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Frank Reed's prediction, and mine, for Michael Dorl's recent Venus lunar
show up an interesting discrepancy. We agree exactly on what the geocentric
lunar distance ought to be, 17d  00.7', but when we calculate the
near-limb-to-Venus angle, there's a difference. I get 16d 05.1'; Frank
calculates 16d 05.5'. So there's a discrepancy of 0.4' between us,
somewhere, in the process of allowing for semidiameter(s) and clearing the
lunar distance. Not an enormous divergence, and certainly much smaller than
the difference Michael Dorl observes with his measured distances. But
clearing the distance and allowing for semidiameter should be a rather
exact science, so I wonder why we disagree by that amount. It might be
enlightening to track it down.

Does Frank's prediction treat Venus as a point, or as a disc that's
illuminated from one side, I wonder? Does it use the planet's
centre-of-light or the edge of its disc? My prediction just treats Venus as
a point which touches the limb of the Moon..

As for refraction, does Frank use the Bennett formula, or a lookup table,
or what? Mine uses Bennett, though slightly tinkered-with.

I'll take a close look at the procedure I use to see if there's any
obvious, but small, error.

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

In a previous message on this topic, I wrote-

"Presumably, at that time of the morning, it was the Eastern side of the
Moon that was lit, and presumably Venus was slightly West of (and well
below) the Moon, so it was a lunar distance measured across the Moon to its
far limb. I ask Michael to confirm whether these assumptions were correct."

Indeed, it's true that at that time of the morning it was the Eastern side
of the Moon that was lit, but looking at the predicted positions, which I
quoted as-

Venus dec 09d 40.1' GHA 27d 59.9' distance 1.09726 AU, alt 27d 19.5' Az
102d 47.7
Moon  dec 19d 29.0' GHA 42d 22.7' distance 0.002647AU, alt 44d 11.8' Az
105d 30.7

it's clear that Venus was to the East, not West of the Moon, and Michael
has replied-
"I measured the distance between Venus and the nearest limb of the moon, the
illuminated limb."

So the lit limb of the Moon was indeed the near one, as Michael has made
clear. Sorry to get that wrong.

I gently chastised Michael, in the following terms-

"Michael's choice of that morning to measure Moon-Venus distance was a bad
one. It was taken shortly before the Moon was due to pass Venus, well to
the North of the planet. So the Moon's path was well clear of Venus, and
the line between Moon and Venus would be way out of line with the direction
of the Moon through the sky, which is nearly at right angles to a line
joining the Moon's cusps (horns). This misalignment reduces significantly
the rate of change of lunar distance, and so reduces the precision of lunar
distance as a measure of time."

He has replied-

"Is the path of the moon really that different from that of Venus?  I
thought the moon orbited pretty
much in the path of the planets; need to check that out too as I remember
someone using that
factoid as one argument that the moon is really a captured planet.  Venus
comes with 2 degrees
20 minutes of the moon at about 22:05 on 10/10/2004."

It's true that the planets and the Moon circulate near to the plane of the
ecliptic, but not that near. The Moon can be 5 degrees off from the
ecliptic, and Venus by 3.4 degrees, and these may be in opposite
directions. That's why the Moon seldom occults Venus as they pass. At the
moment of Michael's observation their ecliptic latitudes differed by about
4 degrees, with their ecliptic longitudes differing by about 15 degrees.
That is enough to seriously affect the angle of the line joining Moon and
Venus, in relation to the direction of the Moon through the sky, and
therefore to slow the changes in lunar distance, significantly.

At the moment of conjunction between them, when the Moon passes Venus, the
line joining them is approximately at right-angles to the direction of the
Moon's travel across the sky. Tthe lunar distance between them, which was
decreasing, stops changing and will later increase again. Near such times,
lunar distances to Venus become useless. That's why it is recommended that
lunar distances are measured to a body only when the lunar distance is at
least 30 or 40 degrees.

I do not say that Michael's observation is valueless for that reason, but
it's suffering from diminishing returns as time passes.

George.

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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.
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