Posts Tagged ‘resonance’

Wikipedia says:

Dansgaard–Oeschger events (often abbreviated D–O events) are rapid climate fluctuations that occurred 25 times during the last glacial period. Some scientists say that the events occur quasi-periodically with a recurrence time being a multiple of 1,470 years, but this is debated. —

The 25 occurrences of 1470 years are represented in this synodic chart posted in the comments of our 2018 blog post:
Possible origin of Dansgaard-Oeschger abrupt climate events.

Re. the ‘debate’, let’s take a line from this paper:
On the 1470-year pacing of Dansgaard-Oeschger warm events
Michael Schulz
First published: 01 May 2002
Citations: 99
‘a fundamental pacing period of ~1470 years seems to control the timing of the onset of the Dansgaard-Oeschger events.’

Another study: Timing of abrupt climate change: A precise clock
Stefan Rahmstorf
First published: 21 May 2003

An analysis of the GISP2 ice core record from Greenland reveals that abrupt climate events appear to be paced by a 1,470-year cycle with a period that is probably stable to within a few percent; with 95% confidence the period is maintained to better than 12% over at least 23 cycles. This highly precise clock points to an origin outside the Earth system; oscillatory modes within the Earth system can be expected to be far more irregular in period.

[bold added]

However, researchers often admit defeat when looking for a viable mechanism to explain its regularity, or just say there isn’t one to date.

Kepler’s trigon – the orientation of consecutive Jupiter-Saturn synodic periods, showing the repeating triangular shape (trigon).

Returning to the synodics chart, a relevant number doesn’t appear in it. The Jupiter-Saturn conjunction of 19.865~ years is an important period in the solar system, and it returns to almost the same position after every three occurrences, as Johannes Kepler noted with his ‘trigon’, centuries ago.

We can work out the rate of movement per conjunction in degrees:
360 – ((360 / S) * J-S) = 117.147 degrees
(360 / 117.147) * J-S = 61.046482y (‘JS-360’)
[Data: ]

Then, from the chart:
1470*25 / ‘JS-360’ = 602.00029
Check: (602*360) / 117.147 = 1849.983 (1850 J-S, see chart)
Since ‘JS-360’ is almost exactly a whole number (602), the Jupiter-Saturn conjunction should be in its original position at the end of the 25 D-O cycles.

Adding 602 to the orbits of each planet = multiples of 25:
223(N) + 602 = 825 (25*33) = 1850-1025(S-N)
[33 = 74-41]
1248(S) + 602 = 1850 (25*74)
3098(J) + 602 = 3700 (25*74*2)

Another way to get multiples of 25:
Add 2 to each orbit number (see chart), and subtract 2 from 602.

More on the 602 number:
602 = 14*43
14*61.046482y = 854.651y
43 J-S = 854.197y
These two results are only about half a year apart, and we find:
43*43 = 1849 J-S
Add 1 = 1850 J-S completing the 25 D-O cycle.

43*61.046482y = 2625 years (2624.9987)
1470:2625 = 14:25 ratio
1470*25 = 2625*14 (hence 602 of ‘JS-360’ = 14*43)

Obliquity note:
28 D-O = 41160 years, a fair match to the expected 41 kyr period.
One paper refers to a fit between D-O and obliquity.
Others support the notion of a link — possibly a topic for another post.
(28*25*1470 = 1,029,000 years)

Example of a 1470 year period from Arnholm’s solar simulator — click on image to enlarge:

Showing Neptune, Jupiter, Saturn and Earth.
* * *
Another one — Jupiter, Neptune, Saturn

Image credit:

The aim here is to show how the synodic periods and orbits of these three planets align with the so-called Grand Synod, a period of about 4628 years which has 27 Uranus-Neptune conjunctions and almost 233 Jupiter-Saturn conjunctions. Its half-period is sometimes referred to as the Hallstatt cycle (2314 years +/- a variable margin).

1. U-N ‘long period’
1420 Uranus-Neptune conjunctions = 1477 Neptune orbits
(for calculations, see Footnote)
1477 – 1420 = 57
Uranus-Neptune 360 degrees return is 1420/57 U-N = 24.91228 U-N long period = 4270.119 years

2. GS : U-N ratio
Grand Synod = 27 U-N = 4627.967 years (= ~233 Jupiter-Saturn conjunctions)
27 / 24.91228 = 1.0838028
1.0838028 * 12 = 13.005633
Therefore the ratio of 4627.967:4270.119 is almost exactly 13:12 (> 99.956% true)

3. Orbital data
Turning to the orbit periods nearest to the Grand Synod:
28 Neptune = 4614.157y
55 Uranus = 4620.927y
(Data: )

4. Factor of 12
These periods fall slightly short of the 27 U-N Grand Synod (~4628 years).
However, multiplying by 12 and adding one orbit to each, gives:
28*12,+1 (337) Neptune = 55534.67y
55*12,+1 (661) Uranus = 55535.14y
27*12 (661 – 337) U-N = 55535.61y

Now the numbers match to within a year +/- 55535 years.
Also, the period is 12 Grand Synods (12*4628 = 55536y), or 13 U-N ‘long’ periods.

5. Pluto data
Pluto’s orbit period is 247.92065 years.
55535 / 247.92065y = 224.003
So 224 Pluto orbits also equate to 12 Grand Synods.

Therefore, a U-N-P synodic chart can be created for that period of time.

6. Neptune:Pluto orbits
Neptune has one more orbit in the period than an exact 3:2 ratio with Pluto – a planetary resonance.
224 P = 112*2
337 N = 112*3, +1
113 N-P = 112, +1

7. Phi factor
Uranus and Neptune both have one more orbit than this ratio:
660:336 = (55*12):(21*16)
55/21 = Phi²
12/16 = 3/4
Therefore the U:N ratio is almost (3/4 of Phi²):1

The U-N-P chart should repeat every 12 Grand synods i.e. every 55,535 years or so.
– – –
360 / Neptune orbit (164.79132) = 2.184581
2.184581 * U-N conjunction (171.40619) = 374.4507
374.4507 – 360 = 14.4507

Obtain nearest multiple of 360 degrees:
1420 * 14.4507 = 20519.9994
20520 / 360 = 57
1420 + 57 = 1477
1420 U-N = 1477 Neptune orbits
1420 + 1477 = 2897 Uranus orbits

There’s been a data update for the three planet system of star YZ Ceti, which featured in our 2018 post: Why Phi? – resonant exoplanets of star YZ Ceti. According to NASA the third planet YZ Ceti d is a ‘super Earth’, about 1.14 times the mass of our planet.

The paper:
‘The CARMENES search for exoplanets around M dwarfs.
Characterization of the nearby ultra-compact multiplanetary system YZ Ceti’
(Submitted on 5 Feb 2020)

With an additional 229 radial velocity measurements obtained since the discovery publication, we reanalyze the YZ Ceti system and resolve the alias issues.


Kepler-90 Planets Orbit Close to Their Star [credit: NASA/AMES]

In part 1 we looked at the inner four planets: b,c,i and d. Here in part 2 we’ll look at the outer four: e,f,g and h – with a dash of d included.

The largest planet in the system is h, the outermost of the eight so far found, and it’s about the same size as Jupiter. It’s ‘an exoplanet orbiting within the habitable zone of the early G-type main sequence star Kepler-90’, says Wikipedia. However, ‘it is a gas giant with no solid surface’, so probably no aliens lurking there.

It wasn’t that easy to find synodic patterns of interest, but here we have two examples, both involving planet h.



The idea is that “Every time the rock sags into the chamber, it creates a resonance and this produces this strange signal that you see far away.” Is this really ‘The Hum’?

Can you hear it? That elemental thrumming emerging just beneath the engulfing din of everyday city and suburban life? 

Well, chances are you’re not losing your mind or developing some extra-human ability akin to comic book superheroes, says SyfyWire.

Better odds are that it’s Mother Earth’s growing pains in the form of loud volcanic stirrings, as revealed in a new study published in the journal Nature Geoscience.


Golden rectangle: Fibonacci spiral

Unusually, the eight planets in the Kepler-90 system were found using machine learning. “It’s very possible that Kepler-90 has even more planets that we don’t know about yet,” NASA astronomer Andrew Vanderburg said.
– – –
From Wikipedia’s Near resonances section on exoplanet Kepler-90:

“Kepler-90’s eight known planets all have periods that are close to being in integer ratio relationships with other planets’ periods; that is, they are close to being in orbital resonance.

The period ratios b:c, c:i and i:d are close to 4:5, 3:5 and 1:4, respectively (4: 4.977, 3: 4.97 and 1: 4.13) and d, e, f, g and h are close to a 2:3:4:7:11 period ratio (2: 3.078: 4.182: 7.051: 11.102; also 7: 11.021).

f, g and h are also close to a 3:5:8 period ratio (3: 5.058: 7.964). Relevant to systems like this and that of Kepler-36, calculations suggest that the presence of an outer gas giant planet facilitates the formation of closely packed resonances among inner super-Earths.”
– – –
Let’s look at it another way i.e. at the synodic periods rather than the orbit ratios, as these tend to deliver more clear-cut results, starting with a model for the first four planets: b,c,i and d, which we’ll call the inner planets. Their orbits of the star are in a range of 7-60 days.


Mount Etna, Sicily

The article says: ‘Every 6.4 years, the axes line up and the wobble fades for a short time.’ This looks a lot like 5.4 Chandler wobbles (CW), so you would have 6.4 years minus 5.4 CW = 1 cycle, i.e. 32:27 ratio = 5 (32-27) cycles.
Much more analysis of this time period and related matters in this 2013 Talkshop post:
Ian Wilson: Solar System Timings Evolved Lunar Orbital Elements Linked to Earth’s Chandler Wobble

New research suggests forces pulling on Earth’s surface as the planet spins may trigger earthquakes and eruptions at volcanoes, reports

Seismic activity and bursts of magma near Italy’s Mount Etna increased when Earth’s rotational axis was furthest from its geographic axis, according to a new study comparing changes in Earth’s rotation to activity at the well-known Italian volcano.


The Sun from NASA’s SDO spacecraft

Making some progress anyway – and finding resonance is a key factor.

A Queen’s University Belfast scientist has led an international team to the ground-breaking discovery of why the Sun’s magnetic waves strengthen and grow as they emerge from its surface, which could help to solve the mystery of how the corona of the Sun maintains its multi-million degree temperatures, says

For more than 60 years observations of the Sun have shown that as the magnetic waves leave the interior of the Sun they grow in strength but until now there has been no solid observational evidence as to why this was the case.

The corona’s high temperatures have also always been a mystery. Usually the closer we are to a heat source, the warmer we feel.

However, this is the opposite of what seems to happen on the Sun—its outer layers are warmer than the heat source at its surface.


Poster from the NASA Exoplanets Exploration Program’s Exoplanet Travel Bureau [credit: NASA/JPL-CalTech]

Before we start – ‘Pulsar planets are planets that are found orbiting pulsars, or rapidly rotating neutron stars.’

Wikipedia tells us:
‘PSR B1257+12, previously designated PSR 1257+12, […] is a pulsar located 2,300 light-years from the Sun in the constellation of Virgo. It is also named Lich, after a powerful, fictional undead creature of the same name.

The pulsar has a planetary system with three known planets, named “Draugr” (PSR B1257+12 b or PSR B1257+12 A), “Poltergeist” (PSR B1257+12 c, or PSR B1257+12 B) and “Phobetor” (PSR B1257+12 d, or PSR B1257+12 C), respectively.

They were both the first extrasolar planets and the first pulsar planets to be discovered; B and C in 1992 and A in 1994.

A is the lowest-mass planet yet discovered by any observational technique, with somewhat less than twice the mass of Earth’s moon.’


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.


Artist’s impression of the Kepler telescope [credit: Wikipedia]

So said researchers in their 2015 study which had that title. Then a third planet was seen.

In the abstract they say:

Methods. Our search through two separate pipelines led to the independent discovery of K2-19b and c, a two-planet system of Neptune-sized objects (4.2 and 7.2 R⊕), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously owing to their proximity to resonance and the alignment of conjunctions.


There doesn’t seem to be any online discussion of this planetary system, first seen in 2014 – but it turns out be interesting anyway.

This is a Lucas series set-up, the planets being b, c, and d in order of proximity to the star.

Starting with the orbits:
19 b = 203.006394 days
10 c = 203.03005
7 d = 203.1565


In 2011, astronomers were saying:
“We’ve crossed a threshold: For the first time, we’ve been able to detect planets smaller than the Earth around another star.”

The planets in question were Kepler-20 e and Kepler-20 f.

In the end six planets were detected: b,e,c,f,d, and g (in order of proximity to their star). Orbit periods range from about 9.38 to 63.55 days, all the planets being closer to the star than Mercury is to the Sun.

A NASA article had the title: Kepler-20, An Unusual Planetary System — referring to the alternate large/small sizes of the planets.


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.


Pairs or multiple systems of stars which orbit their common center of mass. If we can measure and understand their orbital motion, we can estimate the stellar masses.

Relatively nearby, that is…

‘Upsilon Andromedae is located fairly close to the Solar System… (44 light years). Upsilon Andromedae A has an apparent magnitude of +4.09, making it visible to the naked eye even under moderately light-polluted skies, about 10 degrees east of the Andromeda Galaxy.’ – Wikipedia

The larger of the binary stars is ups_And A, which has 4 planets orbiting it: b,c,d and e.

The information on this star system was recently updated, so let’s have a look.


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

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.


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.


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.


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.


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

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

Two other worlds orbit the same star.