NavList:

Andres, you wrote:
" one is sailing with known course and speed and to obtain a fix uses two altitudes with a sextant and a lunar distance at different times ant the chronometer or on-board watch has an error. "

Thanks. There's another way to do this. It may or may not be easier, but I think it illuminates what's going on. The lunar distance yield a "lunar distance line of position" for a given GMT. If GMT is uncertain, then calculate the LOP twice, once for estimated GMT0 and again for GMT0+1 minute. Then advance those LOPs to synchronize them to the later altitude fix based on the course and speed made good. If the lunar distance LOP for GMT0 falls right on the two-body fix, then we know that GMT0 was the correct time within some margin of error. If the two-body fix falls exactly halfway between the two advanced lunar distance LOPs, then the correct time must be GMT0+30 seconds. Other cases are easy to handle. To assess the margin of error, it would also be simple to calculate the LD LOP at GMT0 with the observed distance changed by 0.1'. Typically this will shift the LOP by six nautical miles or more so if the two-body fix is within some miles of the advanced LD LOP, that's about as good as it gets.

-FER

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