Posts Tagged ‘resonance’

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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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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