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    Re: Quick Estimate of Sun Declination
    From: Frank Reed
    Date: 2018 Apr 5, 11:49 -0700

    Herman Dekker, you wrote:
    "But I thought how to memorize the dates between?

    Well, you might want to memorize some dates in between... perhaps. But you don't need to do so. It only takes a few minutes to figure them out.

    To change the scene, let's suppose we're dealing with the third quarter of the year. The equinox this year is on Sep. 22 (really, early on the 23rd UT, but I'll ignore that). The solstice is on Dec. 21. That's 90 days later. In this case, it would be easier to trisect the angle and then bisect those thirds. Each "pie slice" would then be 15 days. It's not much effort to work out which dates fall at 15 day intervals after Sep.22: Oct. 7, Oct. 22, Nov. 6, Nov. 21, Dec. 6, Dec. 21. There... just did that in my head! Didn't even get out the handy spreadsheet. :) Notice, too, that in this case you've got 90 days filling a right angle giving us one degree per day (doesn't always happen) so if you have a protractor or a compass rose, you could easily mark off individual days. Note that this method of generating approximate declination is limited primarily by the earth's variable speed as it orbits the sun. It's faster near perihelion at the beginning of January and slower at aphelion six months later. This is partially, but only partially, compensated by the variable lengths of the seasons, from 90 to 93 days.

    The beauty of this trick for getting approximate declination is that you need no information that you don't already know! Without a doubt, anyone with background in celestial navigation and many people with sufficient knowledge of geography will know that the sun's declination ranges from 23.5 N to 23.5 S (equivalently that those are the latitudes of the Tropic of Cancer and the Tropic of Capricorn). And anyone except a small child would know the dates when the seasons begin and end (at least to within a day or two). Rather than memorizing the dates in between, the next bits of information to add to this low-accuracy system would be estimates of the GHA of the Sun at Greenwich noon or midnight (equivalently the key dates and values of the equation of time). With that you can start to estimate position fixes within a degree or so using the declination quadrant and the values of GHA Sun at noon by plotting them on any convenient spherical surface --like a toy ball. This provides that "desert island" navigation that we contemplate now and then....

    Frank Reed

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