NavList:

   

Reply

franl Reed wrote-

>George H, you've referred to Halley's observations as "lunars". I don't think
>that's necessarily a good idea. They're conjunction and occultation
>observations.

Well, they certainly weren't lunar-distances, which is why avoided that
term. But perhaps the contraction "lunars" is sufficiently ill-defined and
elastic to cover lunar close-conjunctions, and lunar occultations, and any
other method that might come to mind of determining time by observing the
position of the Moon in the sky. Anyway, that's how I have used it.

> These were widely used by astronomers starting around Halley's time, but
>I bet he was one of the very few to observe them at sea.

I know of no others who did. I suspect that astronomers in observatories
would use them for accurate determination of the motion of the Moon,
whereas Halley used them in reverse.

What I described was entirely in terms of close-conjunctions, not
occultations (where the star actually passes behind the Moon). Halley may
well have used occultations too, in his voyages. He gives only sparse
information, so it's hard to tell. A thorough analysis of his observations
may possibly show up some occultations.

We might guess how an occultation might be measured by a competent
astronomer (which Halley certainly was). He could time the moment when the
star disappeared (or reappeared) behind the Moon's dark edge. And if his
eyepiece had a calibrated graticule (or even if it didn't) he could
estimate how far off the Moon's centre the star's track was. And from that,
he could make a good guess at the angular difference between the star
crossing the Moon's edge and passing its centre-line. My guess is that a
skilled observer could guess that angle to a couple of arc-minutes; perhaps
even to one arc-minute.

>The process of reducing observations of occultations and conjunctions was
>considered much more complicated than lunars proper, and so it was never
>considered a real "navigational" method of finding longitude but
>definitely useful in
>the hands of a skilled astronomer.

I think the main difficulty was that the observer needed an intimate
knowledge of the stars down to quite small brightnesses: to identify the
right one and to have its updated ecliptic coordinates, Here, I think
Halley could make use of his special knowledge of the stars, that an
ordinary ship's navigator would not have. He didn't need almanac
predictions of occultations and conjunctions: no Almanac appeared until
decades later. Halley was canny enough to simply look at the sky and
observe the Moon aiming towards a star; as long as he could recognise it
and had a note of its position in the sky, that was enough.

>Also, the horns of the Moon can be
>decidedly variable since the mountains and craters at the poles can hide
>or expose
>large areas. It would be an interesting modern experiment to see how accurately
>one can deduce Greenwich time by watching faint stars line up with the horns of
>the Moon through a low-power telescope (such as might be held stable on a
>vessel at sea).

With a very thin crescent, visibility of the horns might well present
problems, as would also be presented by a very gibbous Moon, which wouldn't
show sharp "corners" at the top and bottom of the shadow-line. It would be
much easier near first and last quarters, no doubt, which show a
roughly-bisected Moon. My guess is that as long as the star was a
close-shave to the Moon, even a naked-eye observer, if experienced, might
be able to judge the star passing the Moon's centre-line to within a couple
of arc-minutes (an eighth of a semidiameter) without making any "detailed
calculations" or corrections, at all. I think the biggest error arose from
the skewness of the lin through the horns, in relation to the ecliptic
plane

>Personally, I doubt that this could be done better than about
>five minutes of time. With proper astronomical instruments and detailed
>calculations, of course, it can be very accurate.

I wouldn't quarrel with Frank's estimate of "5 minutes of time", except
that I think perhaps it may be over-generous to Hanney's technique. If
Halley could estimate his times to 5 minutes, that would give him
longitudes to 1 deg 15', or 75 miles, near the equator. In Halley's time,
longitude to that accuracy would have fulfilled a navigator's wildest
dreams! Of course, the big problem, then, was that the Moon predictions
weren't up to it.

>Speaking of those craters and mountains and their variable orientation, they
>make the limb of the Moon "bumpy". It seems to me that the relative
>unpredictability of the mountains on the Moon's limb would place the
>ultimate limit on
>lunars. From photos I've taken, I would estimate that the mountains and valleys
>along the limb make a zone about 0.05 minutes of arc thick. So the sextant's
>ability to measure angles down to 0.1 minutes is really very close to the
>ultimate limit of lunar distances you could ever measure. Can anyone put better
>numbers on this issue?

The very highest peaks on the Moon are a bit higher that we have on Earth,
about 6 miles. And at the distance of the Moon (mean, about 240,000 miles),
they subtend about 5 arc-seconds. So Frank's estimates are not far out (but
rather irrelevant to Halley). That irregular edge shows up as "Baily's
beads" on many total eclipses of the Sun, as they end with light from the
Sun's limb twinkling through the lunar valleys. I saw the 1999 total
eclipse from my boat in the middle of the English Channel, but Baily's
beads were not very noticeable then, to me (and for no more than a second).

George.

================================================================
contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
================================================================

   

Reply