Planetary positions and data from Mercury to Neptune used in “Signature of the Celestial Spheres” have been calculated according to the VSOP Planetary Theory (Variations Seculaires des Orbites Planetaires, long-term variations of the planetary orbits) developed by P. Bretagnon of the Bureau des Longitudes in Paris and published in 1982, revised for practical application in 1987 in collaboration with G. Francou (many thanks from the author) . The data and calculation procedures needed for application of the VSOP Theory may be found (in a somewhat abbreviated form) in “Astronomical Algorithms” by Jean Meeus. These excellent publications make it possible in principle for anyone to calculate the planetary orbits for periods of several thousands of years to a fantastic degree of accuracy (< one arcsecond = 1/3600 degree) with the use of a simple PC. Jean Meeus abbreviated version is a little less accurate, but completely sufficient for the purposes of this book (the differences are discussed in detail in the appendix to “Signature of the Celestial Spheres”).
As an example you can find here the data that generate the marvellous movement figure of Jupiter, Saturn and Neptune, namely the positions of the three planets at 362 conjunctions from A.D. 18 Nov. 0002 to 14 May 4617. The maximal difference between the reduced version and the full VSOP-Theory is 0.008 degree, much less than the precision of the drawing. In the columns 18 an 19 of the file you will find the x,y-coordinates of the figure Neptune as seen from Saturn at Jupiter/Neptune conjunctions (Signature of the Celestial Spheres, p. 244)
The calculation of the mean values given in Table 6.1 of the book is based on the data in the following files (text-files, max. 122 KB).