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George Huxtable writes:

> But from that, I have, in the past, presumed that when the rate of
> change of the Moon's apparent motion is (for example) halved by the
> effects of parallax, then the accuracy of any GMT deduced from a lunar
> distance measurement will be halved also. However, that conclusion
> doesn't follow: I was wrong.

I'm not convinced; I think you were right.
Imagine you and I take a lunar sight at the same instant.  You
measure the apparent distance exactly correctly; I have an error
of 1'.  If parallactic retardation is severe, our cleared distances
will differ by nearly 2', leading to a difference in GMT of nearly
4 minutes of time.  Put another way, my incorrect measurement gives
the apparent distance that should actually be observed 4 minutes
later than when we made our observations, since the apparent moon
is moving about 1' every 4 minutes.

Therefore, a 1' error in measurement when parallactic retardation
is severe has led to a 4 minute error in time, or a 60' error in
longitude.  Contrast this with the situation where parallactic
retardation is negligible, and we expect a 1' error in measurement
to lead to a 2 minute error in time, or 30 minute error in longitude.

   

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