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Celestial navigation

Fix from 2 or 3 altitudes – the intercept method with position lines

The heart of celestial navigation: from two or three altitudes NauticTools2 works out the position lines, where they cross, the offset from the DR position and the observed position – by the intercept method (Marcq St Hilaire), with a plot and the full working.

• Intercept method
• Position lines
• Cocked hat
• Running fix
• DR offset

Two ways to enter a sight

From the sextant reading

For each sight you enter date, time (UTC), body, DR position and the sextant altitude with index error and height of eye. NauticTools2 then does the whole chain that otherwise fills several work sheets: ephemeris (declination and local hour angle), sextant corrections to the observed altitude Ho, computed altitude Hc and azimuth, and finally the intercept Δh = Ho − Hc. Sun, moon, Venus, Mars and 83 stars are available.

Enter Ho, Hc and Az directly

For exercises in which observed altitude, computed altitude and azimuth are already given. You enter the DR position and Ho, Hc and Az for each sight, optionally with a run between the sights (course, speed over ground and Δt).

How it is calculated

• Position line: Δh nautical miles from the DR position along the azimuth (away from the body if Δh is negative); the position line runs at right angles to the azimuth.
• Two position lines: where they cross is the observed position.
• Three position lines: the three crossings form the cocked hat; the observed position is its centre.
• Running fix: the DR position is advanced by course and distance to the time of the later sight (mid-latitude sailing). The earlier position line moves with it, so its Δh and Az stay the same.
• DR offset: bearing and distance from the DR position at the last sight to the observed position.

Example with a run

Printing, saving, working

The printout contains each position line with its values and working, then the result, the plot and the fix. Inputs can be saved as a data set and loaded again – so instructors can also hand out whole collections of exercises as a file, which you read in under Settings › Import Data.

Related tools

• Sextant Altitude Corrections – from sextant altitude Hs to observed altitude Ho
• Computed Altitude and Azimuth – Hc and Az from DR position, declination and local hour angle
• Sun-Run-Noon Fix – morning position line plus noon latitude
• Ephemeris Calculation – declination and Greenwich hour angle