U.S. Navy and Royal Navy navigators are taught that the accuracy of astro navigation is ±1 minute of arc or 1 nautical mile and that where position lines are derived from astronomical observations, the resultant position is not known as a ‘fix’ but is known as an observed position and is marked on the chart as ‘Obs’.
A wise navigator will always be aware of the inherent errors in astro navigation and will never consider an observed position to be an absolute position. An error of ±1 nautical mile in an observed position in mid-ocean is of little consequence; however, when accurate navigation is necessary such as when approaching land, it can make the difference between life and death.
Errors in Astronomical Position Lines Errors may be introduced into an astronomical position line by a number of contributory errors which are briefly described below.
Errors in the observed altitude. Even when the sextant altitude has been corrected for index error, dip, refraction, semi-diameter and parallax, the resultant altitude reading may still be incorrect owing to a combination of other errors such as incorrect calculated values for dip and refraction.
A pronounced error in refraction is likely to occur when the altitude is below 15o. The dip being affected by refraction is the most likely cause of error; when atmospheric conditions are abnormal, the actual value of dip may differ from the tabulated value by up to 10′.
An error in the observed altitude will lead to an error in the observed zenith distance.
Errors in the calculated altitude. There are accumulative and unavoidable errors caused by the addition and rounding-off of quantities taken from the almanac. There are also unavoidable errors in the method by which the zenith distance and hence the altitude are calculated. These errors vary according to the method being used but generally, the inaccuracies arise because certain quantities are tabulated to the nearest minute and others are rounded-off.
Deck-watch error. If the deck-watch error is incorrect, the GMT and the local hour angle will be incorrect. An error in the LHA will lead to an error in the calculated altitude and this will cause the position line to be displaced.
Errors in the D.R. position. Errors in the course and distance laid down on the chart may result from a combination of inaccurate plotting, compass error. the effects of wind and tidal stream and incorrect calculation of speed made good over the ground.
An error in the DR position and resultant assumed position will lead to errors in the estimated longitude and hence the local hour angle and this in turn will lead to an error in the calculated altitude.
Errors In Observed Positions Derived From More Than One Position Line. Position lines obtained from three astronomical observations are not likely to pass through a common point. The reasons for this are firstly, the observations are not likely to be taken simultaneously since it is not possible to take sextant readings of three different celestial bodies at the same instant. The faster a vessel travels, the greater the movement of the observer between the three observations and the more significant this error becomes even when special methods of calculation such as ‘MOO’ are used.
Secondly, observed altitudes are very seldom correct and therefore, the resultant observed zenith distances will not be correct. For these reasons, the resultant position lines will be displaced and a ‘cocked hat’ will be formed.
Thirdly, because the position within the triangle of the cocked hat is arrived at by guess-work, it is unlikely to be correct.
For these reasons, observed positions derived from more than one position line cannot be regarded as absolute positions.
Links:
Relationship between Altitude and Zenith Distance
Planning Star and Planet observations
Astro Navigation Demystified 
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