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Celestial Navigation - formulas and software

the science of navigating by the celestial bodies (stars, Sun, planets and Moon) - software and formulas to calculate the estimated altitude and azimuth of a star

Nautical Astronomy - Planetariun in Valencia - Hemisferic

....after having collected all the data : estimated latitude and longitude, declination / local hour angle of the observed celestial bodies (stars, sun, moon and planets ) and sextant reading (altitude) ... we must calculate at least four data. We’ll use these to plot lines of position (LOP) on a nautical chart, plotting work sheet, or a simple graph paper to determine the position of the ship.

The data we need are : true altitude, LHA/declination, computed (estimated) altitude and azimuth

We can use this simple excel file to verify (or avoid) the manual calculations !

The file consists of four worksheet.

To prevent damages in cells containing formulae the worksheets are protected and cells are locked, we may use the unlocked cells only (green background).

When we open Excel, Excel automatically selects “Corrections to a sextant obser. “. for us. (The name of the worksheet appears on its sheet tab at the bottom of our document window.)


On January 17th 2016 a Deck Officer takes and records the following sight :

  • Sun ( lower limb ) - sextant altitude 29° 53,5’ at 12h 23m 45s U.T.
  • DR position : Latitude 38°34,2’ North – Longitude 005°32,7’ East
  • Height of eye above the sea level : 2,5 meters
  • Sextant is affected by errors. Corrections: +0,5’ instrument error (eccentricity) and -1,4’ index error

First of all we convert the sextant altitude to observed altitude using “Corrections to a sextant obser. “ worksheet :

1 celestial navigation sun 2 celestial navigation sun lower limb

From the Nautical Almanac – January 17th  2016 :

at 12.00  U.T. :

  •          GHA    357° 31,2               v correction : -0,2’
  •          Declination 20° 47,5’ S      d correction : 0,5’

3 celestial navigation nautical almanac

We calculate LHA and declination using “LHA – declination “ worksheet :

celestial navigation local hour angle astronavigation declination

We solve the formulae of celestial navigation calculating computed (estimated) Altitude and Azimuth using “Altitude - Azimuth“ worksheet :

6 celestia navigation calculations

Difference of altitude = true altitude – computed altitude:  30° 04,5’ – 30° 02,6’ = + 1,9’

Now we can draw the graph: 

astronavigatio LOP

The last worksheet is named “ meridian altitude “. It allows to obtain the latitude after having insertered the meridian altitude and declination.


We have a true altitude at meridian passage of 58° 43,6’ and a declination of 23° 04,9’; N the latitude is 54° 23,3’ North.

8 astronavigation meridian passage 





celestial navigation - nautical astronomy formulas
formula  altitude sine altitude =  (sine latitude * sine declination) + (cos latitude * cos decl * cos polar angle) 
 formula azimuth  cotg azimuth =  ( cotg ( 90-decllination) * cos latitude * cosec polar angle ) - (sine latitude * cotg polar angle )


Celestial Navigation - exercises book


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