Posts Tagged ‘resonance’

Credit: NASA [click on image to enlarge]


In a 2015 Talkshop post we found a resonant period of 486.5 days for the inner three of the four Galilean moons of Jupiter: Io, Europa and Ganymede. Here the researchers find a period of 480-484 days, which clearly looks very much the same as our period, linked to recurring volcanic activity. They find this ‘surprising’, but the repeating alignments of these moons with Jupiter – at the same time interval – look to be more than a coincidence.

Hundreds of volcanoes pockmark the surface of Io, the third largest of Jupiter’s 78 known moons, and the only body in our solar system other than Earth where widespread volcanism can be observed, says Phys.org.

The source of the moon’s inner heat is radically different than Earth’s, making the moon a unique system to investigate volcanism.

A new study in the AGU journal Geophysical Research Letters finds Io’s most powerful, persistent volcano, Loki Patera, brightens on a similar timescale to slight perturbations in Io’s orbit caused by Jupiter’s other moons, which repeat on an approximately 500-Earth-day cycle.

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Credits: NASA’s Goddard Space Flight Center/Chris Smith


Following the report we analyse the orbital data for evidence of resonances.

A planet discovered by NASA’s TESS has pointed the way to additional worlds orbiting the same star, one of which is located in the star’s habitable zone, reports SciTechDaily.

If made of rock, this planet may be around twice Earth’s size.

The new worlds orbit a star named GJ 357, an M-type dwarf about one-third the Sun’s mass and size and about 40% cooler that our star. The system is located 31 light-years away in the constellation Hydra.

In February, TESS cameras caught the star dimming slightly every 3.9 days, revealing the presence of a transiting exoplanet — a world beyond our solar system — that passes across the face of its star during every orbit and briefly dims the star’s light.

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Moons of Pluto


This one may have slipped through the net, so to speak. The link to Pluto is explained below.

Star HD 40307 has six planets orbiting between 7 and 198 days, but here the focus will be on the outer three: e, f and g. These were reported in 2012 (whereas b, c, and d were found in 2008).

However, it seems the resonances described below have been overlooked, if lack of related internet search results can be relied on.

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Credit: NASA’s Goddard Space Flight Center / Scott Wiessinger


Quoting from the abstract of the study in Nature Astronomy:
‘The planets orbit close to a mean-motion resonant chain, with periods (3.36 days, 5.66 days and 11.38 days, respectively) near ratios of small integers (5:3 and 2:1).’

One of the astronomers said: “For TOI-270, these planets line up like pearls on a string. That’s a very interesting thing because it lets us study their dynamical behavior. And you can almost expect, if there are more planets, the next one would be somewhere further out, at another integer ratio.”

“There is a good possibility that the system hosts other planets, further out from planet d, that might well lie within the habitable zone. Planet d, with an 11-day orbit, is about 10 million kilometers out from the star.”

In fact the distance-to-star ratios of the planets (named b,c and d) are very similar:
b:c = 1:1.542 and c:d = 1:1.553 (for comparison Earth:Mars is 1:1.524).

NASA’s Transiting Exoplanet Survey Satellite, or TESS, has discovered three new planets that are among the smallest, nearest exoplanets known to date, reports Tech Explorist.

The planets circle a star only 73 light-years away and incorporate a small, rough super-Earth and two sub-Neptunes — planets about a large portion of the size of our own icy giant.

The sub-Neptune farthest out from the star seems, by all accounts, to be inside a temperate zone, implying that the highest point of the planet’s atmosphere is inside a temperature extend that could support a few types of life.

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Credit: NASA’s Goddard Space Flight Center


First the report, then a brief Talkshop analysis.

NASA’s Transiting Exoplanet Survey Satellite (TESS) has discovered a world between the sizes of Mars and Earth orbiting a bright, cool, nearby star, reports MessageToEagle.com.

The planet, called L 98-59b, marks the tiniest discovered by TESS to date.

Two other worlds orbit the same star.

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Kepler Space Telescope [credit: NASA]


Star Kepler-102 has five known planets, lettered b,c,d,e,f. These all have short-period orbits between 5 and 28 days. Going directly to the orbit period numbers we find:
345 b = 1824.0012 d
258 c = 1824.4263 d
177 d = 1825.1709 d
113 e = 1824.4629 d
(for comparison: about 1-2 days short of 5 Earth years)

For the purposes of this post planet f (the furthest of the five from its star) is excluded, except to say that in terms of conjunctions 8 e-f = 11 d-e. Now let’s look for some resonances of the inner four planets.

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Jupiter – the dominant planet in the solar system

The aim here is to show a Lucas number based pattern in five rows of synodic data, then add in a note on Mercury as well.

There’s also a strong Fibonacci number element to this, as shown below.

The results can be linked back to earlier posts on planetary harmonics involving the Lucas and Fibonacci series (use ‘search this site’ box on our home page).

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Continuing our recent series of posts, with Uranus-Neptune conjunction data an obvious starting point for the table is where the difference between the number of Neptune orbits and U-N synods is 1.

647 U-N takes a long time (~110,900 years) but the accuracy of the whole number matches is very high.

Lucas no. (7 here) is fixed, and Fibonacci nos. follow the correct sequence (given their start no.).
Full Fib. series starts: 0,1,1,2,3,5,8,13,21…etc.
Multiplier: 0,1,1,2,3
Addition: 1,1,2,3,5

The Neptune orbits are multiples of 26 with the same Fibonacci adjustment:
Add 0,1,1,2,3 to the Neptune column numbers to get an exact multiple of 26 (which will be the pattern number in the last column).

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Jupiter – the dominant planet in the solar system

The aim here is to show a Lucas number based pattern in seven rows of synodic data.
There’s also a Fibonacci number element to this, as shown below.
The results can be linked back to an earlier post on planetary harmonics (see below).

The nearest Lucas number equation leading to the Jupiter orbit period in years is:
76/7 + 1 = 11.857142 (1, 7 and 76 are Lucas numbers).
The actual orbit period is 11.862615 years (> 99.95% match).
[Planetary data source]

It turns out that 7 Jupiter orbits take slightly over 83 years, while 76 Jupiter-Earth (J-E) synodic conjunctions take almost exactly 83 years. One J-E synod occurs every 1.09206 years. (83/76 = 1.0921052).

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Orbital (top line) and synodic relationships of Kepler-107, plus cross-checks

The system has four planets: b,c,d, and e.

The chart to the right is a model of the close orbital relationships of these four recently announced short-period (from 3.18 to 14.75 days) exoplanets.

It can be broken down like this:
b:c = 20:13
c:d = 13:8
d:e = 24:13 (= 8:13 ratio, *3)
b:d = 5:2
c:e = 3:1
(1,2,3,5,8, and 13 are Fibonacci numbers)
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Layers of Earth’s atmosphere


Some fairly advanced theorising here, but the possibilities look interesting. For example, could ‘resonant trapping’ exist?

Resonating oscillations of a planet’s atmosphere caused by gravitational tides and heating from its star could prevent a planet’s rotation from steadily slowing over time, according to new research by Caleb Scharf, who is the Director of Astrobiology at Columbia University.

His findings suggest that the effect is enhanced for a planet with an atmosphere that has been oxygenated by life, and the resulting ‘atmospheric tides’ could even act as a biosignature, reports Phys.org.

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Three of Saturn’s moons — Tethys, Enceladus and Mimas — as seen from NASA’s Cassini spacecraft [image credit: NASA/JPL]


This is a comparison of the orbital patterns of Saturn’s four inner moons with the four exoplanets of the Kepler-223 system. Similarities pose interesting questions for planetary theorists.

The first four of Saturn’s seven major moons – known as the inner large moons – are Mimas, Enceladus, Tethys and Dione (Mi,En,Te and Di).

The star Kepler-223 has four known planets:
b, c, d, and e.

When comparing their orbital periods, there are obvious resonances (% accuracy shown):
Saturn: 2 Mi = 1 Te (> 99.84%) and 2 En = 1 Di (> 99.87%)
K-223: 2 c = 1 e (>99.87%) and 2 b = 1 d (> 99.86%)

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A montage of Uranus’ large moons and one smaller moon: from left to right Puck, Miranda, Ariel, Umbriel, Titania and Oberon. Size proportions are correct. [image credit: Vzb83 @ Wikipedia (from originals taken by NASA’s Voyager 2)]


The five major moons of Uranus in ascending distance from the planet are:
Miranda, Ariel, Umbriel, Titania and Oberon

Of these, the first three exhibit a synodic resonance similar to that of Jupiter’s Galilean moons, as we showed here:
Why Phi? – the resonance of Jupiter’s Galilean moons

Quoting from that post:
The only exact ratio is between the synodic periods which is 3:2:1.
It isn’t necessary to have an exact 4:2:1 orbit ratio in order to get a 3:2:1 synodic ratio.

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Exoplanet – NASA impression


YZ Ceti is a recently discovered star with three known planets (b,c and d) orbiting very close to it. Although some types of mean motion resonance, or near resonance, are quite common e.g. 2:1 or 3:2 conjunction ratios, this one is a bit different.

The orbit periods in days are:
YZ Ceti b = 1.96876 d
YZ Ceti c = 3.06008 d
YZ Ceti d = 4.65627 d

This gives these conjunction periods:
c-d = 8.9266052 d
b-c = 5.5204368 d
b-d = 3.4109931 d
(Note the first two digits on each line.)

Nearest matching period:
34 c-d = 303.50457 d
55 b-c = 303.62403 d
89 b-d = 303.57838 d

34,55 and 89 are Fibonacci numbers.
Therefore the conjunction ratios are linked to the golden ratio (Phi).

Phi = 1.618034
(c-d) / (b-c) = 1.6170106
(b-c) / (b-d) = 1.618425

Data source: exoplanets.eu

K2-138 could even have more than five planets. [image credit: NASA/JPL-Caltech]


And it’s a good one. The abstract says: ‘The periods of the five planets are 2.35, 3.56, 5.40, 8.26, and 12.76 days, forming an unbroken chain of near 3:2 resonances.’

The Exoplanet Explorers project has led to the first discovery of a multi-planet system solely through crowdsourcing efforts, as Futurism reports.

Through a project called Exoplanet Explorers, a band of citizen scientists has discovered K2-138, a far-off planetary system that houses least five exoplanets.

This is the first time that a multi-planet system has been discovered entirely through crowdsourcing.

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Although the author appears sold on the idea of trace gases controlling the temperature of planetary atmospheres, the discussion about planets and water is worth a look. The answer to the question may depend on more powerful space telescopes like the James Webb.

Wherever we find water on Earth, we find life writes Elizabeth Tasker at Many Worlds.

It is a connection that extends to the most inhospitable locations, such as the acidic pools of Yellowstone, the black smokers on the ocean floor or the cracks in frozen glaciers.

This intimate relationship led to the NASA maxim, “Follow the Water”, when searching for life on other planets.

Yet it turns out you can have too much of a good thing.

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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