This is an update just for Pierre Semac today - who's always keen on learning about celestial navigation! Today is a simple one, just doing a "Local apparent noon (LAN)" calculation. It's also known as "meridian passage" since using the time when the sun crosses you Longitude is key.
I had a rough idea of the latitude since we've been on this coast for six months but this calculation is primarily used for find it if you don't know exactly. Start with what you 'do' know - a nautical almanac or pre sight computer makes it easy to find out roughly when LAN will occur. This is useful because it means you don't need to stand out on deck for two hours looking for the peak. If you have literaly no idea what you latitude is you can make a graph starting around 1100 hrs. Write down the angle of the sun (using the sextant) and note the time - if the number (angle) is getting smaller you missed it - better luck tomorrow. If it is increasing keep measuring every five minutes or so 'til it starts to decline. The point between rise and fall is you meridian passage. Note down the angle at that time.
For today the angle at LAN - which was at 11:47 EST in Australia (+10 UTC) - was found to be 50 degrees 38.2 minutes.
So - converting back to UTC and using an almanac (note that I used my celestial calc to do this calc) to correct time and Hs (angle observed) we find that for the center of the sun (corrected for shooting to the North) we get a Latitude of -024 degrees 44.8 minutes (neg is south). This is close to the GPS' reading of 24 degrees 45.678 minutes.
So how did we do - OK. The reported position is about 1.5 nm from the actual position. No bad if you consider all we need to do was measure the angle of the sun at its zenith then convert local time to UTC. For more accurate fixes - as in the case of finding a reef pass etc - we'd want to get a three point fix going with more celestial bodies. This is an easy sight to take however and can be worked out in about 10 minutes if you can pre-compute a rough LAN time for your graph.
For a bit of trivia - let say you're in a lifeboat with no nautical almanac to find you LAN at UTC time. There are four times of the year you know exactly where you are if the sun is directly overhead (i.e. Hc = 90 degrees). These are the two equinoxes (if you were right on the equator) and then the two solstices for winter and summer (at roughly 23 degrees 26 minutes N/S).
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