Posts Tagged ‘resonance’

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 Phys.org.

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.

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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.’

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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.

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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.

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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
(data: exoplanet.eu)

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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.

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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.

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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.

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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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