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The variation in the apparent velocity of the moon relative to another
object is folded into the data that Jan has been examining, in that a
known time was used to calculate the theoretical distance, and that
distance was compared to the cleared, observed distance.  Jan reports
the method of calculating the theoretical distance was accurate to a
second of arc, so that whether the apparent velocity was 32 minutes of
arc per hour or 25 minutes of arc per hour is negligible compared to
the precision of measurement.  The precision is 5 seconds of arc at
best, and more likely 10-20 seconds.

Jan presented some data on the actual error in lunar observations.  He
and I were debating on list for a while about how to extrapolate those
data to an expected error for a set of lunar observations made by a
competent observer.  We now are discussing the matter off list.  I hope
if we reach agreement we'll post back to the list.  The basic question
is how accurately can Greenwich time be determined by lunar
observations at sea.

Fred

On Jan 6, 2004, at 2:35 PM, George Huxtable wrote:

> Bill Noyce wrote-
>
>> I've been following the discussion of statistical tests with interest
>> (and
>> not a lot of
>> understanding), but one statement of Jan Kalivoda's stood out:
>>
>>> For lunars, PE of 20" times 4.5 gives 90" = approximately 180
>>> seconds of
>>> time = approximately
>>> 45 minutes of longitude (the exact value depends on the actual
>>> velocity
>>> of the Moon in R.A.).
>>
>> In fact, the actual value depends on the velocity of the apparent
>> moon and
>> comparing
>> body in topocentric coordinates, not RA.  As George Huxtable has
>> pointed
>> out, the rate of
>> change of an observed lunar distance can be surprisingly slow, due
>> mostly
>> to refraction and
>> parallax.  My recollection is that it can be slow enough that a 90"
>> difference in observed
>> distance could correspond to over 300 seconds of time -- is that
>> right, George?
>>
>>        -- Bill
>
> ================================
>
> Response from George-
>
> That's why I think this matter of statistical analysis has been given
> undue
> weight recently on this list. Averaging distances, and averaging
> times, is
> all that's really needed to produce a single effective lunar-distance
> at a
> single effective time.
>

   

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