Why Phi? – resonant moons of Uranus

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 […]

Why Phi? – Jupiter, Saturn and the ice giants

This post on the ice giants Uranus and Neptune follows on from this one: Why Phi? – Jupiter, Saturn and the inner solar system The main focus will be on Uranus. A planetary conjunction of three bodies (e.g. two planets and the Sun, in line) is also known as a syzygy. Here’s the notation for […]

Why Phi? – resonant exoplanets of star YZ Ceti

YZ Ceti is a recently discovered star with three known planets (b,c and d) orbiting very close to it. Although some types of mean motion resonance, or near resonance, are quite common e.g. 2:1 or 3:2 conjunction ratios, this one is a bit different. The orbit periods in days are: YZ Ceti b = 1.96876 […]

APOD: Fibonacci relations appear in IR at Jupiter’s poles – Why Phi?

So to clarify here (because I messed it up earlier) what was presented this morning at #AAS231 were infrared images of Jupiter's north pole (left, via @lrebull) and south pole (right, via @Stardustspeck) showing respectively eight and five cyclones circling central vortices. 😲🤯 pic.twitter.com/lFkfl25wam — Jason Major (@JPMajor) January 9, 2018

Why Phi? – Jupiter, Saturn and the inner solar system

The planetary theory aspect appears a bit later, but first a brief review of some relevant details. In this Talkshop post: Why Phi? – a triple conjunction comparison we said: (1) What is the period of a Jupiter(J)-Saturn(S)-Earth(E) (JSE) triple conjunction? JSE = 21 J-S or 382 J-E or 403 S-E conjunctions (21+382 = 403) […]

Why Phi? – solar and lunar rotation

This started as a search for a period when the Sun and the Moon would both complete a whole number of rotations. The result was: Solar: 25.38 days * 197 = 4999.860 d Lunar: 27.321662 * 183 = 4999.864 d (data sources: see reference notes at end) Taking these as equivalent, we have 197-183 = […]

Why Phi? – the rainbow angle

The minimum deviation angle for the primary bow [of a rainbow] is 137.5° according to Wikipedia. This is known as the rainbow angle. A circle is 360 degrees, so the ratio of the rainbow angle to the circle is therefore the square of the golden ratio i.e. 137.5:360 = 1:2.61818~. – – – Hong Kong […]

Astrophysicists find that planetary harmonies around TRAPPIST-1 save it from destruction: Why Phi?

Excellent – we outlined this ‘resonance chain’ (as they have now dubbed it) in an earlier post here at the Talkshop [see ‘Talkshop note’ in the linked post for details]. When NASA announced its discovery of the TRAPPIST-1 system back in February it caused quite a stir, and with good reason says Phys.org. Three of […]

KAM theorem, and its application to the stability of the Solar system. Why Phi?

I’m not expecting much discussion of this post, I don’t understand it either, though I have run across KAM before in another context, and eventually some light may dawn that illuminates some relationship with our phi-solar system dynamics work. I’ll just leave it here for now so it doesn’t get lost. One random synchrony is […]

Why Phi? – a lunar ratios model

The idea of this post is to try and show that the lunar apsidal and nodal cycles contain similar frequencies, one with the full moon cycle and the other with the quasi-biennial oscillation. There are four periods in the diagram, one in each corner of the rectangle. For this model their values will be: FMC […]

An improvement to Bode’s Law. Why Phi?

I’m working away for the next fortnight, with no internet access. So I thought I’d put up something for the bright denizens of the talkshop to chew on while I’m gone. Bode’s Law is a heuristic equation which gives the approximate distance to the first seven major planets plus Ceres. reasonably well, but then goes […]

Why Phi? – modelling the solar cycle

We’re familiar with the idea of the solar cycle, e.g.: ‘The solar cycle or solar magnetic activity cycle is the nearly periodic 11-year change in the Sun’s activity (including changes in the levels of solar radiation and ejection of solar material) and appearance (changes in the number of sunspots, flares, and other manifestations). They have […]

Why Phi? – Pluto’s eccentric orbit

‘Pluto’s orbital period is 248 Earth years. Its orbital characteristics are substantially different from those of the planets, which follow nearly circular orbits around the Sun close to a flat reference plane called the ecliptic. In contrast, Pluto’s orbit is moderately inclined relative to the ecliptic (over 17°) and moderately eccentric (elliptical). This eccentricity means […]

Why Phi? – lunar eclipses at Stonehenge

Stonehenge Visitors Guide – under ‘Eclipse Cycles’ – says: ‘Now, it’s widely accepted that Stonehenge was used to predict eclipses. The inner “horseshoe” of 19 stones at the very heart of Stonehenge actually acted as a long-term calculator that could predict lunar eclipses. By moving one of Stonehenge’s markers along the 30 markers of the […]

Why Phi? – solar rotation notes

Tallbloke recently acquired a book by Hartmut Warm called ‘Signature of the Celestial Spheres: Discovering Order in the Solar System’ which offers this gem: 588 solar Carrington rotations (CarRots) = 587 lunar sidereal months We’ll call this the HW cycle, about 43.91 years. ‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots […]

Why Phi? – a unified precession model

‘Because of apsidal precession the Earth’s argument of periapsis slowly increases; it takes about 112000 years for the ellipse to revolve once relative to the fixed stars. The Earth’s polar axis, and hence the solstices and equinoxes, precess with a period of about 26000 years in relation to the fixed stars. These two forms of […]

Why Phi? Sylvia & Sons Swing Serenely by Shining Stars

Out at the unfashionable end of the Asteroid Belt, lies a seldom seen squashed spud of rock known as Sylvia. NASA has this: Discovered in 1866, main belt asteroid 87 Sylvia lies 3.5 AU from the Sun, between the orbits of Mars and Jupiter. Also shown in recent years to be one in a growing list […]

Why Phi? – Jupiter and the Full Moon Cycle

A very good Phi-related correlation can easily be found between the period of Jupiter’s orbit and the length of the full moon cycle, as we’ll describe in a moment. First, what exactly is the full moon cycle? One of several definitions given by Wikipedia says: ‘the full moon cycle is the period that it takes […]

Why Phi? – an orbital parameters test

We’ll assume the diagram is self-explanatory but if not, this should help (see opening paragraphs). We’re looking at Aphelion minus Perihelion (A – P) distances of the giant planets. Figures are given in units of a million kms. (lowest value first), using Jupiter as a baseline.

Why Phi? – the resonance of Jupiter’s Galilean moons

The resonance of three of the four Galilean moons of Jupiter is well-known. Or is it? We’re usually told there’s a 1:2:4 orbital ratio between Ganymede, Europa and Io, but while this is not far from the truth, a closer look shows something else.