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Dear Pierre,
Here is my solution:

A. Answer: Lat 47d50.0 N, Long 87ds55.0 W,
(that is 15' East of the wrong position).

Explanation. Let us call the wrong position X and let T
be the wrong GMT used in the reduction.
The question is: find a (correct) position Y where
the sky at the time GMT=T-1min (correct time) looked exactly like
the sky at X looks at time T.
This position Y is evidently 1min=15' East
of X.
So the navigator has to subtract 15' from his Western Longitude.

Another, "more practical" explanation. The only place in
the sight reduction where GMT enters essentially is the
GHA Aries. This increases at the rate of 15' per minute.
So if you use the correct time (which is 1 minute LESS than
the wrong time), to keep the resulting altitudes unchanged
you have to DECREASE your Western Long by the same amount,
because Western Long enters in your computation with the
opposite sign to GHA Aries).

B. Answer:  Lat 47d50.0 N, Long 89d09'

Explanation. The only place the date
enters in the sight reduction process is in the reading of the
almanac entry for GHA Aries. By examining the almanac we see that
this increases by 59' per day. (This happend because
of the yearly Earth rotation around the Sun).
If D was the erroneous date of the observation,
and the correct date is D-1, then the new (correct) GHA Aries
is obtained from the wrong one by adding 59'.
To keep the altitudes unchanged you have to increase your
longitude by these 59' (Western Longitude enters to the site
reduction with the opposite sign to GHA Aries).

This is a solution "for practical purposes",
see the discussion in Georges message
Wed Sep 29 2004 - 16:04:47 EDT.
I mean, that corrections that are less than 0.1' are neglected
in my arguments.

On Sun, 3 Oct 2004, Pierre Boucher wrote:

> Hi everybody,
>
> Your opinion and/or solution to a nav-question
> (from an old examination).
>
> Here it is:
>
> In ploting sights taken on 3 stars, you get an
 erronous PR at L 47? 50.0'N,
> Lo 088? 10.0'W.  What will be the exact PR if after revising all
> calculation you detect the following errors and correct them:
>
> A.      The chronometer was 30 seconds slow instead of
 30 seconds fast .
>
> -------------------------------------------------------
>
> B.      The Greenwich Date was the one day later.
>
>
> Pierre Boucher
>

   

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