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    DRAFT of 'A Perpetual Almanac for the Sun and Stars 2020-2050' (Using difference tables)
    From: Joshua Hunley
    Date: 2021 Mar 7, 09:01 -0800

    One of my lockdown projects is to take a stab at creating a long term almanac for the Sun and stars. Attached is a draft of what I came up with.  I have not done any error analysis but the spot checks I have done have been within a couple of tenths of a minute of the values reported by EzAlmanac. Attached is a draft of what I came up with.

    The Solar table values are the difference of the given time from the value at 1 Jan 0000UT. Four versions were made for the years 2020-2023. To get the E or declination for other years, find the difference at the time of observation - using interpolation and, for every other leap year cycle, factoring in +/- 40 minutes 'orbit time'  - then add it to the 1 Jan 0000UT value for the observation year. Solar declination also has a quadrennial correction. I have not included a correction for E because it is, at most, 10". There is a text file attached to this post which shows the corrections for each year and day.

    The stars table consists of the SHA/Dec of stars at 1 Jan 0000UT 2020; an average of how much those value change from the beginning to the end of each month; the average change in one year; and the absolute change from 2020 to 01 Jan 2025-2050, in 5 year increments. This is to keep errors from creeping in due to the use of averages over many years.

    Since I created this for my own use and curiosity I have only included worked examples for instruction.  If it seems like this is something others would like to use I will write up something more to make it 'user friendly'.

    I have also attached the Equation of Time tables which I removed from the final version, it turns out that when basing the tables on differences, they are simple an arc-to-time version of the E table with sign inversion. Still, trading 8 pages for the conversion may be worthwhile.

    As a side note, it should be possible to eleminate all but the tables for leap years (LY0) and interpolate using 'orbit time' like in the emergency sun tables in the Air Almanac. I have not explored that technique using difference tables though.

    I would appriciate any feedback, suggections or pointing out of blunders on my part. 




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