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There was a most-informative posting on 9 April by Herbert Prinz, on the
various factors that influence the real and apparent motion of the Moon
with respect to other celestial bodies.

Below, I will quote from a paper which was kindly brought to my attention
by list member Steven Wepster, on that same topic. It dates from 1875, and
is part of a contribution by Carl Bremiker, to the journal "Zeitschrift fur
Vermessungswesen" (Journal of surveying?) of 1875, pages 59 to 79.

From 1850, Bremiker had been editor of the German Nautisches Jahrbuch
("Nautical Annual"), so he knew what he was talking about.

I am ashamed to admit to having no German: however, my niece Lucy Mellersh
is fluent in German, but not at all technical. Between us we have put this
informal translation together.

What is especially interesting to me is that Bremiker refers to the serious
effect of parallax on the apparent motion of the Moon with respect to other
bodies, the effect that I have dubbed "parallactic retardation". Bremiker
says that it hadn't, to his knowledge, appeared before in the literature,
and I'm not aware of any English-language mention before or since.

I like Bremiker's "what-if" speculation about the problems that would face
a lunar navigator on the surface of Jupiter, which seems to me to be
advanced thinking for 1875.

Here goes-

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

Concerning the precision with which the longitude can be calculated using
lunar distance, note that at sea those observations made with the best
instruments have a mean error of 10 seconds. In addition to this are the
errors in the tabulated lunar position of about 4 to 6", which are
transferred onto the predicted distance so that when both errors combine,
the total error  is 1/4 of a minute of arc. Because the moon generally
moves half a degree in an hour, an error of half a minute of time or 7.5
minutes of arc in the longitude would follow, or in low latitudes 7.5
miles.

On land, where observations can be more carefully made and the calculations
afterwards can be made with improved moon positions, the error is less.

The instrument error can be substantially reduced when several distances on
the East and West sides of the moon can be measured one after another.

On the other hand the error increases at the same rate as the change in
distance per hour gets smaller, as with the stars Aquila and Fomalhaut
which are far from the lunar path, and with the Sun and also with Venus
which can sometimes have considerable motion in the same direction as the
Moon. It can happen that the relative motion of the moon is only 20 minutes
in an hour. When in good conditions the errors in the longitude are 30
times the error in the distance, this can increase here to 45 times.

Other matters must be considered which depend on the the motion at the
observation point.  These can considerably increase the errors in finding
the longitude. As far as I know, these errors haven't been mentioned in the
relevant literature.  A point on the equator on the Earth moves 900
nautical miles in an hour, and the moon in its path has a mean speed of
2000 nautical miles per hour. Therefore, from a point on the equator the
Moon, when at the meridian, loses 9/20 of the motion with respect to the
stars that it would have if viewed from the centre of the Earth. In these
conditions, the error in the longitude can be 60 or 90 times the error in
the lunar distance. These errors are slightly less in higher latitudes, but
are always worst near to the culmination of the Moon.

Luckily our Moon doesn't go backwards, otherwise all distance measurements
would stop near to the meridians. For an observer on Jupiter, despite the 4
moons, the situation is comparatively worse. A point on the equator there
has an hourly movement of 24,440 nautical miles, compared to which the
movement in the lunar path in the 1st to 4th satellite are 34,536, 27,372,
21,672, and 16,344 nautical miles per hour. The first two could still be
used for measuring distance, the two more distant couldn't be used near the
meridians because they go backwards.

Bremiker.

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

The translation above is only the final part of what may well be a very
interesting paper: the rest remains untranslated so I have no way of
knowing.

George Huxtable.


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