Orbital resonance and the celestial origins of Earth’s climatic changes – Why Phi?

A year after I wrote the original ‘Why Phi’ post explaining my discovery of the Fibonacci sequence links between solar system orbits and planetary synodic periods here at the Talkshop in 2013, my time and effort got diverted into politics. The majority of ongoing research into this important topic has been furthered by my co-blogger […]

Why Phi – the Fibonacci resonances of the TOI-451 exoplanets

This three-planet system has orbit periods ranging from under two to over sixteen days, obviously another very compact group. Their star is slightly smaller and less powerful than our Sun. 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 […]

Why Phi? – resonances of exoplanets LHS 1140 b and c

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. […]

The Why Phi Pi Slice goes camping.

Back in 2013 I wrote a post about the relationship between our favourite number, phi (1.618…) and the famous circularity constant Pi (3.141…). If we divide the circle of 360 degrees by phi, we get 222.5 degrees, leaving 137.5 degrees as the remainder. In that post I noted that: The area ‘A’ of a sector […]

Why Phi? – exoplanetary resonances of HD 40307

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 […]

Why Phi? – exoplanetary resonances of Kepler-102

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 […]

Why Phi? – Jupiter-Venus harmonics and the Fibonacci/Lucas series

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 […]

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

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 […]

Why Phi? – the Saturn-Uranus connection

This is an easy data table to interpret. The Uranus orbits are all Fibonacci numbers, and the synodic conjunctions are all a 3* multiple of Fibonacci numbers. [Fibonacci series starts: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …etc.] In addition, the difference between the two is always a Lucas […]

Why Phi? – more Jupiter-Saturn orbital harmonics

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.

Why Phi? – some Earth-Mars orbital harmonics

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 […]

Why Phi? – Jupiter-Earth harmonics and the Lucas series

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 […]

Why Phi? – the Kepler-47 circumbinary system

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 […]

Why Phi? – Resonances of exoplanetary system Kepler-107

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 = […]

Why Phi? – a luni-solar link

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 […]

Why Phi? – a lunar evection model, part 2

It turns out that the previous post was only one half of the lunar evection story, so this post is the other half. 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 […]

Why Phi? – a lunar evection model

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 […]

Why Phi: is the Moon a phi balloon? – part 2

Picking up from where we left off here… 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 […]

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

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 […]

Why Phi? – a long-term Jupiter-Saturn-Uranus model

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 […]