Latitude is fairly easy to work out, if you have some device like a
sextant or kamal to measure the maximum height of the sun (Hs) or other
object and doing a sight reduction. Sin(Hc) = Sin(dec) * Sin(lat) +
Cos(dec) * Cos(lat) * Cos(LHA) and Cos(Z) = [Sin(dec) - Sin(lat) *
Sin(Hc)] / [Cos(lat) * Cos(Hc)] where Hc = calculated altitude, dec =
declination, lat = latitude, LHA = Local Hour Angle, Z = azimuth. Use
your DR latitude for lat.

Latitude by Polaris works the same way. Remember that the height of
Polaris is several minutes from true 90 degrees.

Longitude. You need accurate GMT to find longitude. There are methods for
determining longitude like finding lunar distance, but these fill books.
There is no easy way to determine longitude other than accurate GMT.

RA = GHA (Aries) - GHA (Body), where GHA = Greenwich Hour Angle.

There are many excellent sites that go into detail about your question.
Type celestial navigation into Google.

Mike Boersma

Abdul Ahad wrote:

With modern GPS systems now (or soon to be) available on an average
person's wrist watch, this is purely a question of historic and
academic interest!

Can someone please re-iterate the calculations and easiest method
necessary to work out latitude and more importantly *longitude*
based on observations of the Sun and stars from a specific point on
the Earth's surface?

This is an 'all surface terrain' question (not just confined to
positions at sea), and I am assuming there is no 'dead reckoning'
info. available to the navigator and he/she does not have any almanacs
to hand, except an Astronomy handbook giving simple info like the R.A.
and declination of the 100 brightest stars and sunrise and sunset
times for various latitudes throughout the year, positions of bright
planets, etc.

In the northern hemisphere, I know geographic *latitude* can be simply
deduced from the elevations of Polaris (at night) or the midday Sun
(if you know its approximate declination) above the local horizon.
Also, if you have a chronometer keeping GMT, then simply taking the
transit time of the Sun due south at midday to equate to 1200 hrs
local time and working out its difference from GMT will give you a
very "rough" idea of your local time zone and hence approx.
*longitude* band.

How do you then further refine the calculations to make your longitude
deductions accurate to say within a *few degrees*? How do concepts
like hour angle and Greenwich Mean Sidereal Time (GMST) come into the
equation? As its purely for academic purposes, I do not wish to press
for too much complications in the methodology...so simple diagrams and
ideas would suffice.

Thanks.
Abdul Ahad