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Frank Reed wrote in
[NavList 1757] Re: lunars with and without altitudes

After a bit of personal denigration-

| Well, first of all, you definitely have not invested enough effort
to
| understand it yet (evidenced by your comments with respect to the
Moon's  altitude
| --see below).

he went on to say-

| I have said AGAIN AND AGAIN that the altitude of the  Moon
| reduces the accuracy ONLY if the other object is more or less
directly above
| or below the Moon (same azimuth, in other words). If the  Moon and
Sun
| (that's the only available object in the summer Arctic) are at
about the same
| altitude, which they would be for that week or so out of each  month
when the Moon
| is visible in the high Arctic, then the accuracy of this  procedure
is NEARLY
| THE SAME as when the Moon is straight overhead in the  tropics. Why
is that
| so? Because the corresponding "cone of position" intersects  the
Earth's surface
| almost vertically when the Moon and Sun are low in the sky  and at
about the
| same altitude.

Well, I am doing my best to understand these arguments, but remain
puzzled.

Here's the problem-

The Moon is displaced from its geocentric position by two effects,
parallax and refraction, which both vary with altitude, and combine
together. Part of the clearing process, for a lunar, is to correct its
observed position for those effects.

I presume that in Frank's proposal, the converse process is being
used; that by measuring the displacement of the Moon from its computed
geocentric position, its altitude is being deduced, without benefit of
horizon. Have I got that right?

I can see how the correction for clearing can be calculated from the
altitude, but the reverse process is not nearly so simple. If you plot
the combined effect of parallax and refraction of the Moon, against
altitude, because refraction and parallax vary in opposing directions,
you end up with a double-valued result. If for simplicity you take the
horizontal parallax for the Moon to be nominally 60', then you end up
with a maximum displacement of about 54.5' at an altitude of 15
degrees. Either side of that, a certain measured displacement results
in two values for altitude. If the displacement was 52', for example,
the resulting altitude could be either 22 degrees or 8degrees. For a
wide range of
altitudes near 15 degrees, the displacement hardly changes from 54.5',
so a displacement of that amount provides very little information
about what the altitude is. For angles below 30 degrees, the slope of
the curve of displacement versus altitude is considerably reduced from
its maximum value at high altitudes, simply because of the (cos alt)
variation of parallax. That must reduce considerably the precision of
any deduction of Moon altitude from the Moon's displacement, at low
altitudes, compared with its high-altitude value.

In an earlier posting, I understood that Frank had recognised that as
a problem, when he wrote, in NavList 1379, " It has large changes in
its altitude correction
with altitude (except from about 7 to 15 degrees)."

But now, in the passage copied above, he appears to say that there are
circumstances in which the precision is maintained, even at low Moon
altitudes. I ask him to tell us, then, where any lower Moon altitude
limit lies, if there is one. Does he claim that the accuracy holds
even at Moon altitudes of 15 degrees? If so, would he please explain
how that happens?

I am still hoping to get from Frank, some time, a statement of a
procedure to adopt (computer program or simply a set of rules to
follow), and it would be interesting to see how such a procedure
handles the double-valued curve of displacement with altitude.

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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