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    Re: Celestial Navigation without a sextant.
    From: George Huxtable
    Date: 2008 Mar 8, 17:39 -0000

    40 South asked-
    | Supposing one was in a small boat with an accurate timepiece and the
    | necessary tables, how accurate could you determine your longitude by
    | observing the rising or setting of the sun or any other celestial
    | body?
    There have been several responses, but I suggest that they have missed an
    important point.
    Yes, in theory, if you happen to know your latitude well, then an
    observation of the moment of Sunrise will give your local time, which can be
    compared with Greenwich time to give your longitude. You could use the
    predictions in the Nautical Almanac, but these are to the nearest minute of
    time only, and for Greenwich noon at the middle day of a block of three
    days, and for broad bands of latitude. You could interpolate, to some
    extent, but a better way would be to do the job by trig or tables, for that
    known latitude, date, and time, allowing for Sun semidiameter, refraction,
    and dip.
    The best you can expect is to observe a sunrise from the Equator, near the
    equinox, when it comes vertically out of the sea at 15 degrees in each hour.
    At other latitudes, and other times, the ascent of the Sun is at a shallower
    angle, much shallower at high latitudes, so its rate of rise is
    correspondingly less, and any error in measuring Sun altitude reflects in an
    enhanced error in time, and therefore in longitude.
    Now, here's the rub. Although sunrise/sunset predictions are based on a
    presumed value of refraction, at an observed altitude of 0 degrees, which
    will be something like 33 or 34 arc-minutes, that is no more than a rough
    approximation. At sunrise/sunset, the light is having to pass through an
    immense thickness of atmosphere, at a glancing angle, and is badly affected
    by unknown and unpredictable refraction as it passes through the various air
    layers, at unknown temperatures. That is why the Sun's image can get so
    distorted as it nears the horizon, and even if there's no apparent
    distortion, the whole Sun can get displaced, vertically, by these refraction
    effects. It's not unusual for the actual refraction at the horizon to be
    half a degree out from that predicted value, sometimes even more, so
    depending on its sign, it could double, or nullify, the predicted
    refraction.. In polar latitude, the effects can be greater still. That's why
    navigators keep clear of celestial altitudes when they are less than 10
    degrees or so. At higher altitudes, refraction is much less, and, more
    important, more precisely predictable.
    Measured at the equator, every minute of refraction error will result in a
    4-second error in timing sunrise, and thus a 1 minute error in longitude. At
    higher latitudes, the errors will be enhanced. So timing sunrise/sunset will
    never provide a precise value for longitude. But if a rough ball-park figure
    will suffice, it could do the job.
    40South continues-
    | Also, assuming you had a compass and were north or south of the
    | tropics, would it be possible to estimate your latitude by taking a
    | bearing of the setting or rising of a celestial body?
    I'm not sure why he applies the restriction of being "north or south of the
    tropics". Again, in theory, yes. Again, it's affected by the vagaries of
    refraction near the horizon. But a bigger source of error is the difficulty
    of measuring that bearing. On land, with a theodolite and a known
    North-South line, it can be measured precisely. At sea, it's affected by the
    uncertanties of the magnetic compass. It's hard to read azimuth to better
    than a degree or so at the best of times, and then there are additional
    errors in allowing for deviation and variation. Historically, a
    sunrise/sunset azimuth was used the other way round. With latitude known
    (from a noon Sun sight, followed by a bit of DR) it was used, on a wooden
    vessel, to check magnetiic variation.
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    To post to this group, send email to NavList@fer3.com
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