Celestial navigation explained - page 6

LOPs, cocked hat and common sense

Common sense is judgment without reflection, shared by an entire class, an entire nation, or the entire human race (Giambattista Vico (1688-1744), Italian philosopher)

The observer astronomic position O is at the intersection of the 2 LOPs.

With 3 sextant observations, you get 3 LOPs and if you are very good and very lucky at the same time, you could end up with LOPs intersecting like this:

perfect one point intersection

Most often, however, you will get LOPs intersecting like this:

triangle intersection

This triangle is known as a cocked hat cocked hatafter its resemblance to the common three-cornered hat of the times when these navigation techniques were developed.

Where is exactly the observer astronomic position O?

Well, the common sense is telling us that O is exactly in the middle of the triangle:

Unfortunately, the common sense is seriously misleading here...

If (and only if) the observations azimuths are spread over more than 180°, then the most probable position (MPP) is inside the cocked hat, but with a probability of only 25%!

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