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Sun's Information and Sight Reduction

Below is a form using JavaScript that provides the Sun's information and sight reduction - for the years between 1979 and 2020:

[The error for GHA and Declination of Sun calculated by this script in most of the cases should not exceed 0.3' which is considered as very small when compared with the accuracy of human observation by marine sextant.]

I wish to thank Oscar W. Underwood III, a retired American engineer, for information he provided that enable me to extend my Sight Reduction program from the year 2000 through 2020.

Dead Reckoning Position

Latitude : degrees minutes
Longitude : degrees minutes

Date and Time - GMT

Date : The  day of the  month of the year 
the Julian day (Day of Year) equivalence is 
Time :  hr  min  sec

Sun's Information 

Declination : degrees  minutes
Greenwich Hour Angle : degree  minutes 
Calculated Azimuth :
Calculated Altitude : degrees  minutes

The Sun as seen from 

with Latitude  (degrees North) Longitude  (degrees East)
Calculated Azimuth :
Calculated Altitude : degrees  minutes

The Intercept (Marcq Saint-Hilaire) Method

The article in the general sight reduction script briefly describes the history of navigation by celestial observations. The practice of position fixing by celestial bodies has been used by navigators in ocean passage until accurate and low cost electronic navigation aids, like transit satellite and GPS, are available.

Sun sights during the daylight hours and stars sights during twilight are obtained to determine the ship's position. The Marcq Saint-Hilaire or intercept method is the most popular way to reduce a sight for a line of position.

The intercept method uses the difference between the observed true altitude (obtained by correcting the sextant altitude for index error, reflection, dip, etc) and the calculated altitude (obtained by sight reduction tables or calculations) of the ship's DR position to give an intercept for plotting the line of position on chart or plotting sheets.

The Intercept (Marcq Saint-Hilaire) MethodThe figure on the right shows the principle of the intercept method. If we take the celestial body as the centre of a circle, the position circle formed by using the zenith distance (90 degrees - altitude) of the calculated altitude as radius will pass through the DR position and that for the observed true altitude should pass through the observer's position. Given that the celestial bodies are so far away from the earth, we can safely assume that the arc of these position circles passing the observer's vicinity are in straight lines. These position lines are running prependicular to the Azimuth of the celestial body concerned.

The result of a sight provides us with the following information :-

  • the calculated altitude;
  • the observed true altitude; and
  • the azimuth of the celestial body.
The intercept as measured from the DR position is therefore the difference between the true and calculated altitudes. It should be plotted towards the body's azimuth if the true altitude is greater than the calculated altitude.

To make the above simple

The practice of reducing a sight to a line of position is summerized as below :-

  • Obtain the altitude of a celestial body by sextant and note the GMT
  • Correct the sextant altitude for index error, reflection, dip, etc to produce the true altitude
  • Using the GMT and DR positions to calculate the calculated altitude and azimuth of the body (by the above form or nautical tables and almanacs)
  • The intercept is equal to (true altitude - calculated altitude) and named as "towards" if the result is positive or "away" if the result is negative
  • Plot the DR position on the chart or plotting sheet
  • Plot a line in the direction of the azimuth passing through the DR position
  • Measure the intercept distance in minutes of Latitude from the DR position and cut on the azimuth line above in the azimuth direction if "towards"
  • Draw a line perpendicular to the azimuth line through the cutting point on the azimuth line which is your line of position
  • A fix is obtained if you run more than one line of position having different azimuths to the same time base


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