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    Re: Latitude by noon Sun sight
    From: Frank Reed
    Date: 2019 Dec 4, 09:34 -0800


    What you need to consider is the rate of change in the Declination for the date in question. You say the Dec is changing 6' in 24 hours. Today the Dec of the Sun is falling at a rate of about 8' in 24 hours (conveniently that's 1' every three hours). Suppose you're doing a LAN sight on June 21. The Dec is basically constant all day to the nearest minute of arc, so you don't need to know UT better than the +/-12 hours. That's the best case.

    The most extreme rates of change in the Sun's Dec occur on the equinoxes. You can see this easily by drawing a graph of Dec versus date. It closely resembles a standard "sine curve", and you can see directly that the maximum slope occurs at the March and September equinoxes when the Dec graph crosses the zero line. If you check, you'll find that on those dates, the rate of change is about 23-24 minutes of arc per day. In other words, the sub-Sun point is moving North or South at almost exactly one knot. That's the maximum rate for the year, and it's a good estimate for a month on either side of each equinox. So if you want the Sun's Dec accurate to a minute of arc, then the most accuracy you ever need in UT for a noon sight is +/- half an hour or so. If you want the Dec accurate to a tenth of a minute, then you'll want UT to +/- three minutes or so. In practice, worrying about tenths in Dec is overkill, but it's rarely true that you don't know what the UT is at all, so I usually recommend getting the UT at LAN to +/- five to ten minutes. This also corresponds to the "hang time" in many latitudes, so it's a reasonable level of concern.

    Frank Reed

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