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Bill asked, about the Moon data in the daily pages of the almanac-

>"I am not certain how the moon diagrams in the lower hand corner of the
>daily pages are correlated to time. My best guess is that the
>percentage-lighted figure is for 12:00 UT."
>
>I should have said "percentage lighted figures" instead of "moon diagrams."
>
>As the lighted portion of the moon changes from day to day, I *assume* as
>the Sun/Moon/Earth changes while to moon is visible, the percentage lighted
>will also change to some degree.  If the daily page states "52%" it might
>range from 50% to 54% during the viewing period.
>
>My corrected question is:  Is the percentage figure given on the daily page
>tied to a specific GMT/UC?  If so, what?
>
>I understand I have failed to take observer position into account as of yet.

================

My guess is that the percentage lighted figures are at the time of
Greenwich Noon, but for a mythical observer who is at the centre of the
Earth. Usually, the almanac is careful to define such matters, but I can
find no mention in the back pages.

Bill should be able to check this for himself, though. When the Moon is lit
just 50%, then it seems to me that the Moon-Sun lunar distance must be just
about 90 degrees. (Actually, something like 89.85 degrees, which is as near
as dammit.)

Bill has access to a number of sources of lunar distance. For example, from
Frank Reed's or Steven Wepster's web pages. All he has to do, then is to
check the timing of a 90deg lunar distance against an almanac page which
gives 50% illumination.

There's an interesting historical connection here. Once the distance of the
Moon had become known (by measuring its parallax), the next question was
"how far is the Sun, and what's the size of the Solar system?". Attempts
were made to measure the angle between Sun and Moon, when the Moon was just
50% illuminated. At that moment, the angle between Earth and Sun, measured
at the Moon, must have been 90 degrees, so by drawing similar triangles it
should have been possible to find the ratio between the distances of the
Sun and Moon. Unfortunately, the Sun is so much further, that the measured
angle was also 90 degrees, an near as anyone could tell. So the result was
that a lower limit could be set, that the Sun must be at least so many
times the distance of the Moon, but as for measuring its actual distance,
the only answer was "very large".

As for the observer's position on the Earth's surface, depending on where
he is, the direction of the Earth's viewpoint of the Moon can change by
about a degree either way (which is the parallax of the Moon). For an
observer in the tropics, then near moonrise and moonset this could shift
the apparent shadow edge by about 1 degree either way (measured round the
Moon's equator) with respect to the Moon's profile. I leave it to Bill to
estimate what effect that would have on the percentage illuminated.

George.

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01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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