Dear Thomas,
You ask interesting questions and the
answers depend slightly on just how
precisely you want the model the way
the sun goes round the ecliptic.
QUESTION 1
... do [Gemini and Cancer] share
*exactly* the same region [on a
sundial] or not?
I think it is reasonable to DEFINE
the 12 regions of the Zodiac as being
bounded at 30-degree intervals of
solar *longitude*. So Aries extends
from 0 to 30 and so on.
On the ecliptic, these 12 regions are
distinct and there is no sharing.
When you look at the corresponding
intervals of solar *declination*
you do, as you say, get sharing.
In your example:
Sign Longitude Declination
range range
Gemini 60 to 90 20.15 to 23.44
Cancer 90 to 120 23.44 to 20.15
As you see, Gemini and Cancer share the
same range of declinations but for Gemini
the declination is increasing and for
Cancer is decreasing.
The answer to your question is YES.
So far, this theory has nothing to do with
the *shape* of the Earth's orbit but it does
assume that the orbit is a plane which is
isn't exactly.
[Solar latitude hovers around zero but it
isn't exactly zero. A REALLY pedantic
discussion about whether Gemini and Cancer
exactly overlap would take a book!]
You then ask about dates. That makes the
story very much more complicated but it
doesn't stop Gemini and Cancer sharing
the same region on a sundial.
QUESTION 2
Is the starting date May 20 of one in line
with the end-date July 22 of the other or not?
You go too fast. Who says the starting date
is May 20? It sometimes is and it sometimes
isn't. You have to worry about the leap-year
cycle and Pope Gregory XIII and his friends.
At the moment we are living close to the middle
of an almost 200-year run of pure Julian
calendar. There are no omitted leap-years
between 1904 and 2096 inclusive. This means
there is a steady drift in all the dates you
are interested in.
The starting *declination* of one IS in line
with the ending *declination* of the other but
when you worry about dates everything becomes
harder.
The only sensible answer to this second
question is NO. It is no because the dates
change from year to year. See the answer
to Question 4, but first...
QUESTION 3
The angles of the ecliptic longitude for
the zodiacs are equally distributed (each 30°),
[YES that's right] but what about the angles
in the earth's orbit around the sun (ellipse)?
I don't quite understand this. The ecliptic
longitude is the same as the angle of the Earth's
orbit round the sun (though you might want to
change the sign or add 180 degrees).
The answer is THEY ARE THE SAME.
QUESTION 4
And what about the dates?
They are horrible! I have already said there is
a steady drift in the dates but it is worse than
that because of the precession of the equinoxes.
The answer is THE DATES ARE A MESS and...
QUESTION 5
The lengths (in terms of time) of the zodiacs
are not equal, but are they constant each year?
The answer is UNFORTUNATELY NO. It is easy to
see that they are not constant by thinking about
this time of year. We have just entered the
sign of Capricorn and at this time of year the
Earth is closest to the sun.
That's good news because it gets winter over
quicker. Capricorn doesn't last long! Also,
this explains why the lengths are not constant.
Unfortunately, there will come a time when we
are furthest from the sun in winter. Capricorn
will take longer and we could find the northern
hemisphere covered in ice.
[ There will then be conferences about trying to
raise the levels of carbon dioxide :-) ]
QUESTION 6
Can anybody give me a better reference than
Wikipedia...
The best thing you can do is to ask your girlfriend
to buy you a copy of "Astronomical Algorithms" by
Jean Meeus as a Christmas present. You can then
write a proper program to model the Earth-Sun
system. It took me about 2000 lines of code before
I was happy with it but it is a very good way of
answering your questions!
Best wishes
Frank
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