Here’s a small foretaste from Astronomical Calendar 2016. Since I’m having to work with rising anxiety to get it ready for the printer, I might as well spin off blog posts from it. For one thing, you may be able to point out features I could improve.
I came to the bit about “The Sun’s Progress through the Constellations” (on page 32 in Astronomical Calendar 2015).
Precession isn’t something we’re born with understanding of. We often have to think twice (at least, I do) about which way the astrological signs of the zodiac slide in relation to the astronomical constellations. Does the Sun cross the boundary into the real starry Aries before or after it enters the astrological sign of the same name? When astrology says the Sun should be in Aries, is it “still in Pisces” or “already in Taurus”? It’s one of those many two-way hesitations that plague the mathematically non-instinctive.
It was to make the matter clearer to myself that I devised the little diagram:
Even while making it I had felt it could communicate its message more immediately with if I added some color. So this time around I set about doing that.
The program that draws it is named acsuent.for – gobbledegook, to anyone but me. I have to have a sort of shorthand to locate what I want among the 321 Fortran programs I seem to have written. It’s short for “Astronomical-Calculating SUn ENTering-constellations program.” Its initial purpose was to find for any year the 25 dates when the Sun enters the 12 zodiacal signs and the 13 (because of Ophiuchus) actual constellations along the ecliptic. But at some point I made it also produce this diagram.
I now thought it would be easy to apply blue to the two boxes for Aries, for example. But it took me several more hours than I had expected. This is typical of efforts to correct or extend a program.
To draw and fill the box for Aries, instead of just drawing a line at the date when the Sun enters Aries, the program has to know at that same moment the date when the Sun will enter the next constellation, Taurus; but the only other date it could be told to remember at that moment was the one it had previously calculated, for entering Pisces. So it was drawing the boxes, but at the moment of calculating for Aries it was drawing the box for Pisces; which was confusing. As I was going to bed I realized (this also is typical of arrivals-at-solutions) the simple answer: deal with the events in backward order. Just change the line
I’m sure you see what I mean. In Basic, a language that many people used to know, it would be
FOR J = 25 TO 1 BY -1
There remained a problem with the constellations that cross the line for January 1 and therefore have to appear in two parts. To help me gaze at the problem, I used colors for the problem boxes and slid them out from where they were hiding:
It was about then that I thought this example of wrestling with a process might be interesting enough to tell you about.
I saw how to solve the problem by use of the number 0, and at last:
Yes! Clearer, I think, is the sliding downward (later in time) of the constellations in relation the signs, like geological formations on either side of a fault; and that the Sun now makes its way from Taurus into Gemini almost exactly at the date (the June solstice) when it’s supposed to be advancing from Gemini into Cancer; that the imaginary signs are equal spans whereas the irregularly shaped constellations’ widths along the ecliptic vary; that the Sun spends the longest time in Virgo, and the shortest in Scorpius (because Ophiuchus usurps a stretch of the ecliptic).
Using three shades of color proved clearer than two; and, by trial, using them in the order from darker to lighter proved clearer, emphasizing that the four quarters of the year start at the equinoxes and solstices.
I’m limited to black and blue (actually, cyan) in printing all but a few pages of the Astronomical Calendar, because four-color printing is far more expensive. But on the monitor, we can do what we like.
You may have an opinion on choices of colors. I think they should keep to the rhythm of three. (So it’s hardly possible to make the “watery” constellations bluish, or for me to indulge my feeling that the letrer A is green.)
And finally: how about running the program for distant epochs, and seeing the changes made by precession?
Here side by side are the states of the constellations as now and a thousand years ago.
The change looked even more vivid when I had the two diagrams in windows on top of each other on the monitor, before pasting one into the other, and could flick from one to the other with a keystroke (control-F6) and watch the constellations jump.
A thousand years ago, the constellations were half a constellation-width back. The Sun was only in the middle of Gemini, not its end, when the sign was changing from Gemini to Cancer. But wait – is my thick line for the solstice in the right place? Yes, according to Jean Meeus’s Astronomical Tables, page 326, the solstice in 1016 fell on June 16 (Julian calendar).
I feared that “Capricornus” off the bottom betrayed yet another glitch that I had to find and eradicate. But no, it was right: I had told the program to write each constellation’s name two millimeters down from the date where the Sun enters it, and when I greatly magnify the diagram I can see that there are two lines at the bottom: a very narrow strip for Capricornus. In 1016 the Sun entered Capricornus (as my program also told me) in the early hours of December 31.
Let’s try for two thousand years ago, around the time when the astrological signs were fixed:
Yes, the constellations are back alongside the signs. Back then the Sun really did enter Aries when the casters of horoscopes said that it did. It’s a bit false to talk about the boundaries of the “real” constellations back then. If there were boundaries, they were loose; those we now draw on starry maps were finally agreed only in 1930.
All this about one four-inch-high marginal embellishment for the Astronomical Calendar. Not, so far, a strategy for saving time in making these blog posts.
–I see one more glitch. The names of Capricornus and Scorpius in the astrological column should be “Capricorn” and “Scorpio”. I thought I had fixed that in the program, but realize it was only in the calculating and not in the plotting part of the program. I’m not going to re-make all those illustrations now.