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On Jan 9, 2004, at 8:49 AM, Noyce, Bill wrote:

> 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.

I agree with Bill in this analysis, and with George in his original
post.

Fred

   

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