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Glenn asked-

"You wrote that for a time sight,if the sightrd body is near due east or
west, the resulting time sight will depend little on the observers
latitude.

My question now is, what is the procedure for obtaining the time from that
sight?"

A fair question. It might be useful to us both if Glenn tells us what
navigational texts he uses to work from, which might make it easier to
provide references.

======================

Local time can be derived from the position of any object in the sky that's
away from your North-South meridian, if its altitude is measured, its
position is predicted in the almanac, and the observer knows his latitude.

There's a simple formula for obtaining its Local Hour Angle (LHA), which is
the angle subtended at the pole by which it differs from your local
meridian, measured in degrees, positive Westerly.

cos LHA = (sin alt - sin lat sin dec) / (cos lat cos dec)

in which lat and dec have to be given a consistent sign, positive North,
and the observed altitude must have been corrected for the usual suspects.

It's most often applied to the Sun. By definition, the Sun has a LHA of
zero at local apparent noon, and changes at 15º per hour. So if you
determine the Sun's LHA from the above equation, and divide by 15, that
gives the time interval in hours, before or after noon, of your local
apparent time. Deciding which called for commonsense; if toward the East,
and rising, it was before noon, and vice versa. In those early days, Local
Apparent Time was simply "the time".

Until 1834, that was just what a mariner needed, because Greenwich Apparent
Time was the timescale that was used in the almanacs. So when he measured
and cleared a lunar distance, then compared the result with the almanac,
what that provided was a value of Greenwich Apparent Time, at which his
measured value was predicted. The time difference between that and his
local apparent time would tell him his longitude, at 15º per hour. Easy.

But then in 1834, when chronometers had become prevalent, almanacs became
based on mean time, which a chronometer could keep. Since then, Greenwich
Time, from a lunar or a chronometer, would always be Greenwich Mean Time.
And from then on, Local Apparent Time always had to be adjusted, by a
quantity to be found in the almanac, and misleadingly labelled "Equation of
time" of up to a quarter of an hour or so either way, to become "Local Mean
Time". The difference between Local Mean Time and Greenwich Mean Time then
provided longitude from Greenwich, at 15º per hour.

==================

Using a more modern almanac still, however, longitude can now be obtained
much more simply from a knowledge of GMT (from lunar, chronometer,
wristwatch, or radio)and a measurement of altitude of any suitable body. It
doesn't any more call, explicitly, for working out local time, which gets
bypassed.

Instead, knowing GMT, you look up in the almanac the predicted declination
and GHA of the body; Sun, Moon, star, or planet. (for a star that involves
adding GHA Aries and SHA of the star). Use its dec, with the observed alt,
and your known lat, to find the LHA of the body, in the equation shown
above. Subtract LHA from GHA. And the result is your (Westerly) longitude;
the Westitude. (Hope I've got that right...)

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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