About Calculators
The Casio fx300ES Plus is an excellent and
inexpensive calculator at about $11. It features natural input so
you enter a formula just as it would be written on paper. Entering
degrees, minutes and seconds is simple. The Casio has 1 memory position
but there are 8 positions for variables so you have 9 memory locations.
You can
review many of the previous entries you make.

Hc = sin^{1}[sin(declination) x sin(Latitude) + (cos(Latitude) x cos(declination) x cos(LHA)] ‣ And now as it
would be entered into the Casio calculator... Sin^{1}(Sin(Latitude) x Sin(declination) + Cos(Latitude) x Cos(declination) x Cos(LHA) NOTE If the heavenly body's declination is Contrary name to your Ap Latitude enter a negative sign before it. ‣ Why would you want to determine Hc using a calculator? It's
faster than looking up in Pub. No. 249, highly accurate, you don't need
a lot of printed out pages of Latitudes
from Pub. No.
249.
Pub. No. 249 doesn't cover any sight of a heavenly body with a declination greater than 29º (except Vol 1 for a few select stars) so you'd have to use Pub. No. 229 which is extremely large. 
Determine
Local
Apparent Noon using GHA Form Determine Local Apparent Noon using
GHA In Western
Longitudes
((Your
Longitude – Sun GHA less than your Longitude) / 15) + GHA
integral hour Example
‣The GHA less than your Longitude on January 21, 2016 is 72° 11.7' (at 17:00 GMT).
‣Arrange
the formula like this: ((75º 44' – 72° 11.7')
/ 15) + 17
‣
Answer= 17:14:09.2 GMT (LAN for
January 21,
2016 at W 075º 44')Another way ‣ (Your Longitude – GHA less than your Longitude) ‣
Take the answer to “TABLE 3Conversion of Arc
to Time” and convert the figure to time.
‣
Then add the
result to the GHA integral hour.In Eastern Longitudes ((360 – Your
Longitude) – Sun
GHA less than your Longitude) / 15 + GHA
integral hour Example
‣
You're located at E 124º 37'. When is LAN
(Local
Apparent Noon) on Febuary 8, 2017?First find your longitude's angular distance West of Greenwich
‣Arrange
the formula like this: 360°–124º 37' = 235°23.0'
‣
Answer= 03:55:41.2 GMT (LAN for Febuary 8, 2017 at E 124º 37')‣Using The Nautical Almanac for 2017 and the date of Febuary 8, 2017 find the GHA which is less than your Longitude's angular distance West of Greenwich. ‣ Answer= 221° 27.7' (at 03:00 GMT). ‣Finally, arrange the formula like this: (235°23.0' – 221° 27.7') / 15 + 3 Another way ‣ (360° – Your Longitude)= your longitude's angular distance West of Greenwich ‣Then (Your longitude's angular distance West of Greenwich – GHA less than your Longitude) ‣
Take the answer to “TABLE 3Conversion of Arc
to Time” and convert the figure to time.
‣
Then add the
result to the GHA integral hour. 
obtain
Longitude
A Noon sight will help determine your Latitude fairly accurately and Longitude approximately. ‣Take
and record 3 Sun sights onehalf hour before an estimated LAN Local Apparent Noon. Space the
shots about 5 minutes apart. Record the date and Greenwich time of each shot. Label
the shots in
the order they were taken 1A, 2A and 3A.
‣Wait
for the Sun to MP (Meridian
Passage) and drop back down to the last Height of sextant (Hs) Sun sight
you took (which was sight number 3A) and record
the time of the sight in Greenwich time. Label it 3P.
‣Set your Sextant to the Height of sextant (Hs) of the 1rst
shot you took before LAN and wait for the Sun
to drop back down to that Hs and record the time of that sight in Greenwich time. Label it 1P.
You should now have are 3 averaged time figures that are
fairly close together.
You now have, hopefully, a fairly accurate time when LAN occured. Label this "LAN Averaged" ‣Get The
Nautical
Almanac and find the GHA of
the Sun for the day and hour on which you took the
sights.
‣Record the whole hour GHA in degrees. ‣Using the Increments & Corrections Table find the "LAN Averaged" minutes and seconds (of time) in degrees for the time of the sight. ‣Add the GHA degrees
and GHA increments
together this is the approximate Longitude
of your location. But.....if you were sailing along in a
boat that Longitude is
behind you now by the distance you travelled since the determined Local Apparent Noon IF you're
travelling due East or due West only. So,
depending upon your speed add or subtract a few estimated miles to your
position depending upon the direction you're heading. If heading West add a few estimated miles. If
heading East subtract a few
estimated miles. It shouldn't be much if you're
sailing.

Noon
sight Determine Latitude For exampleIf you're near W 060º then LAN will be at Greenwich time PLUS 4 hours or 16:00 GMT. ‣Using your sextant "follow the Sun up" until it just
hangs in the sky neither rising nor falling. ‣Record
the sextant height and the date and
time.
‣ Correct the sextant for Dip, Index Error and use the Altitude Corrections Table for the main correction to get the Ho (Height observed). ‣ Latitude= (90º
– Ho) + declination of Sun see Rules below.
Example (90º – Ho
(53º 5.3') + declination
(N04º 47.6')= 41º 42.3'
‣
Make sure to enter the correct declination
sign!
‣
If
the declination is of Contrary Name to
your Latitude then enter a  (minus) sign before it
