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On 20 June, in [5530] I analysed Jeremy's recent lunar distance, in some
detail, explaining how it could be calculated out, in the general case, and
arriving at numerical answers.

In [5588], Frank Reed has considered the matter as a special case, with
opposite azimuths, and shown how several approximations and simplifications
are then valid in those special circumstances, but makes no reference to
that previous work.

I can confirm  that the agreement with my own analysis is indeed as good as
he claims, within the errors that would be expected from taking almanac
tabulations which are given only to the nearest tenth of an arc-minute.

Indeed, that observation was rather a "special", in two respects, not just
one. The azimuths were opposite, AND also the lunar distance was very nearly
90 degrees.(well, over 85, anyway...)

Thare are several points that arise from Frank's posting.

1. A similar simplification occurs when the Moon and other-body azimuths are
the same, just as when they are opposite.

2. How can an observer be sure that the geometry is such as allow him to
make those simple approximations? How much leeway does he have? Can Frank
provide simple rules-of-thumb? If the effort involved in answering that
question is comparable with the effort involved in doing the full
calculation, one might as well choose the latter.

3. If a learner is taught that "this is how lunars are worked out", from
such a simplified and unusual example, then he will find himself at a loss
when in reality he gets confronted by one that calls for spherical trig, not
just adding and subtracting.

4. Frank's final step was to compare the cleared distance with one computed
from a known GMT. But that hides the real purpose of lunars, which were
taken in order to discover unknown GMT; not as for testing prowess in using
a sextant. The final step should be in establishing the GMT; and this can
then raise interesting questions of iteration if altitudes are computed
rather than measured, because an initial estimate of GMT will be asked for.

5. I find it hard to reconcile the effect of the Moon parallax / refraction
on this observation, stated as being 27.2', with Frank's statement, in
[5574]-
"PS: And a reminder: don't fuss over the exact interpolated altitude of the
Moon. When the lunar distance is close to 90 degrees, the altitude of the
Moon can be way off and it will not affect the calculation significantly."
(a point that Frank has made in previous postings).

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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