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

[Pamela Richards <spirlhelix@xxxxxxxxx>]

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
> knew about
>   > "transits". . . that is, I think you mean
> aspects
>   > between planets.
>   
> Sorry, I meant in the modern sense of planets
> crossing the sun's disk.
> Could pre-telescope astronomers observe a transit of
> Venus, say by
> looking at a pinhole-camera projection of the sun?
> (Presumably they
> would have been capable of computing the approximate
> time of the
> transit, and thus would know when to look.)
> 
>   > Say, a lunar eclipse is taking place at night.
> One person in an
>   > Eastern location sees the eclipse occur on the
> Western horizon.
>   > ... calculations can be taken to show the time
> of the eclipse in
>   > different locations, and the differences can be
> noted.
> 
> Yes, that is precisely what I meant.  Was this
> method actually used?
> How accurate could it be? 
> 
> All the best,
> 
> --stolfi
>
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=====
"I'd rather learn from one bird how to sing, than to teach ten thousand stars how not to dance."


		
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