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Glenn wrote-

"I understand that you can get a fix by using the altitudes of the two 
bodies used to get the lunar distance.  I thought there might be a shorter 
method to get longitude if you have no way of knowing your local time."

If you have no way of knowing the local time, you have no way of getting 
your longitude from a celestial observation. One requires the other. 
Longitude (from Greenwich) is simply the difference between Greenwich Time 
and your local time, turned into an angle (at 15º per hour). It could be 
the difference between Greenwich Mean Time and Local Mean Time. Or, just as 
well the difference between Greenwich Apparent Time and Local Apparent 
Time; those differences are identical.

You can get local time by measuring the altitude of either of the two 
bodies which was used to get a lunar distance. Or the altitude of any other 
predicted body. The only requirement is that it should be well away from 
the meridian, so that its altitude is changing quickly with time, rising or 
falling.

Glenn continied-
"The only time sight I know of requires your latitude."

Yes that's correct, except in special circimstances when the sighted body 
is exactly to your East or West. A navigator was usually expected to have a 
good idea of his latitude, even if he didn't know his longitude.

He concluded-
"Is a DR latitude good enough?"

It depends on many factors. If the observation on which the DR was based 
was taken only a few hours ago, yes; the DR latitude should be within a 
very few miles. If the sky has been cloudy for several days, in which time 
the vessel has been beating against stormy weather, the ensuing DR 
l;atitude is likely to be imprecise, and therefore, so will be any time 
sight that relies on knowing that latitude. And then the resulting 
longitude will be imprecise also. But again, if the sighted body is near 
due East or West, the result time-sight will depend little on the 
observer's latitude.

What has to be kept in mind, when making a lunar observation, is the 
inherent imprecision of getting Greenwich Time from the lunar distance. If 
the lunar distance could be observed with an error of only 1 arc-minute, 
and there were no other sources of error, then that would provide Greenwich 
Time to no better than about 2 minutes of time. If local time were known 
precisely , that would give rise to an error of about 30' in the longitude. 
That error usually dominates a lunar longitude observation. As long as the 
error in local time is small compared with that 2 minutes, then errors in 
local time will add little to the overall error. So the requirement for 
precision, in the local-time component of the lunar longitude process, is 
rather undemanding.

The simple answer to Glenn's question, then, is that usually a DR latitude 
will be good enough. And at sea, there may be no alternative.

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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