Five petals of Venus

To return to the subject of how orbits appear when plotted geocentrically (that is, with the Earth stationary).

Mars geocentric sphere

This is how Mars’s Earth-based movements appear over a span of two years: one loop toward us at Mars’s opposition, contrasting with a wide swing around the far side of the Sun.

Now Venus: what pattern do its geocentric motions make?  The pattern is shaped by the famous Venus cycle.

(By the way, I had this post ready to go a week ago.  Then Microsoft struck.  I’ve only just got back my internet connection.)

Over 8 years, each phenomenon – each relative position of Earth, Venus, and Sun – occurs 5 times, and then over the next 8 years they repeat 5 times almost identically.  For Venus, the tight inward loops are the inferior conjunctions, in which Venus passes between us and the Sun; the wide swings are centered on the superior conjunctions, when Venus passes around the far side of the Sun.  So the general pattern is (as Anthony Barreiro commented) a “lovely five-petalled rose.”  The tight loops are the stamens of the rose, the wide swings are the petals.

When I try to plot a geocentric picture in the same way as the one for Mars, but over eight years (2016-2023) to show the complete rose, it is bewilderingly cluttered: five overlapping tracks, eight-times-twelve little Venus globes at monthly intervals – already too much without the ecliptic-plane grid and other details.  So here is the oicture in a more simplified version: still calculated in three dimensions, but, by moving the viewpoint to the north ecliptic pole, it becomes a flat plan of Venus’s path.

Venus geocentric orbit

Earth is in the middle; the vernal-equinox direction is to the right; the yellow spots are the Sun at the beginning of each month.  The rest is the rhythmic motions of Venus.

You’ll still have trouble deciphering which part of the track is for which year (I’ve used white, cyan, magenta, yellow for 2016, 2017, 2018, 2019, and again for 2020, 2021, 2022, 2023) but it doesn’t matter greatly.  You can see the five inferior conjunctions, in their five directions.  If you trace across the circle from each loop to the next, you see that they are not adjacent to each other but 2/5 pf the way around, like the five points of a pentagram.

Rough pentagram

(A pentagram, from the cover picture story of Astronomical Calendar 2015.)

The directions of the five inferior conjunctions determine their differing characters, by determining their places in Venus’s “true” (heliocentric) orbit, which is tilted and slightly elliptical.

2017 Mar 25: in Pisces; Venus passes 8 degrees north of the Sun; distance from us 0.28 AU (astronomical units, Sun-Earth distance); diameter of Venus’s (mostly dark) disk 60″ (arc seconds).
2018 Oct 26: in Virgo; 6° degree south of Sun; 0.27 AU; 62″.
2020 Jun  3: in Taurus; 0.5° north of Sun; 0.29 AU; 58″.
2022 Jan  9: in Sagittarius; 5° north of Sun; 0.27 AU; 63″.
2023 Aug 13: Cancer-Leo-Hydra border; 7° degrees south of Sun; 0.29 AU; 58″.

March 2017 is the next of those wonderful occasions, like March 2009, when we in the northern hemisphere have a chance to see Venus pass so far north of the Sun that it may be visible near to both sunset and sunrise of the days near, and even the day of, inferior conjunction.  And years of the 2023 type are the similar opportunities for south-hemisphere dwellers.

Having brought Venus into conjunction with petals and the southern hemisphere, I may be forgiven for remembering the limerick that rhymes in éili@.

There was a young gal from Australia
Who went to a ball as a dahlia.
When the petals unfurled
It was known to the world
That the dress – as a dress – was a failure.


17 thoughts on “Five petals of Venus”

  1. For the tropic year 364,5 days (31492800 s)

    Every 8 years, Venus orbits the Sun 12,96 times while the Earth orbits the Sun eight times.
    12,96 x 27 days(Dragon month)=349,92 ; 349,92 /48 (weeks)=7,29 ; 7,29( synodic week) x 80=583,2 days
    583,2 x 5 = 364,5 x 8 = 2916. i.e. there are exactly 5 Venus cycles in every 8 years.
    583,2 / 1,6= 364,5
    583,2/ 27 days(Dragon month)=21,6
    583,2/ 29,16(synodic month)=20
    583,2/ 29,5245(ecliptic month)=19,75308641975309

    For the tropic year 364,5833333333333 (31500000s)
    364,5833333333333 x 1,6=583,3333333333333
    583,3333333333333 / 364,5833333333333=1,6

    12,96 x 27,00617283950617 days(Dragon month)=350 ; 350 /48 (weeks)=7,291666666666666 ; 7,291666666666666( synodic week) x 80=583,3333333333333 days
    583,3333333333333 x 5 = 364,5833333333333 x 8 = 2916,666666666667. i.e. there are exactly 5 Venus cycles in every 8 years.

    583,2/ 27,00617283950617 days(Dragon month)=21,6
    583,3333333333333 / 29,16(synodic month)=20
    583,3333333333333 / 29,53125(ecliptic month)=19,75308641975309

    262,5 (Venus evening star or morning star)* 86400=22680000
    262,5 (Venus evening star or morning star) x 2+ 1/10 Synodic period Venus=583,3333333333333 (Synodic period Venus)

    195955200000000 (Constant of Nineveh) / 22680000/ 86400s=100 cycles (Venus evening star or morning star)

    100 cycles (Venus evening star or morning star) / 2= 50
    50 x 583,3333333333333=29166,66666666667days
    29166,66666666667days / 364,5833333333333=80 years

    80 years x 31500000s=2520000000s (29166,66666666667days )

    2520 cycles Wenus (period orbital ; superior conj.) / 364,5833333333333 days or 364,5= 4032 years
    1260cycles Wenus (period orbital) ; superior conj.) / 364,5833333333333 days or 364,5= 2016

    4032+2016=6048 years

    Day rule for the year : 80 years= 80 days
    31 +28+21 = Spring equinox
    262,5 days= Autumnal Equinox
    262,5 days / 36= 7,291666666666666 ( synodic week)
    7,291666666666666 ( synodic week) x 50= tropical year

  2. Vénus, embora seja um planeta é chamado «Estrela da Manhã», percorre nos céus o chamado «Ciclo de Vénus» de oito anos e muito importante na cronologia de quase todas as civilizações desde a Suméria, Babilónia, Egípcia, Maya, Grega, Romana tendo um dos seus expoentes no Templo de Jerusalém onde as colunas Jachim e Boaz serviam também para a sua observação ligado ao Arquitecto Irmão HIRAM e que se traduz na rosa e na estrela de cinco pontas que se preserva até hoje na simbologia da Maçonaria.
    Gosto mais da estrela de seis pontas, sou mais do S :-) L, mas isso fica para outro dia…

    1. My rough attempt to translate Abilio’s Portuguese:
      Venus, though it is a planet, is called “Morning Star”, it runs in the heavens the so-called “Cycle of Venus” of eight years, very important in the chronology of almost all civilizations from the Sumerian, Babylonian, Egyptian, Mayan, Greek, Roman, having one of its exponents in the Temple of Jerusalem, where the Joachim and Boaz columns also served for its observation by the architect, the brother of Hiram, and that translates to the pink five-pointed star that is preserved today in the Masonic symbology.
      I like the six-pointed star, it is more like an S, but that is for another day …

  3. I am entranced! Is it even possible that ancient astronomers could have plotted this “design”? It seems to be the form for centuries old art. Lynn

    1. Good question. There immediately spring to mind the epicycles of the system before Copernicus’s, the Ptolemaic. In this, a planet moved around a small circle (called an epicycle), and the center of this circle traveled around a larger circle (called the deferent) around the earth. I’m not sure how similar the resulting curve would be to the “petalled” Venus geocentric orbit, until I try to plot it for a fictitious planet, which I may do.

  4. The plan view of Venus’ orbit reminds me of the patterns my daughter and I traced out with her Spirograph drawing kit!

    You mentioned the challenge of seeing Venus near, or even directly on, the day of inferior conjunction. That could be a little “life goal” for an amateur astronomer, namely to see Venus on its date of inferior conjunction at each of the above “inferior conjuction seasons.” I have seen it on the June date (at both of the transits, in 2004 and 2012), the October date (it turned out to be the easiest because our skies are typically the clearest and most transparent in October in Virginia, despite being south of the Sun), and the January date (in 2006 a week before my daughter was born, and then again in 2014). Paradoxically, I have missed it on the exact date of inferior conjunction in March, which should be the “easiest” if only considering the northern elongation above the Sun. I also have not yet had success in August.

    I am curious to know if any of Guy’s blog readers have been successful in seeing Venus on its inferior conjunction date, and in particular if any of you have good enough eyesight to be able to detect Venus’ crescent with the unaided eye. I most certainly do not, even corrected with glasses.

  5. Wonderful. Again.
    Now, ever since hearing the Ruff & Rodgers binaural heliocentric rendering I’ve wondered what it would sound like from a geocentric perspective – hint hint. (I refer to their rendition of Kepler’s Harmony of the Spheres – done many years ago)
    There are so many software orrerys out there – some that allow a vantage point from various points in the solar system – or even farther – but they’re all visual; the ear integrates information differently than does the eye – and such a binaural audio-orrery from other positions would be very interesting I think. Just imagine listening, from a Martian-topo-centric perspective, Phobos and Deimos flying around in opposite directions. Or, from our Moon, the earth just sitting there while everything else does its dance. hmmm.

    1. Or the speeded-up experience of a star within a globular cluster.
      I’m almost dismayed to hear of all these extensions of software. Back before there were any of them (or any that I knew of), my own first steps in programming the positions of things as seen from centers other than the sun seemed like exploration.

      1. Indeed, I left programming a long time ago partially because it was hard to stomach putting all that effort into making optimum efficiency of memory and cycles (what I called a software diamond) only to have vastly superior hardware with vastly inferior software run circles around the hard-earned result – often before it was even complete. – And that was before the PC even entered the market… I ran about ten years worth of planetarium projector settings on an IBM1130. That unit probably represented an optimum in lasting value – its replacement, a Prime 750 supermini, was in the dump in only 3 years – since a vastly superior replacement cost outright what maintaining the Prime cost for only a few months. That’s when I bailed.
        In any event – The cosmos is a spherical sensation – and it is, visually, the task (which you do so well) to represent space on a flat sheet of paper (or screen) – whereas the binaural rendering allows one to perceive spherically with the ear (without the encumbrance of the visually analogous planetarium dome). So, I’m serious about hinting at a new version collaboration – say, from a geocentric or otherwise vantage. I have several times done human orrerys – characterizing movements with persons walking various paths – and doing the three basic systems (Ptolemaic, Copernican and Brahe-ic). Mars is especially fun – sneaking slowly behind the Sun like a stalking fox, then roaring in at opposition, Jupiter/Saturn making stately little loops – and of course Venus with her petals.

        1. If we ever have an Astronomical Convocation I hope we will perform Paul’s human orrery, perhaps while holding peppercorns, etc., at appropriate distances from a basketball. Young athletes can perform the inner planets’ race around the Sun, or Earth. I’ll be Neptune, occasionally stepping deosil or widdershins as directed by Paul.

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