I emphasize that saying that each third of an ecliptic-month is 10 degrees is not an approximation. An ecliptic-month is defined as exactly 1/3 of an astronomical- quarter…1/3 by ecliptic-longitude, not by time or days.
An astronomical-quarter is the ecliptic interval between a solstice & an equinox…90 degrees along the ecliptic. On Fri, Oct 14, 2022 at 11:33 PM Michael Ossipoff <email9648...@gmail.com> wrote: > BTW, I like sundials that tell the ecliptic-months, Aries thru Pisces. > > …for which one would need the Solar declinations for the beginning of each > ecliptic-month, & preferably also for some fractions of each > ecliptic-month, such as 1/3 & 2/3. > > On Fri, Oct 14, 2022 at 10:16 PM Michael Ossipoff <email9648...@gmail.com> > wrote: > >> >> >> ---------- Forwarded message --------- >> From: Michael Ossipoff <email9648...@gmail.com> >> Date: Fri, Oct 14, 2022 at 10:16 PM >> Subject: Re: How to turn ecliptic longitude into solar declination? >> To: Steve Lelievre <steve.lelievre.can...@gmail.com> >> >> >> >> >> Or you could just use the ecliptic longitude, reckoned as usual from the >> Vernal Equinox…multiply its sine by the sine of the obliquely & take the >> inverse sine of the result. >> >> I’d suggested that other way because there are some spherical >> trigonometry formulas that require an argument between 0 & 90 degrees. >> >> …but that isn’t one of them. >> >>> >>> >>> On Fri, Oct 14, 2022 at 6:49 PM Michael Ossipoff <email9648...@gmail.com> >>> wrote: >>> >>>> Multiply the sine of ecliptic longitude (reckoned forward or backwards >>>> from the nearest equinox) by the sine of 23.438 or whatever the current >>>> obliquity’s exact value is). >>>> >>>> Take the inverse sine of the result. >>>> >>>> On Fri, Oct 14, 2022 at 4:57 PM Steve Lelievre < >>>> steve.lelievre.can...@gmail.com> wrote: >>>> >>>>> >>> Of course you’ll know when the declination is negative or positive, so >>> mark it accordingly. >>> >>> >>> >>> Hi, >>>>> >>>>> For a little project I did today, I needed the day's solar declination >>>>> for the start, one third gone, and two-thirds gone, of each zodiacal >>>>> month (i.e. approximately the 1st, 11th and 21st days of the zodiacal >>>>> months). >>>>> >>>>> I treated each of the required dates as a multiple of 10 degrees of >>>>> ecliptic longitude, took the sine and multiplied it by 23.44 (for >>>>> solstitial solar declination). At first glance, the calculation seems >>>>> to >>>>> have produced results that are adequate for my purposes, but I've got >>>>> a >>>>> suspicion that it's not quite right (because Earth's orbit is an >>>>> ellipse, velocity varies, etc.) >>>>> >>>>> My questions: How good or bad was my approximation? Is there a better >>>>> approximation/empirical formula, short of doing a complex calculation? >>>>> >>>>> Cheers, >>>>> >>>>> Steve >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> --------------------------------------------------- >>>>> https://lists.uni-koeln.de/mailman/listinfo/sundial >>>>> >>>>>
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