Celestial Sight Reduction – Step by Step

Step 1: Calculate True Altitude and True Zenith Distance

This step corrects the sextant reading to account for observer height (dip), index error, semi-diameter of the Sun, atmospheric refraction, and parallax. The corrected angle is the true altitude. The true zenith distance is then calculated as:

trueZD = 90° - trueAlt

Step 2: Calculate Computed Zenith Distance

This uses the estimated position (DR latitude), the declination of the celestial body, and the Greenwich Hour Angle (GHA) to calculate the computed zenith distance (CZD) using spherical trigonometry and the haversine formula.

Meridian Distance is based on whether the latitude and declination are in the same hemisphere.

Step 3: Calculate Intercept and Azimuth

The intercept is the difference between the computed and observed zenith distances, representing the distance (in nautical miles) from the assumed position to the line of position (LOP):

intercept = (trueZD - calcZD) × 60

The azimuth is the bearing from the observer to the celestial body, determined using spherical trigonometry.