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    Longitude and time: was [NAV-L] Star-sight discrepancy
    From: George Huxtable
    Date: 2005 Aug 26, 15:31 +0100

    This discussion has changed tack somewhat, and I have altered the
    threadname to reflect it.
    Bill, referring to star observations, had said-
    > >> previously noted by another list member, 6 seconds time would account
    > for an
    > >> approx 1.5 nm error in latitude, possibly less in longitude.
    > >
    >George relied:
    > > Not necessarily so. For example, near to noon, a 6-second time error would
    > > have no effect at all on calculated latitude.
    to which Bill responded-
    >I recall T was shooting a star, not the Sun. 
    Sorry, a slip-of-the mind on my part. ~I should have said "near to meridian
    passage", not "near to noon".
    Bill continued-
    >   You do raise an
    >interesting point regarding stars.  Wouldn't a star also have a brief
    >period--relative to its declination/observed altitude--where change in
    >observed altitude appeared to stall while it makes its meridian passage?
    It certainly would, just like the Sun does around noon.
    Fred wrote-
    >Yes.  A principle means of establishing latitude on land, where a plumb
    >bob or spirit level can be used to establish one's "horizon."  At sea,
    >with only a short time at twilight when both the real horizon and stars
    >are visible, tough to find a star undergoing meridian passage (and
    >wasting time better spent obtaining a 3-point or 4-point fix).
    Exactly so.
    However, Fred expanded the subject to longitude determination, in a later
    >Oops.  I believe by timing the actual moment of meridian passage,
    >longitude also can be determined, but I'm getting far out of my depth
    >to which Bill replied-
    >I recall toying with the idea,
    >and looking for bright stars that would be making their meridian passage
    >during prime viewing time to discover--as you pointed out--the opportunities
    >are few and far between.
    and Fred added-
    >Aside from the plumb bob, land-based astronomers also had
    >the advantage of having accurate and precise pendulum clocks, from the
    >1500s or 1600s onward.  Additionally, they could mount their telescopes
    >to swing exactly north south, to observe meridian passage.
    That's an important difference. Because their telescopes could be arranged
    to swing precisely in a North-South plane, about an East-West axis,
    meridian passage could be timed very precisely, as an object passed the
    crosswires, travelling sideways, without recourse to observing altitude or
    seeing the horizon. So transits at stars could be accurately observed at
    any time of night. Indeed, at Greenwich, a special telescope was fixed
    immovably to look only at Sirius, as it passed, day (Sirius being so
    bright) or night, for regulating the observatory's clocks. All that was
    needed was a clear sky at the right moment.
    It's different for us at sea, because we can't arrange to observe when
    exactly an object passes due South, compasses having so many defects. All
    we can do is to measure changes of altitude; as Fred says "I believe by
    timing the actual moment of meridian passage, longitude also can be
    determined, but I'm getting far out of my depth here".
    This takes us back to a long series of arguments on Nav-l about timing the
    moment of noon from observations of Sun altitude. I will try to summarise
    the salient points of that argument, in a way that I hope all can accept.
    It is, indeed, impossible to determine the moment of noon at noon itself,
    because then the altitude is unchanging. It has to be done by measuring
    altitude around noon, before and after, to determine the centre of symmetry
    of its rise and fall. This calls for a somewhat-protracted series of
    observations. The further they extend, before and after noon, the more
    accurate will the result be. Henry Halboth has demonstrated how, by
    observing equal altitudes, he can obtain the moment of noon by very precise
    measurements made from land, in this way, over a reasonably short period..
    However, two problems arise when timing noon in that way in real-life at
    sea. First, the perturbations produced by the state of the sea add
    inaccuracy to the altitudes, particularly from a small vessel, and thus
    impose a requirement for a longer series of observations to maintain the
    same precision of timing. Second, the apparent time of noon is affected
    considerably by North-South motion of the vessel and require a careful
    correction to be made, which may not be easy if that speed component is not
    well known, or is changing around noon, as might well happen with a sailing
    In spite of those difficulties, the "longitude-around-noon" procedure has
    its proponents, particularly Frank Reed. In his case, I think it is
    primarily for pedagogical reasons. The principle of the procedure is easy
    to grasp, and requires no spherical trig. From that one set of observations
    around noon, if Greenwich Time is known, both latitude and longitude can be
    found, without any plotting.
    More precise alternatives are-
    1. Make a "time-sight", the altitude of the Sun several hours before or
    after noon (or both), and calculate the time-interval from noon from the
    change in altitude between its value then and its value at noon.
    Corrections have to be made for the distance travelled by the vessel in the
    2. Don't bother with local noon, but instead work out the geographical
    position of the body knowing Greenwich Time, and starting from an assumed
    position, determine a position line to be drawn on a chart, according to
    Sumner and St. Hilaire. Cross that with another position line, for another
    body, or at another time making allowance for distance travelled in the
    interim. And there you are. It applies for any celestial body, under all
    I have tried to be fair with that summary, but we will see if it stirs up
    further argument.
    Now, back to Fred'ssuggestion, that the moment of meridian passage of a
    star could be determined in a similar way to that of timing
    altitude-around-noon of the Sun. The arguments against that procedure all
    apply to the star, but there's an extra problem, that makes the method
    almost impossible in the case of the star. It's this. There's a limited
    time-span, of a few minutes only (less than 20, usually, though maybe more
    in high latitudes) between stars appearing at twilight in the evening and
    the horizon becoming too dark to see; and conversely in the morning. That
    doesn't really allow enough time for a decent measurement, by changing
    altitude, of the moment of culmination of a bright star, even if, by luck,
    that moment happened to be right in the middle of the twilight period.
    Now for a rather trivial matter. Bill apologised for a perceived slight, in
    not referring to an earlier posting of mine about anomalous dip. Thanks,
    Bill, but it's of no matter. I'm not sensitive about such things. Fred's
    comment, on my behalf, was just right.
    >Bill wrote:
    > >> It seems there are
    > >> differing views on how best to deal with fog--get as high as you can
    > vs get
    > >> as low as you can.
    >George replied:
    > >
    > > I doubt that. For fog, I doubt that anyone will argue with the rule "get as
    > > low as you can". Where it's good advice to "get as high as you can", is in
    > > wave or swell conditions, to put the waves or swell onto a horizon that's
    > > as far away as possible.
    >I was thinking back to a post by one of our professional mariners, who spoke
    >about being on the bridge--which was above the fog.  If I recall he could
    >see the tops of buildings poking out of the fog along the shore/banks.  My
    >assumption, perhaps erroneous, was that if a ship were in a *patch* of fog,
    >it may be possible to get above it, and if very lucky see a clear horizon.
    >Perhaps wishful thinking, and probably a low percentage shot.
    Yes, possible but most unlikely, that fog could bank up below the bridge
    and yet allow a clear view of the horizon. Such things can occasionally
    happen, no doubt. A view of distant building-tops, above the fog level, is
    more possible, but wouldn't help in taking an altitude.
    Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
    or from within UK 01865 820222.
    Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
    5HX, UK.

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