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 […]

## Search Results

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

Posted: January 17, 2021 by**oldbrew**in Astronomy, Fibonacci, Maths

Tags: exoplanets, phi, resonance

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

Posted: May 18, 2020 by**oldbrew**in data, Fibonacci, Phi

Tags: exoplanets, phi, resonance

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.

Posted: May 12, 2020 by**tallbloke**in design, Phi

Tags: teepee, tent design, tipi

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

Posted: July 31, 2019 by**oldbrew**in Astrophysics, Fibonacci

Tags: exoplanets, phi, resonance

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

Posted: July 13, 2019 by**oldbrew**in Analysis, Fibonacci, Lucas, Maths

Tags: exoplanets, phi, resonance

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

Posted: May 26, 2019 by**oldbrew**in Fibonacci, Lucas, Maths, Phi, solar system dynamics

Tags: phi, planetary theory, resonance

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

Posted: May 16, 2019 by**oldbrew**in Analysis, Astrophysics, Phi

Tags: exoplanets, phi, planetary theory

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

Posted: May 6, 2019 by**oldbrew**in Fibonacci, Lucas, Maths, Phi, solar system dynamics

Tags: phi, planetary theory, solar system

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

Posted: May 2, 2019 by**oldbrew**in Fibonacci, Lucas, Maths

Tags: phi, planetary theory

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

Posted: May 1, 2019 by**oldbrew**in Fibonacci, Lucas, Maths

Tags: phi, planetary

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

Posted: April 29, 2019 by**oldbrew**in Fibonacci, Lucas, Maths, Phi, solar system dynamics

Tags: phi, planetary theory, resonance

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

Posted: April 16, 2019 by**oldbrew**in Astrophysics, News, Phi

Tags: exoplanets, phi

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

Posted: February 8, 2019 by**oldbrew**in exploration, Fibonacci, Phi

Tags: exoplanets, phi, resonance

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

Posted: December 11, 2018 by**oldbrew**in moon, Phi, solar system dynamics

Tags: moon, phi, solar, solar - planetary theory

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

Posted: December 2, 2018 by**oldbrew**in Fibonacci, moon, Phi, solar system dynamics

Tags: moon, phi

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

Posted: November 16, 2018 by**oldbrew**in Fibonacci, moon, Phi, solar system dynamics

Tags: moon, phi

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

Posted: November 9, 2018 by**oldbrew**in Astrophysics, moon, Phi

Tags: moon, phi

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

Posted: September 1, 2018 by**oldbrew**in Astrophysics, Fibonacci, Phi, solar system dynamics

Tags: exoplanets, moon, planetary theory, resonance

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

Posted: July 22, 2018 by**oldbrew**in Cycles, Fibonacci, Phi, solar system dynamics

Tags: phi, planetary theory, solar system

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 […]

## Why Phi? – resonant moons of Uranus

Posted: April 7, 2018 by**oldbrew**in Astronomy, Fibonacci, Phi, solar system dynamics

Tags: moon, phi, planetary, resonance

The five major moons of Uranus in ascending distance from the planet are: Miranda, Ariel, Umbriel, Titania and Oberon Of these, the first three exhibit a synodic resonance similar to that of Jupiter’s Galilean moons, as we showed here: Why Phi? – the resonance of Jupiter’s Galilean moons Quoting from that post: The only exact […]