Re: VMs: Identifying VMS stars, and the longitude problem

[Pamela Richards <spirlhelix@xxxxxxxxx>]

Hi, Jorge

I also forgot one thing!  A planet 15 minutes from a
perfect conjunction with the Sun is called "cazimi",
and is held to be fortified by its position "in the
heart of the Sun".  This is when the "transit" you are
describing might occur.

But as to how the passage of a "cazimi" might have
been visually observed, I'm afraid I still don't know!

Warmly,

Pam  

--- Pamela Richards <spirlhelix@xxxxxxxxx> wrote:

> Hi, Jorge
> 
> The problem of predicting lunar and solar eclipses
> was
> pretty well solved in antiquity, probably as far
> back
> as the Babylonians.  Ptolemy describes his method in
> the Almagest, but this is in my own words:  
> 
> A lunar eclipse occurs when the ecliptic (path of
> the
> Sun) intersects with one of the Nodes of the Moon
> (the
> path of the Moon).  The approach of the Sun to the
> North and South Nodes, or Head (Caput Draconis) and
> Tail of the Dragon, (Cauda Draconis) respectively,
> heralded the approach of an eclipse.
> 
> After you figure out which month that will be (not
> terribly difficult, as the Nodes move quite slowly
> and
> regularly, usually retrograde, with an approximately
> eighteen and a half year return), you look at the 
> Full Moon nearest the Node, which was not difficult
> to
> predict, either.  The date the Sun reaches a perfect
> opposition with the Moon (Full Moon)is the date of
> the
> Lunar eclipse.      
> 
> Lunar eclipses occur every twelve months and are
> easier to observe than Solar ones, the Earth casting
> a
> larger shadow on the Moon than does the Moon on the
> Sun.  So you have to be in a certain location to see
> them.  Solar eclipses also occur every twelve
> months,
> alternating each six months with eclipses of the
> Moon.
>  They are seen when the Moon is New.
> 
> As for the accuracy of timekeeping methods at night,
> I
> have heard that water clocks were quite accurate and
> were in use in ancient times.  And, if nothing else,
> observation of the stars using an astrolabe would
> also
> yield very accurate time-keeping results.  
> 
> I'm not well-informed about methods of observing the
> planets crossing the disc of the Sun.  I do know
> that
> there was a great reaction on the part of
> astrologers
> to the "combustion" of a planet or star; if it was
> within 17 degrees of the Sun, it was invisible until
> it "escaped the beams of the Sun", 17 degrees on the
> other side of the Sun.  We see this happen once
> monthly during the New Moon.  These times were noted
> as the "Heliacal rising and setting" of that star or
> planet.  The invisible star or planet was thought to
> be nearly as good as dead--to have no effect-- while
> conjunct the Sun, and to be resurrected when finally
> it became visible once more.
> 
> I hope this is of use.
> 
> Warmly,
> 
> Pam
> 
> --- Jorge Stolfi <stolfi@xxxxxxxxxxxxx> wrote:
> 
> > 
> >   > [Rene:] Yes, I tried this for longitude,
> oblique
> > ascension etc,
> >   > but a match could not be achieved, even just
> > looking at the nr. of
> >   > 9-pointed stars per VMS zodiac sign, making no
> > assumption about
> >   > the order in which they appear in each sign.
> (It
> > is not guaranteed
> >   > that there should be an order) Clearly, one
> > should allow also for
> >   > incidental mistakes in the figures, plus the
> > uncertainy which
> >   > tables, if any, are behind it.
> >   
> > Perhaps Fourier analysis can see through all that
> > noise? Say that you
> > make two lists of pairs (longitude,magnitude):
> > (VL[i],VM[i]) taken
> > from the VMS Zodiac diagrams, and (CL[i],CM[i])
> > taken from the star
> > catalogs, excluding perhaps stars above a certain
> > latitude. Then look
> > at the two lists as periodic impulse sequences,
> and
> > compute their
> > Fourier coefficients VF, CF of frequency 1. If the
> V
> > pairs are indeed
> > related to the C pairs, even with large random
> > shifts in longitude and
> > many errors in the magnitudes, comparison of the
> two
> > coeffs may
> > confirm the relationship and reveal the general
> > nature of the
> > measurements (risings, settings, or culminations).
> > 
> > Assuming that brighter stars are more likely to be
> > used in the VMS
> > than fainter ones, I would truncate both lists at
> > some minimum
> > magnitude, and encode the magnitudes in linear
> > rather than logarithmic
> > scale (i.e. 16,8,4,2,1 rather than 1,2,3,4,5). But
> > these are just
> > steps in the dark...
> > 
> >   > [Dan Gibson:] The Arabs used several ways to
> > determine latitude...
> >   
> > Yes, but latitude ("what parallel") is the easy
> one.
> > Just measure the
> > height of something celestial over the horizon, on
> a
> > north-south line;
> > put in a correction for the season of year; and
> you
> > will have a very
> > accurate and absolute value for the longitude. The
> > culmination of any
> > celestial body will do; it doesn't matter whether
> > the event happens at
> > different times in different places. This trick
> > surely was known 
> > from remote antiquity.
> > 
> > Elmar's question, and my guessed aswer, are about
> > longitude ("what
> > meridian"), which has been a mostly unsolved
> > navigation problem until
> > the 17th-18th century. For that you need to relate
> > local measurements
> > to those made at some reference longitude, *and
> you
> > need to know the
> > time interval between those measurements*, within
> a
> > fraction of one hour.
> > 
> > My guess is that Ptolemy and other ancient
> > astronomers could have
> > determined the relative longitude of cities by
> > comparing the local
> > times (or the moon's position over the horizon)
> when
> > a lunar eclipse
> > was reported to have reached its maximum.
> Obviously
> > this method is
> > useless for sea navigation (unless one has very
> > accurate predictions
> > of lunar eclipses, which presumably were not
> > available until
> > recently).
> > 
> > Note however that one can get very rough
> longitudes
> > by estimating city
> > distances from travel time. From distances in the
> > North-South
> > direction you get the conversion factor between
> > miles and degrees,
> > which you then use to convert East-West distances
> > into degrees.
> > 
> > (Solving the "longitude problem" for ships would
> > have meant fame and
> > fortune to the inventor. Galileo was among the
> many
> > frustrated
> > inventors-to-be. After discovering the four
> > satellites of Jupiter, he
> > noticed that their regular movements around the
> > planet could provide
> > the needed "clock". He tried to sell his method to
> > several kings of
> > Europe, but none was willing to pay for his
> secret.
> > The problem was
> > solved for good only with the development of
> > accurate ship clocks, a
> > century or so later.)
> > 
> >   > [Pam:] As for your questions about Ptolemy, he
> 
=== message truncated ===


=====
"I'd rather learn from one bird how to sing, than to teach ten thousand stars how not to dance."


		
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