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 <[email protected]> wrote: > > > ---------- Forwarded message --------- > From: Michael Ossipoff <[email protected]> > Date: Fri, Oct 14, 2022 at 10:16 PM > Subject: Re: How to turn ecliptic longitude into solar declination? > To: Steve Lelievre <[email protected]> > > > > > 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 <[email protected]> >> 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 < >>> [email protected]> 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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