NavList:

This relates to Jim Van Zandt's recent posting under threadname "The
*&^%$#@ Moon".

I'm overwhelmed, and rather impressed, by Jim Van Zandt's mathematical
exercise, for testing which limb of the Moon, upper or lower, is the
sharp one, to observe when it's nearly full. It's far beyond me to
confirm or refute it. However, I can propose a different test,
simpler, in my view, and rather more intuitive. Whether they
correspond to the same thing, Jim may be able to deduce. If not, one
(perhaps even both) must be wrong.

This is how I see it.

At full Moon, the Sun and Moon are at almost exactly opposite points
in the sky. Their GHA will differ by 180 deg, and the Moon's
declination will be the same as that of the Sun but with opposite
sign. At least, that would be the case if the Moon and Sun followed
identical paths through the sky, around the ecliptic, but they don't,
not quite. The Moon can diverge from that path by up to 5 degrees,
because of the tilt of its orbit to the ecliptic. However, at full
Moon, a tilt of the sunlight falling on its surface by 5 degrees will
pull in the shadow-edge from part of the limb by no more that .06', so
from now on I will neglect that tilt, and presume that the Moon
follows the same path as the Sun.

Before full Moon, it's always the Western edge of the Moon that is
lit, and crisp. The Eastern edge is shadowed and fuzzy, and would give
the wrong answer if used for an observation. This will be true, no
matter where on Earth the Moon is viewed from. And after full Moon, of
course, the contrary applies; it's the Eastern edge that must be used.
Within a few (say 4) hours of full Moon, it doesn't matter which, the
Moon's edge is lit all round.

The situation we are considering is an observation made away from the
moment of full Moon, so it becomes important to choose the right limb;
but not so far from full that it's immediately obvious which limb is
the sharp one.

Whatever the phase of the Moon, if we observe it near the moment of
meridian passage, its shadow-pattern will always be symmetrical about
a horizontal line through its centre. In that case, there's always a
sharp line round 180 deg of its edge, from its upper limb to its lower
limb, on one side or the other, with a fuzzy edge on the other side.
In that case, it doesn't matter which limb is used, because there will
always be a crisp edge or cusp extending to both upper and lower
limbs.

What about observations before meridian passage, and after? The
following rule will apply, as I see it.

Before full Moon-

Before meridian passage, use upper limb, and vice versa.

After full Moon-

Before meridian passage, use lower limb, and vice versa.

Near full Moon, meridian passage will always occur near local
midnight.

I put this forward with some diffidence, being by no means certain
that I have everything right. What do others think?

George.

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



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