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    Re: shortest twilight problem...
    From: George Huxtable
    Date: 2010 Jun 29, 12:04 +0100

    I should have added to my last note about twilight length, in commenting on 
    Marcel's claim-
    
    "A further contribution comes from the sun's change in declination.
    Isn't this around the equinoxes? I would therefore expect the longest
    twilight for a given latitude (below latitudes where the sun in summer
    may not reach 18 deg below the horizon) to be around the spring
    equinox."
    
    Not as I see it.
    
    The length of twilight depends, almost entirely, on the angle at which the 
    rising or setting Sun meets the horizon. When it rises or fall vertically, 
    in the tropics, then the time to reach -18�, at 15� per hour, is its 
    shortest, at 1 hour 12 min (neglecting refraction effects). At higher 
    latitudes, the further it gets from the vertical, the longer twilight will 
    be. Its slope, at the horizon, is steepest at the equinoxes, as I see it 
    (without doing any calculations). So then, the twilight will be shortest; 
    not longest, as Marcel writes.
    
    But Marcel has picked up a fine-point here, which may be one of the 
    complicating factors that I had missed in my simplistic thinking. The 
    changing declination of the Sun makes little difference to the length of 
    twilight, but it does have a small effect, and will lengthen sunset 
    twilight slightly at the Spring equinox. Conversely, it will shorten 
    twilight slightly at sunrise in Spring. But that is only a tiny effect, 
    caused by a shift in Sun position of around 1 arc-minute per hour, compared 
    with 15 degrees per hour of its regular motion.
    
    George.
    
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message ----- 
    From: "George Huxtable" 
    To: 
    Sent: Tuesday, June 29, 2010 11:18 AM
    Subject: [NavList] Re: shortest twilight problem...
    
    
    |I had written, about the date of shortest twilight-
    ||
    || > At first sight, the question appears to be an entirely trivial one. It
    || > seems to me (without thinking about it too hard) that there are two
    | days in
    || > the year when twilight is shortest, which are the days of the
    | solstices,
    || > and those dates are unrelated to the observer's latitude. Is that too
    || > superficial a view? Are there fine-points to the question that have
    | quite
    || > escaped me?
    |
    | and Marcel responded-
    |
    || I don't quite agree with you, George. Without going in to details, the
    || length of twilight is shortest near the equator and gets longer when
    || moving to the poles. It therefore does depend on latitude. Or, did I
    || misunderstand your reflections?
    ||
    || A further contribution comes from the sun's change in declination.
    || Isn't this around the equinoxes? I would therefore expect the longest
    || twilight for a given latitude (below latitudes where the sun in summer
    || may not reach 18 deg below the horizon) to be around the spring
    || equinox.
    |
    | ===================
    |
    | Marcel is wrong (I suggest) about his first point, but absolutely right
    | about his second.
    |
    | Yes, the length of twilight certainly does depend on latitude, but the
    | question was not about the length of twilight, but the DATE of the 
    shortest
    | twilight. And that, as I see it does not depend on latitude. Does Marcel
    | agree?
    |
    | But I was quite wrong about dating the shortest twilight to the 
    solstices.
    | I should have written "equinoxes", as he says. Indeed, I thought
    | "equinoxes", checked the twilight lengths, at equinox dates, from the
    | Almanac, just to be sure, and then mistakenly wrote "solstices". Sorry
    | about that. These things happen. Thanks to Marcel for bringing it to my
    | notice and giving me a chance to correct my words.
    |
    | George.
    |
    | contact George Huxtable, at  george@hux.me.uk
    | or at +44 1865 820222 (from UK, 01865 820222)
    | or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    |
    |
    |
    | 
    
    
    
    
    

       
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