ (as they have now dubbed it) in an earlier post here at the Talkshop [see ‘Talkshop note’ in the linked post for details].

When NASA announced its discovery of the TRAPPIST-1 system back in February it caused quite a stir, and with good reason says Phys.org.

Three of its seven Earth-sized planets lay in the star’s habitable zone, meaning they may harbour suitable conditions for life.

But one of the major puzzles from the original research describing the system was that it seemed to be unstable.

“If you simulate the system, the planets start crashing into one another in less than a million years,” says Dan Tamayo, a postdoc at U of T Scarborough’s Centre for Planetary Science.

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Credit: IB Times


It’s not yet known what the origin of asteroid (or comet) ‘Bee-Zed’ is or if it’s one of a class of similar objects in retrograde co-orbital resonance, as Phys.org reports. The researchers say ‘how it got there remains a mystery.’

For at least a million years, an asteroid orbiting the “wrong” way around the sun has been playing a cosmic game of chicken with giant Jupiter and with about 6,000 other asteroids sharing the giant planet’s space, says a report published in the latest issue of Nature.

The asteroid, nicknamed Bee-Zed, is the only one in this solar system that’s known both to have an opposite, retrograde orbit around the sun while at the same time sharing a planet’s orbital space, says researcher and co-author Paul Wiegert of Western’s Department of Physics and Astronomy.
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Exoplanets up to 90 times closer to their star than Earth is to the Sun.

Exoplanets up to 90 times closer to their star than Earth is to the Sun.


We did know something about this system already, but more work has led to today’s announcement.

Astronomers have never seen anything like this before, says Space.com: Seven Earth-size alien worlds orbit the same tiny, dim star, and all of them may be capable of supporting life as we know it, a new study reports. 

“Looking for life elsewhere, this system is probably our best bet as of today,” study co-author Brice-Olivier Demory, a professor at the Center for Space and Habitability at the University of Bern in Switzerland, said in a statement. 
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HR 8799 system [image credit: Many Worlds]

HR 8799 system [image credit: Many Worlds]


It can’t get much more obvious than this. The report says ‘it’s a one-two-four-eight resonance’ of the orbits of these massive planets, but we find it’s much nearer to 1:2:4:9, with the outer planet taking 450 years for one orbit.

The era of directly imaging exoplanets has only just begun, but the science and viewing pleasures to come are appealingly apparent says Many Worlds.

This evocative movie of four planets more massive than Jupiter orbiting the young star HR 8799 is a composite of sorts, including images taken over seven years at the W.M. Keck observatory in Hawaii. The movie clearly doesn’t show full orbits, which will take many more years to collect.

The closest-in planet circles the star in around 49 years [report incorrectly says 40]; the furthest takes more than 400 years. But as described by Jason Wang,  an astronomy graduate student at the University of California, Berkeley, researchers think that the four planets may well be in resonance with each other.
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Synchronized orbits of the Kepler-80 system [Credit: Florida Institute of Technology]

Synchronized orbits of the Kepler-80 system [Credit: Florida Institute of Technology]

Another example of planetary resonance has been discovered thanks to NASA’s Kepler space telescope.
H/T Phys.org

Located about 1,100 light years away, Kepler-80, named for the NASA telescope that discovered it, features five small planets orbiting in extreme proximity to their star.

As early as 2012, Kepler scientists found that all five planets orbit in an area about 150 times smaller than the Earth’s orbit around the Sun, with “years” of about one, three, four, seven and nine days.

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The Kepler-223 planetary system, which has long-term stability because its four planets interact gravitationally to keep the beat of a carefully choreographed dance as they orbit their host star. [credit: W.Rebel]

The Kepler-223 planetary system, which has long-term stability because its four planets interact gravitationally to keep the beat of a carefully choreographed dance as they orbit their host star.
[credit: W.Rebel]


As the report says: ‘Kepler-223’s two innermost planets are in a 4:3 resonance. The second and third are in a 3:2 resonance. And the third and fourth are in a 4:3 resonance.’ They are ‘far more massive than Earth’. Interesting to say the least.

The four planets of the Kepler-223 star system seem to have little in common with the planets of Earth’s own solar system. And yet a new study shows that the Kepler-223 system is trapped in an orbital configuration that Jupiter, Saturn, Uranus, and Neptune may have broken from in the early history of the solar system.

“Exactly how and where planets form is an outstanding question in planetary science,” said the study’s lead author, Sean Mills, a graduate student in astronomy & astrophysics at the University of Chicago. “Our work essentially tests a model for planet formation for a type of planet we don’t have in our solar system.”

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Io, Europa and Ganymede - three of Jupiter's four Galilean moons

Io, Europa and Ganymede – three of Jupiter’s four Galilean moons

The resonance of three of the four Galilean moons of Jupiter is well-known. Or is it?

We’re usually told there’s a 1:2:4 orbital ratio between Ganymede, Europa and Io, but while this is not far from the truth, a closer look shows something else.

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lunar_TYTallbloke writes: Stuart ‘Oldbrew’ has been getting his calculator warm to discover the congruences in various aspects of the Lunar orbit around Earth, and its relationship to Earth-Moon orbit around the Sun. Emerging from this study are some useful insights into longer periods, such as the ‘precession of the equinoxes‘.

Some matching periods of lunar numbers:
86105 tropical months (TM) @ 27.321582 days = 2352524.8 days
85377 anomalistic months (AM) @ 27.55455 days = 2352524.8 days
79664 synodic months (SM) @ 29.530589 days = 2352524.8 days

These identical values are used in the chart on the right (top row). The second row numbers are the difference between the numbers in the first row (TM – AM and AM – SM).
The derivation of the third row number (6441) is shown on the chart itself [click on the chart to enlarge it].

The period of 6441 tropical years (6440.75 sidereal years) is one quarter of the Earth’s ‘precession of the equinox’.
Multiplying by 4: 25764 tropical years = 25763 sidereal years.
The difference of 1 is due to precession.

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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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