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NASA’s exoplanet hunter (TESS)
[image credit: MIT]
Planets b and c are a fraction of Jupiter’s size, but planet d is vast with a radius of over four Jupiters, or about 45 Earth radii.
Wikipedia says:
LHS 1140 is a red dwarf in the constellation of Cetus…The star is over 5 billion years old and has 15% of the mass of the Sun. LHS 1140’s rotational period is 130 days…LHS 1140 is known to have two confirmed rocky planets orbiting it, and a third candidate planet not yet confirmed.
Planet b was in the media spotlight in 2017:
LHS 1140b: Potentially Habitable Super-Earth Found Orbiting Nearby Red Dwarf – Sci-News.
“This is the most exciting exoplanet I’ve seen in the past decade,” said Dr. Jason Dittmann, an astronomer at the Harvard-Smithsonian Center for Astrophysics and lead author of the Nature paper.
. . .
“The LHS 1140 system might prove to be an even more important target for the future characterization of planets in the habitable zone than Proxima b or TRAPPIST-1,” concluded co-authors Dr. Xavier Delfosse and Dr. Xavier Bonfils, both at the CNRS and IPAG in Grenoble, France.
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.
Credits: NASA’s Goddard Space Flight Center/Chris Smith
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
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.
Kepler Space Telescope [credit: NASA]
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.
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).
Kepler-47 system [Image Credit: NASA/JPL Caltech/T. Pyle]
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.
– – –
Now at the Talkshop let’s take a quick look at the data.
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).
Distances not to scale.
In addition, the difference between the two is always a Lucas number. And that’s it for Saturn-Uranus, which would make for a very short blog post.
But it’s possible to go further.
We’re now looking for a pattern arising from the Jupiter-Saturn synodic conjunctions and the orbit periods.
Focussing on the numbers of Jupiter orbits that are equal, or nearly equal, to an exact number of Saturn orbits (years), a pattern can be found by first subtracting the number of conjunctions from the number of Saturn orbits.
A simple pattern emerges when looking at the Earth-Mars synodic conjunctions.
Focussing on the numbers of Mars orbits that are equal, or almost equal, to an exact number of Earth orbits (years), the pattern can be found by subtracting the number of conjunctions from the number of Mars orbits.
The difference between the two sets of numbers follows the Fibonacci series, which is strongly related to the golden ratio.
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).
Kepler Space Telescope [credit: NASA]
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’?
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)
(more…)
This was a surprise, but whatever the interpretation, the numbers speak for themselves.
‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured relative to the stars, but because the Earth is orbiting the Sun, we see this period as 27.2753 days.’ – Wikipedia.
What happens if we relate this period to the lunar draconic year?
Image credit: interactivestars.com
There are two variations to lunar evection, namely evection in longitude (the subject of the previous post) and evection in latitude, which ‘generates a perturbation in the lunar ecliptic latitude’ (source).
It’s found that the first is tied to the full moon cycle and the second to the draconic year.
Apogee = position furthest away from Earth. Earth. Perihelion = position closest to the sun. Moon. Perigee = position closest to Earth. Sun. Aphelion = position furthest away from the sun. (Eccentricities greatly exaggerated!)
Lunar evection has been described as the solar perturbation of the lunar orbit.
One lunar evection is the beat period of the synodic month and the full moon cycle. The result is that it should average about 31.811938 days (45809.19 minutes).
Comparing synodic months (SM), anomalistic months (AM), and lunar evections (LE) with the full moon cycle (FMC) we find:
1 FMC = 13.944335 SM
1 FMC = 13.944335 + 1 = 14.944335 AM
1 FMC = 13.944335 – 1 = 12.944335 LE
Since 0.944335 * 18 = 16.9983 = 99.99% of 17, and 18 – 17 = 1, we can say for our model:
18 FMC = 233 LE (18*13, -1) = 251 SM (18*14, -1) = 269 AM (18*15, -1)
See: 3 – Matching synodic and anomalistic months.
(more…)
Credit: universetoday.com
Three well-known aspects of lunar motion are:
Lunar declination – minimum and maximum degrees
Orbital parameters – perigee and apogee distances (from Earth)
Anomalistic month – minimum and maximum days
Standstill limits due to the lunar nodal cycle
‘The major standstill limit of the moon can be reached if the lunar node is near the vernal (or autumnal) point, and with the moon at its max. distance from the equator, equal to a declination at present days of 23.44° + 5.1454°= 28.59°.
The minor standstill limit of the moon can be reached if the lunar node is near the vernal (or autumnal) point, and with the moon at its min. distance from the equator, equal to a declination at present days of 23.44°- 5.1454° = 18.29°.’
http://iol.ie/~geniet/eng/moonperb.htm#nodes
28.59 / 18.29 = 1.5631492
4th root of 1.5631492 = 1.11815
This number leads to the key to the puzzle.
Here we find a match between the orbit numbers of Jupiter, Saturn and Uranus and see what that might tell us about certain patterns in the solar system.
715 U = 60072.044 years
2040 S = 60072.895 years
5064 J = 60072.282 years
Data source: Nasa/JPL – Planets and Pluto: Physical Characteristics
The Jupiter-Saturn part of the chart derives directly from this earlier Talkshop post:
Why Phi? – Jupiter, Saturn and the de Vries cycle
Tallbloke's Talkshop 