The above applet is intended to show how a technique
introduced by Claudius Ptolemy in the second century
was used to predict the location of Mercury along the Zodiac
at any time and date.
Because the method is so complicated,
a newcomer to Ptolemy's methods
may find it difficult to understand.
When the applet is first seen,
the yellow circle showing the position of the mean Sun,
and the red circle showing the True Position of Mercury
will be rotating.
A good way to see the individual lines of the Mercury applet is to set the date roughly to the beginning of August 1500 by clicking on the applet at the appropriate moment.
The Mercury applet shows the following:
A scale of the Zodiac has a point marked 'Earth'
in the centre.
A line marked 'Aux' is drawn to the Zodiac
at an angle about which Mercury exhibits symmetry.
This line is commonly drawn right across
the circle of the zodiac and
is known as the line of apsides.
The line is roughly shown in the position it had
in the year of 1500 A.D..
A small yellow circle
marks the end of a construction line from Earth
whose angle is equal to the difference between
the mean Sun and the Aux now measured from the Aux
on the opposite side of the line of apsides.
In other words, this construction line is at an angle
so that it forms a mirror image of
the line to the mean Sun, about the Aux.
A line from the Equant point
parallel to the line showing the mean Sun
touches the deferent circle at the centre of
the epicycle circle.
A red line from Earth is drawn to
the centre of the tiny circle.
The method which Ptolemy used to determine the position in the Zodiac of Mercury is the most complicated of the methods he devised for each of the planets. Unfortunately, it is still not a very good method and is mainly of interest in verifying Mercury's calculated position as published in the Middle Ages.
PurposeI wrote the applet mainly because I wanted to understand how Ptolemy's method arranges that Mercury travels on both sides of the Sun, with a touch of retrograde motion, and the way the maximum elongations of Mercury from the Sun change according to its angle from the Aux.
Unfortunately, the ratio of the Equant to the deferent is small, so the radius of the tiny circle used to find the position of the centre of the deferent is also small. Applet's are limited in their resolution, and the result is that the deferent circle and the epicycle scale appear to jump around instead of moving around smoothly.
Despite these limitations, I learned quite a lot from studying the relative movements of Mercury and the Sun. I hope you do, too.
References:Pedersen, Olaf (1974). A Survey of the Almagest. Edidit Bibliotheca Universitatis Hauniensis Vol.30. Odense University Press, Denmark. ISBN 87 7492 087 1.
Particularly the diagram on page 316.
Evans, James (1998).
History and Practice of Ancient Astronomy.
Oxford University Press. ISBN 0-19-509539-1.
Sadly, the book doesn't cover Mercury and the Moon.
When I asked when he would be bringing out a supplement
to cover these, (library, MHS Oxford)
he said that he had moved on to other things.
Gingerich, Owen (1968).
The Mercury Theory from Antiquity to Kepler.