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Disclaimer: These are computer generated tables. Use on your own risk. The accuracy has been checked as good as possible but can not be guaranteed. This means, if you get lost on the oceans because of errors in this publication I can not be held liable. For security relevant applications you should buy an official version of the nautical almanac.
The Nautical Almanac 1981
Celestial Navigation useful Formulas
The Casio fx-300ES Plus is an inexpensive calculator at about 11 USD. It features natural input soyou enter a formula just as it would be written on paper. Entering degrees, minutes and seconds isvery simple. The Casio fx-300ES Plus has 9 memory locations and you can review many of theprevious entries you make using a special key on the calculator.
Determine Hc using a calculator
Hc = asin[sin(Declination)*sin(Latitude) + cos(Latitude)*cos(Declination)*cos(LHA)]
As it would be entered into the Casio calculator
Sin-1(Sin(Ap Latitude) x Sin(Declination) + Cos(Ap Latitude) x Cos(Declination) x Cos(LHA)
Declination is the declination of the Celestial body you're observing. When the heavenly body's declination is Contrary name to your Ap Latitude enter a negative sign before it.
Latitude is the Latitude where you are, think you are or where you would like to determine Hc for.Typically, you'll be using an Assumed position Latitude or Ap Latitude as it's called.
In Western Longitudes
LHA is the Local Hour Angle which is derived from subtracting your whole number value ofLongitude (Assumed or otherwise) from the whole number value of GHA (Greenwich Hour Angle).
In Eastern Longitudes
LHA, in Eastern Longitudes, is determined by rounding up the GHA figure to the next highestwhole degree figure then adding the DR. Longitude to GHA to obtain LHA. Only add the wholedegree DR. Longitude figure to the rounded up whole degree GHA figure. If the resulting LHAfigure is greater than 360 then subtract 360 from the figure to obtain the LHA.
Why would you want to determine Hc using a calculator?
It's faster than looking up in Pub. No. 249 and Pub. No. 229, highly accurate and you don't need alot of printed out pages of Latitudes from Pub. No. 249 and Pub. No. 229. Pub. No. 249 Vol. 2 & 3don't cover any declination greater than 29 degrees so you'd have to use Pub. No. 229 which isextremely large.
Celestial Navigation useful Formulas
Z = acos[(sin(Declination) sin(Ap Latitude) x sin(Hc)) (cos(Ap Latitude) x cos(Hc))]
As it would be entered into the Casio calculator...
Cos-1((Sin(Declination) Sin(AP Latitude) x Sin(Hc)) (Cos(AP Latitude) x Cos(Hc)
If the heavenly body's declination is Contrary name to your Ap Latitude enter a negative sign beforeit.
To put Z into the right quadrant, apply the following rules-
In Northern Latitudes LHA greater than 180....Zn=Z LHA less than 180...........Zn=360 Z
In Southern Latitudes LHA greater than 180....Zn= 180 Z LHA less than 180...........Zn= 180 + Z
Determine Z independent of Hc
L is latitude and d is declination. When the heavenly body's declination is Contrary name to your Ap Latitude enter a negative sign before it.
The sign convention used in the calculation of this azimuth formula is as follows: from Bowditch Chapter 22 CALCULATIONS AND CONVERSIONS, page 331
1) If latitude and declination are of contrary name, declination is treated as a negative quantity;2) If the local hour angle is greater than 180, it is treated as a negative quantity. If the azimuth angle as calculated is negative, add 180 to obtain the desired value. Determine Refraction 0.96 Tan of (Ha)
Determine Dip using feet 0.97 x (Square Root of He (Height of Eye) in feet)
Determine Dip using meters 1.76 x (Square Root of He (Height of eye) in meters )
...fair winds...clear skies and following seasTheNauticalAlmanac.com
Explanation of The Nautical Almanac Daily Pages
1 Date based on GMT/UT
2 Time based on GMT/UT (this is just integral hour only)
3 Mer. pass- meridian passage of Aries at the Prime Meridian- Greenwich- 0. Time figure is GMT/UT.
GHA v correction and Declination d correction. The amount to correct v and d for is determined by theminutes and seconds of time of the planet observation and is found in the Increments and Correctionspages of The Nautical Almanac. The Increments and Corrections pages are also known as The YellowPages as that's the color of the paper in the USNO published Nautical Almanac.
4am- is the magnitude or brightness of the planet. A bright planet will have a minus sign beside the figure. Afainter planet will have no sign beside its magnitude figure.
5Stars- SHA, Sidereal Hour Angle, and Declination. 59 stars are listed. Typically, only 57 stars are used fornavigational purposes in both Northern and Southern Hemispheres.
6 Mer. pass- planet meridian passage time at the Prime Meridian- Greenwich- 0. Time figure is GMT/UT.
7SHA- planet SHA at the time of meridian passage at the Prime Meridian- Greenwich- 0. Planet SHA iscalculated by subtracting planet GHA from Aries GHA. Time figure is GMT/UT.
8 Horizontal parallax- for Venus and Mars.
9 Date based on GMT/UT
10 Time based on GMT/UT (this is just integral hour only)
11 SD- Semi-diameter of the Sun. One half of the angular width of the Sun as observed on earth.
12d- the amount the declination of the Sun changes per hour. If there's a minus sign beside the declination figure in the Dec column then the Sun is in the Southern hemisphere.
The Moon's GHA v correction. The amount to correct the Moon's GHA using v is determined by theminutes and seconds of time of the Moon's observation and is found in the Increments and Correctionspages of The Nautical Almanac. The Increments and Corrections pages are also known as The YellowPages as that's the color of the paper in the USNO published Nautical Almanac.
14 SD- Semi-diameter of the Moon. One half of the angular width of the Moon, as observed on earth.
The Moon's declination d correction. It's the amount of declination the Moon changes per hour. Howeverthe amount to correct the Moon's declination using d is determined by the minutes and seconds of time ofthe Moon's observation and is found in the Increments and Corrections pages of The Nautical Almanac. Thed correction is algebraically added.
An easy way to determine whether to add or subtract the d correction found in the Increments andCorrections pages is by examining the Moon's declination trend in The Nautical Almanac. If the declinationis increasing (regardless of its sign + or -) from the integral hour of the observation you made then add thed increment and increase the value of the declination. If the declination is decreasing (regardless of itssign + or -) from the integral hour of the observation you made then subtract the d increment anddecrease the value of the declination. Make sure to put the sign back on the corrected declination soyou know which hemisphere the Moon's in.
The Increments and Corrections pages are also known as The Yellow Pages as that's the color of the paperin the USNO published Nautical Almanac.
16HP- the angle between two lines, one from the center of the Moon to the center of the Earth, the otherfrom the center of the Moon to the edge of the Earth. This angle is about 56', but it changes slightly fromday to day as the distance to the Moon changes along its elliptical path around the Earth. Source- starpath.com
17 Sun- Eqn. of Time- Equation of Time is the difference between GMT/UT and LAN at Greenwich. Thefigures listed are for GMT/UT at 00h and 12h. If you look at Mer. Pass just to the right of the Eqn. of Timeyou'll find, approximately, when the Sun crosses The Prime Meridian (at Greenwich). The figures in the 12h
column indicate, approximately, how many minutes and seconds are subtracted, or added, to 12 todetermine when Local Apparent Noon is at The Prime Meridian. You can calculate, approximately, whenLAN is at your Longitude by adding, or subtracting the amount of time difference between you and
Greenwich and the Equation of Time.
Example- May 30, 2016. Mer. Pass is at UT 11:57. 12h is 02:25. This means subtract 2 minutes and 25seconds from UT 12 to calculate when Meridian Passage is at Greenwich. So at W 075 meridian passagewould occur at about- 12 hours + 5 hours MINUS 2 minutes and 25 seconds, or UT 16:57:35.
18Sun- Mer. Pass just to the right of the Eqn. of Time is the approximate GMT/UT when the Sun crosses ThePrime Meridian (at Greenwich) for that specific date.
Moon- Mer. Pass- is the approximate GMT/UT when the Moon crosses The Prime Meridian (at Greenwich)or The International Date Line for that specific date. Upper means the GMT/UT when the Moon crossesThe Prime Meridian (Greenwich) and Lower means the GMT/UT when the Moon crosses The InternationalDate Line (180).
20 Moon- Age- this is the number of days past a new Moon. Typically, there are 29 days in a lunar month.
Moon- %- the amount of the Moon's illumination. 100% would be a full moon. 49% would be about of the Moon is illuminated.
21*see note at
(morning) Twilight- Naut.- the approximate GMT/UT when mornin