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    Re: Luni-Solar Distance
    From: Lars Bergman
    Date: 2010 Oct 20, 08:47 -0700

    George wrote, in reply to Douglas Denny, in 14133:
    “If the time was known, there would be no point in taking a lunar. That's the purpose of measuring a lunar-distance; to determine the time. So there's a bit of a paradox, in calculating altitudes with which to clear a lunar, for which time and position are both needed. To get round it, you have to assume a trial longitude first, and then use the lunar observation to refine that assumption.”
    And in 14145:
    “I don't know of any texts which have considered this question of a need for reiteration when altitudes have been calculated, and wonder whether travellers were even aware of its potential for causing error. Can anyone point to such a publication?”
    ---
    In above context, the purpose of measuring a lunar-distance is to determine a standard time, i.e. the time at Greenwich. To calculate an altitude, knowledge of Greenwich time is not necessary, but the local time must be known. Latitude is assumed known and an approximate Greenwich time in order to find the declination from the almanac. Thus, an altitude observation to determine the local time should therefore be executed as near in time to the distance observation as possible. The error in time then depends only on the regularity of the watch and of the ship’s (or traveller’s) reckoning between the two observations.
    To find the altitude corrections, some rework may be necessary. Normally, parallax and refraction are found from the apparent altitude, thus all tables are arranged with apparent altitude as argument. When altitudes have been calculated, some iterations are necessary to find the proper values. The aim is to end up with an apparent altitude that, reduced in the normal way, gives the same value of true altitude as that found by calculation.
    In some Swedish manuals for navigation (e.g. Pettersson in 1876) the process of calculating altitudes are described in some detail, involving iteration not of the lunar calculation but of the altitude calculations.

    Lars
    59N 18E
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