Venus synodic calendar
Sep. 18th, 2012 08:49 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
steorran_woruldeThis is a calendar concept sketch that could go either with Earth or with Domil, since Domil is astronomically equivalent to Earth. Chances are that if it sticks to anything outside itself, it'll get assigned to some Domil culture, but it might just stay on its own without getting integrated into anything larger.
So I was thinking about the coincidental neat relationship between the length of Earth's year and the length of Venus's synodic period relative to Earth and Sun.
It takes about 365.25 days for Earth to return to the same place relative to the sun and the surrounding stars. (1 earth year.)
It takes about 583.9 days for Venus to return to the same place relative to the Earth and the Sun (for instance, from one inferior conjunction to another). (1 Venus synodic period.)
If we round each of those to the nearest integer, we get:
365 days * 8 = 2920 days
584 days * 5 = 2920 days
So basically, every 8 years, Earth, Venus, the Sun, and the stars are all in alignment; or, equivalently, Earth's back at the same time of year, and Venus is back in the same configuration with Earth.
If you connect the dots between the inferior conjunctions of the 5 synodic periods that go into this 8-year cycle, it makes a pentagram shape. Each point of the pentagram marks a different time of year that a inferior conjunction can happen at; the spaces between them basically divide the year into 5 equal segments.
So what happens if we divide 365 days into 5 seasons of equal length?
365 days / 5 = 73 days (Isn't that a beautiful nother coincidence? There's no reason the number of days in the (nominal) year had to be divisible by 5, but it is.)
5 seasons of 73 days each make up a 365-day year.
But also, 8 seasons of 73 days each make up a Venus synodic period:
73 days * 8 = 584 days.
That makes a nice basis for a calendar.
If you work out the details, it seems that successive inferior conjunctions don't actually occur exactly 584 days apart; probably the slight ellipticalities of orbits are what make the timing off by a few days sometimes (and I'm not talking here about calendrical drift that comes from the fact that Venus's actual synodic period is just shy of 584 days). So the calendar wouldn't be a perfect match to actual astronomy, but would be close.
There's actually more that makes this calendar work tidily, too. But before I get into that, let me give a sketch of one possibility of time divisions, starting with the first date given in the pentagram link I gave: that there was an inferior conjunction of Venus on October 29, 2010. For the sake of things working out tidily, I'm going to say that that's the beginning of the 5th 'season'; that allows the 1st 'season' to currently start in January. So we get this pattern.
For comparison, the actual dates of inferior conjunctions in that time period (according to the pentangle image I linked) are:
2010 Oct 29, 2012 Jun 6, 2014 Jan 11, 2015 Aug 15, 2017 Mar 25, 2018 Oct 26.
Not exactly the same, but close; the difference between 2018 Oct 27 in the calendar and Oct 26 in actuality is probably a matter of calendrical drift (the calendar will be too long for the synodic cycle by about half a day every 8 years), but the other inaccuracies are probably more due to differing speeds at different parts of orbit.
Arranging the same dates in a table of 8 columns rather than 5 gives a table that aligns with the synodic cycle rather than Earth's year - rather than each column being at the same rough time of year, each column has Venus in the same relation to Earth. For spacesaving I've written dates in compressed format.
In this table, column 1 holds all the dates that approximately correspond to inferior conjunctions. But it turns out that some other columns of the table also roughly correspond to other significant points in Venus's synodic cycle. Comparing with the Wikipedia page on Aspects of Venus, column 5 basically corresponds to the timing of superior conjunction. This makes sense and is probably predictable, since column 5 is halfway around the cycle from column 1, and superior conjunction is the opposite configuration to inferior conjunction - Venus directly behind sun rather than Venus directly in front of sun. The fact that column 8 nearly corresponds to Greatest Eastern Elongation and column 2 nearly corresponds to Greatest Western Elongation must be a nice coincidence, though. (Columns 3, 4, 6, and 7 still don't correspond to any significant points of Venus's cycle.)
I've already mentioned calendrical drift. This calendar will be too long by about 1 day every 16 years (every 10 synodic cycles). So there's probably an anti-leap day somehow or other - a day that gets omitted in order to bring things back into sync with the synodic cycle. (It will get out of sync with the calendar year; staying in sync with the synodic cycle is more important.)
But, back to seasons and the 8-year/5-synodic-period cycle which is the overarching unit of this calendar.
There are 40 73-day seasons in the 8-year cycle. We could count years or synodic periods or both within that cycle, but I think it would actually be quite neat to make it so that you have co-running counts of seasons according to an 8-season cycle and a 5-season cycle, so that they come back into synch every full 8-year cycle. (This is a version of the "coexisting cycles of different lengths" phenomenon that I mentioned in my basic timekeeping principles post.) If the 8-season Venus cycle had each month have a name (for the sake of example, call them mnemonically An Bil Cor Den Es Fon Ger Han, with An being the season that starts with inferior conjunction) and the 5-season solar cycle each had a name for each month (let's call them again mnemonically Ag, Ba, Cu, Di, El), then calling a season by its combination of names (like An-Ag, or Cor-Di, or Han-El) would uniquely distinguish its place in the full cycle.
I had more thoughts, such as about whether the points of significance should be aligned with the middles of seasons or the beginnings of seasons, and how seasons might be subdivided, but they are tenuous enough that I'm not going to put them down here now.
So I was thinking about the coincidental neat relationship between the length of Earth's year and the length of Venus's synodic period relative to Earth and Sun.
It takes about 365.25 days for Earth to return to the same place relative to the sun and the surrounding stars. (1 earth year.)
It takes about 583.9 days for Venus to return to the same place relative to the Earth and the Sun (for instance, from one inferior conjunction to another). (1 Venus synodic period.)
If we round each of those to the nearest integer, we get:
365 days * 8 = 2920 days
584 days * 5 = 2920 days
So basically, every 8 years, Earth, Venus, the Sun, and the stars are all in alignment; or, equivalently, Earth's back at the same time of year, and Venus is back in the same configuration with Earth.
If you connect the dots between the inferior conjunctions of the 5 synodic periods that go into this 8-year cycle, it makes a pentagram shape. Each point of the pentagram marks a different time of year that a inferior conjunction can happen at; the spaces between them basically divide the year into 5 equal segments.
So what happens if we divide 365 days into 5 seasons of equal length?
365 days / 5 = 73 days (Isn't that a beautiful nother coincidence? There's no reason the number of days in the (nominal) year had to be divisible by 5, but it is.)
5 seasons of 73 days each make up a 365-day year.
But also, 8 seasons of 73 days each make up a Venus synodic period:
73 days * 8 = 584 days.
That makes a nice basis for a calendar.
If you work out the details, it seems that successive inferior conjunctions don't actually occur exactly 584 days apart; probably the slight ellipticalities of orbits are what make the timing off by a few days sometimes (and I'm not talking here about calendrical drift that comes from the fact that Venus's actual synodic period is just shy of 584 days). So the calendar wouldn't be a perfect match to actual astronomy, but would be close.
There's actually more that makes this calendar work tidily, too. But before I get into that, let me give a sketch of one possibility of time divisions, starting with the first date given in the pentagram link I gave: that there was an inferior conjunction of Venus on October 29, 2010. For the sake of things working out tidily, I'm going to say that that's the beginning of the 5th 'season'; that allows the 1st 'season' to currently start in January. So we get this pattern.
Year Season 1 Season 2 Season 3 Season 4 Season 5 2010 Oct 29 2011 Jan 10 Mar 24 Jun 5 Aug 17 Oct 28 2012 Jan 10 Mar 23 Jun 4 Aug 16 Oct 28 2013 Jan 9 Mar 23 Jun 4 Aug 16 Oct 28 2014 Jan 9 Mar 23 Jun 4 Aug 16 Oct 28 2015 Jan 9 Mar 23 Jun 4 Aug 16 Oct 28 2016 Jan 9 Mar 22 Jun 3 Aug 15 Oct 27 2017 Jan 8 Mar 22 Jun 3 Aug 15 Oct 27 2018 Jan 8 Mar 22 Jun 3 Aug 15 Oct 27
For comparison, the actual dates of inferior conjunctions in that time period (according to the pentangle image I linked) are:
2010 Oct 29, 2012 Jun 6, 2014 Jan 11, 2015 Aug 15, 2017 Mar 25, 2018 Oct 26.
Not exactly the same, but close; the difference between 2018 Oct 27 in the calendar and Oct 26 in actuality is probably a matter of calendrical drift (the calendar will be too long for the synodic cycle by about half a day every 8 years), but the other inaccuracies are probably more due to differing speeds at different parts of orbit.
Arranging the same dates in a table of 8 columns rather than 5 gives a table that aligns with the synodic cycle rather than Earth's year - rather than each column being at the same rough time of year, each column has Venus in the same relation to Earth. For spacesaving I've written dates in compressed format.
1 2 3 4 5 6 7 8 10Oct29 11Jan10 11Mar24 11Jun05 11Aug17 11Oct29 12Jan10 12Mar23 12Jun04 12Aug16 12Oct28 13Jan09 13Mar23 13Jun04 13Aug16 13Oct28 14Jan09 14Mar23 14Jun04 14Aug16 14Oct28 15Jan09 15Mar23 15Jun04 15Aug16 15Oct28 16Jan09 16Mar22 16Jun03 16Aug15 16Oct27 17Jan08 17Mar22 17Jun03 17Aug15 17Oct27 18Jan08 18Mar22 18Jun03 18Aug15 18Oct27
In this table, column 1 holds all the dates that approximately correspond to inferior conjunctions. But it turns out that some other columns of the table also roughly correspond to other significant points in Venus's synodic cycle. Comparing with the Wikipedia page on Aspects of Venus, column 5 basically corresponds to the timing of superior conjunction. This makes sense and is probably predictable, since column 5 is halfway around the cycle from column 1, and superior conjunction is the opposite configuration to inferior conjunction - Venus directly behind sun rather than Venus directly in front of sun. The fact that column 8 nearly corresponds to Greatest Eastern Elongation and column 2 nearly corresponds to Greatest Western Elongation must be a nice coincidence, though. (Columns 3, 4, 6, and 7 still don't correspond to any significant points of Venus's cycle.)
I've already mentioned calendrical drift. This calendar will be too long by about 1 day every 16 years (every 10 synodic cycles). So there's probably an anti-leap day somehow or other - a day that gets omitted in order to bring things back into sync with the synodic cycle. (It will get out of sync with the calendar year; staying in sync with the synodic cycle is more important.)
But, back to seasons and the 8-year/5-synodic-period cycle which is the overarching unit of this calendar.
There are 40 73-day seasons in the 8-year cycle. We could count years or synodic periods or both within that cycle, but I think it would actually be quite neat to make it so that you have co-running counts of seasons according to an 8-season cycle and a 5-season cycle, so that they come back into synch every full 8-year cycle. (This is a version of the "coexisting cycles of different lengths" phenomenon that I mentioned in my basic timekeeping principles post.) If the 8-season Venus cycle had each month have a name (for the sake of example, call them mnemonically An Bil Cor Den Es Fon Ger Han, with An being the season that starts with inferior conjunction) and the 5-season solar cycle each had a name for each month (let's call them again mnemonically Ag, Ba, Cu, Di, El), then calling a season by its combination of names (like An-Ag, or Cor-Di, or Han-El) would uniquely distinguish its place in the full cycle.
I had more thoughts, such as about whether the points of significance should be aligned with the middles of seasons or the beginnings of seasons, and how seasons might be subdivided, but they are tenuous enough that I'm not going to put them down here now.
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no subject
Date: 2012-09-19 09:35 am (UTC)And the bit about the coexisting cycle reminds me of the East Asian 10/12 cycle that repeats every 60 years (10 Heavenly Stems, 12 Earthly Branches); there, too, combinations are used to uniquely identify any of those 60 years.
It also reminds me a bit of the Maya calendar with 13 numbered days and 20 named days for a cycle of 260 days.
no subject
Date: 2012-09-19 01:04 pm (UTC)no subject
Date: 2012-09-19 06:44 pm (UTC)no subject
Date: 2012-09-19 06:53 pm (UTC)no subject
Date: 2012-09-20 02:29 pm (UTC)no subject
Date: 2012-09-20 05:24 pm (UTC)From the Wikipedia article on the Mayan calendar, it sounds like they did use a strictly 365 day year (with no intercalary days or months), and also tracked a 584-day Venus cycle, which does come close to this. The Wikipedia article doesn't mention an 8-year unit being derived from these, though they clearly would come into realignment...