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    Re: Lunars: how to use the prop.log tables?
    From: Frank Reed
    Date: 2016 Aug 31, 10:40 -0700

    A couple of quick thoughts:

    • You can get loads of lunars data in various formats from my web site at http://www.reednavigation.com/lunars/.
    • I do not include PL diff values since I find them rather pointless (see below).
    • PL diff values were not included in the almanacs in the "heyday" of lunars. They were added starting in 1834. Before then lunarian navigators looked up their own PL diff values.
    • It's easy to do the interpolation ignoring proportional logs entirely. You should try it with p.logs at least once for historical feel, but otherwise... why bother with them?

    The interpolation without proportional logs:
    Suppose I have a cleared Jupiter-Moon lunar distance of 83° 12.3' (modified from your original example) taken on January 1, 2015, and I know from the almanac that the true geocentric LD at 12:00 UT was 84° 35'.3 while at 15:00 UT the true distance was 82° 56'.8. First, we need the rate of decline (or increase as the case may be). It's just a subtraction. In this case, the distance declines 1° 38.5' or 98.5' in 180 minutes of time. The cleared observed value is lower than the initial 12:00 distance by 1° 23.0' or 83.0'. Setting up the proportion, we have T/83.0 = 180/98.5 which implies T = 83·180/98.5 or T = 151.67 minutes. Note that the difficulty of this little division problem was quite high two centuries ago, and that's why proportional logs were originally invented. Today, it's no issue. This is the number of minutes that have passed since 12:00 so the actual time is 14:31:40.

    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

       
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