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Keith's Mercury Applet using Aux, Equant, Deferent and Epicycle
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.
Clicking anywhere in the applet window (except on a button, of course) will stop the action.
Clicking on one of the buttons will change the action to be faster or slower, backwards (clockwise) or forwards (anticlockwise). You can stop it at any date after 1500 A.D..
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 from 'Earth' to the Zodiac has a yellow circle at the end. This circle represents the Sun. It roughly shows the position of the MEAN Sun along the Zodiac on the date shown at the top-centre of the window. (The mean sun indicates the position of the Sun assuming it moves through the same angle every day.)
Almost at the end of this line is a small green circle which shows the MEAN position of Mercury around the Zodiac on the date shown at the top-centre of the window. (The mean position of Mercury is the same as that of the Sun.)
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 little way along this line from the Earth point is a point marked 'Equant'.
Separated by the same distance further along this line is a point at the centre of a tiny circle marked, 'Tiny circle of deferent centre'.
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 centre to the circumference of the tiny circle of the deferent centre has been drawn parallel to the construction line.
The point where this radius line touches the circumference is the centre of the large circle marked as the Deferent. [The consequent 'wobble' of the deferent circle as the Sun travels around the Zodiac is best seen after clicking on the 1yr button.]
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.
The epicycle circle has an anticlockwise signa scale with its origin at the furthest point on the line drawn from the Equant point.
A red line from Earth is drawn to
the centre of the tiny circle.
A red radius line is drawn on the tiny circle.
A red line from the end of this line is drawn to the centre of the epicycle.
A red radius line is drawn to the point on the epicycle scale of the mean argument of Mercury, found in tables for the appropriate date and time.
A red line from Earth through this point reaches the Zodiac scale and is marked with a red circle. Its position marks Ptolemy's 'True Position of Mercury'.
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.
I 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.
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.
Presented at the XII International Congress of the History of Science, Paris, August 1968.
Smithsonian Instutution, Astrophysical Observatory, Cambridge, Massachusetts 02138.
(seen in Library, MHS, Oxford.)
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