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George,

You wrote:

>>That seems a rather unnecessary step. All they needed was a star
>>catalogue, with angular measures equivalent to SHA or Right Ascension --
>>the sort of thing that the astronomers back home should have been
>>working on anyway.
>>
>
> I think Trevor is wrong here. The longitude difference can be deduced from
> the difference in time (measured by star positions) of a common observed
> event (Moon eclipse). Without accurate predictions of the Moon's position,
> it was, presumably, impossible to predict the exact moment of the lunar
> eclipse. All that could be done was to go back to Beijing, after the event,
> and find out at what time (measured by those same stars) it had occurred
> there (hoping it had been a clear night). It wasn't the star-timings that
> were unpredictable, it was the Moon event.


I think you misunderstand me. My suggestion is that the Chinese mariners
could return from their voyaging to report that they had reached an
Arabic trading port, where the local astronomers recorded that, at the
time of the last lunar eclipse, Sirius was on the meridian. The
astronomers in Beijing could then check their records and note that, at
the same point in the same eclipse, Denebola was on their meridian.
Consulting the star catalogue, which I am suggesting they had likely
prepared and were working on refining, they would see a difference in
the time of meridian passage of those two stars of 5 hours 4 minutes,
which would mean a difference in longitude of the two observatories of
76 degrees. Hence they would place Zanzibar within a degree of its true
position, relative to the Celestial Empire.

What I consider to be rather unnecessary is the determination of the 5
hour 4 minute difference in the time of meridian passage _after_ the
explorers returned with their report. I suspect that it was known and
recorded long before for quite other purposes. (Though later in the same
e-mail, I qualified that suggestion by noting that the post-hoc
determination of the time difference might be needed if either
observatory selected a minor star as being on the meridian, in an
attempt to get more precision. I would not expect that pre-modern star
catalogues listed more than, perhaps, the 1st and 2nd magnitude stars.)


You continued:

>>>There is no way to time a lunar eclipse with "absolute precision", as
>>>anyone who has watched one will know. The whole event is fuzzy and
>>>indefinite. [snip] the moment of the Moon entering completely into full
>>>shadow is indeterminate
>>>
>>
>>I have watched a number of lunar eclipses and what still surprises me is
>>that the umbra has a rather sharp edge -- not sufficient to satisfy
>>those who like to fuss over the precise moment that one of the moons of
>>Jupiter passes into the shadow of its parent but very much sharper than
>>if the penumbra shaded steadily into the umbra. Why this should be so, I
>>have never figured out. But it is.
>>
>
> Well, yes and no.

I think that about summed it up: Not absolute precision and not to compare 
with observations of the Jovian moons (once telescopes became available) but 
still something more than a slow gradation from full sunlight to the umbra.

> I still doubt that either Trevor or I could do much better in timing
> the first or last moments of full-eclipse, than the "5 or 10 minutes" that
> I suggested.

Maybe. Without trying it, I'd not like to guess at a precision of timing.

But, before the telescope, was the limit really the extent of "fuzziness" at 
the edge of the umbra? In my own case, without glasses I would have trouble 
doing better than seeing that the Moon is there. However, I suspect that good 
eyesight was a requirement of the job description for astronomers in the era 
before Gallileo, so perhaps they were limited by the definition of the edge 
of the umbra, not by their own visual acuity.


And finally:

>>>Menzies tells us that the key event that had to be timed (with a star), was
>>>what he calls U3, at the first signs of emergence from full umbra. This
>>>seems surprising, as U2, the entry into full umbra, would have been equally
>>>useful, and the combination of the two more useful still.
>>>
>>
>>I would suggest that the observer has no warning that U2 is coming until
>>it has arrived. It would be some little while, even a few minutes, after
>>U2 before anyone would know that it had been passed. U3, in contrast,
>>can be anticipated as the patch of umbra visible on the Moon's disc
>>becomes smaller and smaller.
>>
>
> I really can't understand what Trevor is saying here. Menzies defined U2
> and U3 as follows-
>
>
>>U2 - second
>>contact, when the moon has just fully entered the umbra and is totally
>>covered; U3 - third contact, when the moon first starts to emerge;
>>
>
> So U2 happens at the end of a period when the observer has watched the
> umbra spreading across the Moon until the final moment when the Moon's disc
> becomes completely dark. How can Trevor possibly claim that the observer
> "has no warning"?
>
> It's U3 of which the observer "has no warning". From the Moon being
> completely dark, the first sliver of light is seen, at one edge.
>
> Either Trevor's picture of this is wrong, or mine is. Which?

Mine, I'm afraid.

I didn't read Kieran's message carefully enough, so missed the point that 
George noted, and then had no special reason to re-check Kieran's message 
when replying to George's.


I supposed that U1 was when the moon first entered the Earth's shadow
(i.e. the penumbra), rather than the umbra itself, U2 the point when it
first enters the full shadow (i.e. the umbra), rather than the point of
fully entering the umbra, and so on for U3 and U4.

I agree that the definitions as written fit with George's interpretation
and that U2 would then make more sense than U3 -- Frank's reasons for
preferring U3 notwithstanding.

But, thus defined, there must be many partial lunar eclipses which never
achieve U2 or U3, the centre of the umbra passing sufficiently north or
south of the Moon that one of its poles remains in the penumbra
throughout. Hence, I would suggest that the best of the four is
Kieran's/George's U4, which I was taking to be U3.


Trevor Kenchington


--
Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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