I have devised, with the help of resources found free on the Web, a realistic parametrized model that will calculate the positions of Jupiter and the Earth in space. The Sun occupies the center of the coordinates.
My model is written in R, a freely available open source version of the renown S system (from the AT&T statistics research dept). The source is a simple ASCII text file model.r. The planetary position modeling comes from Paul Schlyter.
A projection on the Ecliptic of the orbits of the Earth and Jupiter for one synodic year (time for Earth to go around the Sun and catch up with Jupiter). The distance scale is correct even though the aspect ratio is flattened. The Earth starts from the blue dot (Jan 1, 2002), goes once around the Sun and proceeds to the red dot. Jupiter just does an orbit fraction from its red dot to blue dot.
A graph of the varying Jupiter-Earth distance over two synodic years. Again with correct distance scale. Two years are show to mark the slight aperiodicity due to the the small orbit eccentricities of Earth and Jupiter.
A graph showing the magnitude of the observable effect. The y axis is the delta between the observation time and the occurrence time. The sticky thing about this is that we need the occurrence time, and to very high accuracy as I'll show next.
The next graph illustrates the shift in the plot if the true eclipse period is understated or overstated by as little as 1 part in 100,000. If the error is 1 in 10,000 the curve is not even recognizable. Clearly having to know this number accurately to 1 part in 100,000 to deduce another one (c) to only a 1 part in 10 is distasteful. The solution is not to use any predefined period but simply generate one from fitting the data to the curve.
