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Brad Morris wrote-

I have been playing with the Occultation reduction as given by Bowditch, 
1849.  It is spectacularly cumbersome.  For example, he indicates that we 
should get the latitude and longitude of the moon from the Nautical Almanac. 
These terms are not explained elsewhere in the Navigator nor provided in the 
current Nautical Almanac, so what is the student to do?  Woodhouse, "A 
Treatise on Astronomy", 1823, explains that these are the heliocentric 
coordinates of the moon.  My conversion of the Moon's GHA from the NA to the 
heliocentric latitude and longitude takes 40 rows in an excel spreadsheet 
(step by step, I am sure this can be minimized).  I cannot prove the 
conversion yet, but that's just one example!  I have parts of the 
occultation reduction, but as of right now, cannot complete it.  This 
remains a fascination!

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

I think Brad may be barking up the wrong tree here. I've no knowledge of 
Woodhouse, and haven't looked up an old Bowditch. However, I presume that 
the latitude and longitude of the Moon, that Bowditch refers to, will not be 
heliocentric, but the geocentric quantities, as we see the Moon from Earth 
(from its centre). They will be the ecliptic (or celestial) latitude and 
longitude, measured not from the Equator, as terrestrial lat and long are, 
but from the plane of the Ecliptic, with longitude starting from Aries. So 
they are similar to declination and Right Ascension (RA), except that they 
are measured with respect to the tilted plane, that of the Earth's orbit 
round the Sun. Early almanacs would tabulate Moon predictions for both sets 
of coordinates.

If you have dec and RA of a body, and know the tilt  at that date (which 
varies very slightly year on year, currently 23.438�) it's straightforward 
to calculate the ecliptic latitude, from-
sin lat = sin dec cos tilt - cos dec sin tilt sin RA
and the ecliptic longitude, from -
tan long = ( sin RA cos tilt + tan dec sin tilt ) / cos RA

These came from Meeus, Astronomical Algorithms (which everyone who tills 
such ground should own) equations 13.2 and 13.1.

Ecliptic quantities were used for solar system predictions, one reason being 
that for such bodies the latitude doesn't depart from zero by more than a 
few degrees.

It's a pity, and a source of much historical confusion in, that the same 
basic names of latitude and longitude were adopted for two such different 
pairs of quanties, the ecliptic and the geographical.
================

About Chauvenet''s view of occultations, Brad writes-
"If Chauvenet states that a navigator CAN see the occultation at sea, then 
we should not doubt him."

Nobody doubts him. It's just a case of how frequent they are.

You can watch a bright star occult with the naked eye, and time its 
disappearance very precisely, even at sea. But bright-star occultations are 
rare, and don't come to order. You can watch a dimmer star with the aid of a 
telescope, but the motion of a ship limits the power of a telescope, because 
you need to keep the star in continuous view to see it vanish. Shackleton 
could time four occultations in a day, because, in ice, there was no motion 
to limit the power of his telescope, which could be on a stand. So his 
telescope allowed him to time stars down to 5th magnitude, of which there 
are plenty occulting, and for which he must have had good documentation. You 
need to identify them in advance, and know their precise position in the 
sky. Easy today, but not so easy in history.

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

Brad concludes- "Some of the Woodhouse's methods are land navigation only, 
but I do not think that is prohibited on the list."

Far from it; land navigation has provided some fruitful discussions.

I must take a look at Woodhouse some time. Chauvenet produces a (different) 
long list of longitude methods, one of those being the Electric Telegraph, 
in its early days then. But many of those are only useful on land.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 


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