Fwd: How to turn ecliptic longitude into solar declination?
-- Forwarded message - From: Michael Ossipoff Date: Fri, Oct 14, 2022 at 10:16 PM Subject: Re: How to turn ecliptic longitude into solar declination? To: Steve Lelievre 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 > 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 >>> >>> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: How to turn ecliptic longitude into solar declination?
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: > 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 > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
How to turn ecliptic longitude into solar declination?
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
