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On Dec 13, 2004, at 12:00 PM, Ken Muldrew wrote:

>> Now suppose we measured both distances EXACTLY with our sextant
>> and want to deduce longitude (or chronometer corr., does not matter)
>> Averaging the two reduction results will give you nothing.
>> Both will give the same error in time/longitude.
>
> I don't see how that follows. One error puts you too far West of your
> true
> position, the other error puts you too far East. Averaging the two
> cancels
> the systematic error of the moon being in the wrong place.
>

I believe Alex is correct about this.  First, assume the errors are in
the RA not the declination, which is reasonable (and that the positions
of the stars are accurate).  Essentially, the almanac puts the moon too
far along in it's orbit or not along far enough.  If it's too far
along, it will be closer to the star in the east and farther from the
star in the west.  Thus the error in the eastern distance will be of
opposite sign from that of the western distance, but both distances
will give a time that is greater than the correct time.

I wanted to work out a numerical example before responding to Alex, but
haven't had the opportunity.

Fred

   

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