Multiple resonances of the eight planet system of Kepler-90, part 2

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.

Multiple resonances of the eight planet system of Kepler-90, part 1

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.
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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.”
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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.

NASA’s TESS satellite claims its first Earth-size exoplanet in the habitable zone

Having one side of the planet constantly facing the star due to tidal locking could make habitability tricky though. There are three known planets in the system.
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From Wikipedia:
NASA’s Transiting Exoplanet Survey Satellite (TESS) has discovered its first Earth-size planet in its star’s habitable zone, the range of distances where conditions may be just right to allow the presence of liquid water on the surface.

Scientists confirmed the find, called TOI 700 d, using NASA’s Spitzer Space Telescope and have modeled the planet’s potential environments to help inform future observations.

Six hot rocky exoplanets orbiting very close to their stars could shed light on the geology of planets in our solar system

A researcher said of one of the new finds: “It is hard to see how the planet got there!”
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Six ‘very hot’ rocky exoplanets orbiting stars in the local region of the Milky Way hold the key to understanding more about how the Earth was formed, astronomers claim.

Researchers from the Open University have been studying planets discovered by the European Space Observatory’s planet-hunting telescope in Chile.

They are orbiting stars between 160 and 440 light years from Earth and all have hot surfaces with temperatures of around 2,012F to 3,272F.

The new findings could shed light on the geology of Earth and other rocky planets in the Solar System including Mercury, Venus and Mars, researchers say.

Full Daily Mail report here.

Resonances of the first (pulsar) exoplanetary system ever found

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.’

One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

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.

Resonances of the Kepler-184 three-planet system

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)

Lucas resonances in six-planet Kepler-20 system

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.

NASA quip: ‘Honey I Shrunk the Planetary System’

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.

A nearby binary star system with four planets

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.

TESS discovers habitable zone planet in GJ 357 system

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.

Why Phi? – exoplanetary resonances of HD 40307

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.

NASA’s TESS discovered three new planets nearby, including temperate ‘sub-Neptune’

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.

L 98-59b is the smallest planet yet discovered by TESS satellite

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.

Why Phi? – exoplanetary resonances of Kepler-102

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.

Why Phi? – the three planets of the Kepler-47 circumbinary planet system

Kepler-47 system [Image Credit: NASA/JPL Caltech/T. Pyle]

Astronomers have discovered a third planet in the Kepler-47 system, securing the system’s title as the most interesting of the binary-star worlds, says NASA’s Exoplanet Exploration team.

Using data from NASA’s Kepler space telescope, a team of researchers, led by astronomers at San Diego State University, detected the new Neptune-to-Saturn-size planet orbiting between two previously known planets.

With its three planets orbiting two suns, Kepler-47 is the only known multi-planet circumbinary system. Circumbinary planets are those that orbit two stars.

Continued here.
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Now at the Talkshop let’s take a quick look at the data.

Why Phi? – the Kepler-47 circumbinary system

Kepler Space Telescope [credit: NASA]

A headline at Phys.org today reads:
‘Astronomers discover third planet in the Kepler-47 circumbinary system’

The report starts:
‘Astronomers have discovered a third planet in the Kepler-47 system, securing the system’s title as the most interesting of the binary-star worlds. Using data from NASA’s Kepler space telescope, a team of researchers, led by astronomers at San Diego State University, detected the new Neptune-to-Saturn-size planet orbiting between two previously known planets.

With its three planets orbiting two suns, Kepler-47 is the only known multi-planet circumbinary system. Circumbinary planets are those that orbit two stars.’

In this system the two stars orbit each other about every 7.45 days.

What can the latest information tell us about these planets, including newly discovered planet ‘d’?

Why Phi? – Resonances of exoplanetary system Kepler-107

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)

These Exoplanets Are Forever Half Dark and Covered in Clouds

An artist’s image of a hot-Jupiter exoplanet [credit: NASA]

But they seem to have something in common that scientists were not expecting: their nightside temperature.

New research shows how the nightside of all hot Jupiters is covered in clouds, reports Discover Magazine.

Cloudy Hot Jupiters

“Hot Jupiters” exoplanets that resemble our own Jupiter, except for being, well, hot, have another side to them.

We mean this literally: The planets usually don’t rotate [see Tidal Locking note below], so one side is always facing their star, and the other remains in permanent night.

A new study is suggesting that these night sides probably all look the same, no matter where you go in the universe.

Why Phi? – Saturn’s inner moons and exoplanets of Kepler-223

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%)