Re: Calculate the declination of the Sun in your head
From: Joshua Hunley
Date: 2021 Mar 3, 18:31 -0800
Dave, the same question occurred to me. I had looked at Table 4 in Pub. 249 and said, "Surely I can come up with something more straightforward than this!" only to discover that I really couldn't.
I worked with this a day or two ago, and decided that while possible, it was not really practical. The two complexities I found were related to:
- the equation of time
- leap years
Stars are simply easier.
Calculating differences from the beginning of the year seems to help by resetting one's calculation to a known sane point each year, rather than requiring one to account for all of the 'fiddly bits' that physics wants to throw at us beyond the short term.
If one is calculating the difference in GHAS between 01 Jan 0000UT (or 31 Dec... just call it ZERO) and any date in the year, that difference is pretty consistent between leap year cycles cf differences for 2020-2023 are off by at most 10" for 2048-2051, less for earlier cycles. (Based on numbers pulled from Horizons). This difference tracks the change in EoT throughout the year (convert to HMS and subtract from EoT at ZERO). In the long term sun tables 'E' = 5deg - (Time2Arc[EoT]).
Someone far smarter than I can probably fit that difference to an equation for each year of a cycle, maybe even a 'rule of thumb'. I have no clue how involved those equations might be though. Someone on the web did do a harmonic analysis of the EoT, but that was for multiple years.
Using tables, it takes up 16 pages for the 4 year cycle. It is probably possible to do it with just the tables for the leap year but that would cause more complications using them -- Navigation techniques, seem to me to trade size/bulk for complexity as if there is some law of nature involved... :)