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Frank Reed wrote-

| If the lunar distance is short, you have to be more careful in the
altitude.
| At a distance of ten degrees, an error of one minute in either
altitude will
| yield a tenth of a minute error in the clearing process.

That didn't fit my expectations, so I cooked up some trial values. I
presumed an observed star altitude, above the true horizontal, of 70
degrees, an observed Moon altitude (of its centre) of 80 degrees, and
an observed lunar distance (between centres) of 10 degrees.

With such high altitudes, I ignored refraction altogether, so the only
correction to make was for Moon parallax, for which I assumed a value
of horizontal parallax to be 1 degree.

Those figures correspond to a deduced azimuth difference, between Moon
and star, of zero degrees, which seemed entirely reasonable.
Correcting the observed Moon altitude for parallax increased it to
80.173648 deg., and then the corrected lunar distance became 10.173648
degrees.

But say that there was an eror in the Moon altitude determination,
which resulted in a smaller altitude, by just 1 arc-minute. Everything
is as before, except that the observed Moon altitude is now 79.983333
degrees, and its corrected value is 80.157268 degrees. What would be
the resulting change in corrected lunar distance?

To fit those observations, the azimuth difference between Moon and
star must now become 2.36 degrees. With that value of azimuth
difference, and our new corrected Moon altitude of 80.157268, and star
altitude 70, and observed lunar distance 10 degrees, just as before, I
now get a value for corrected lunar distance of 10.173371 degrees,
just .0165 arc minutes less than before.

That is, an error of one minute in Moon altitude results in a 60th of
a minute error in the clearing process, not a tenth of a minute as
Frank quoted. One of us must be wrong. Considering my recent
lamentable record in trig errors, it could be me.

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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