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the following methods are used to achieve the long-term accurate precession computations:  double precession - double precessing, where the long axis precesses around the short axis. damped precession - a double precessing method enhanced to be suitable for very high speed running of the program. it is important to not forget that even at only 1/1,000,000th of rotation per second, the moon's motion around the earth can be detected from the earth's motion itself.  


a recent machine supported book from refractory mathematics and physics, written by e. lee about the astronomical precession uses the damped precession algorithm to compute the long axis precession to nearly 20+ digit precision. this is done using the standard astronomical period table, of course. this page in his book serves as a useful example of the long term precession program.


orbits are calculated with a bespoke matrix method using the parsec orbital period list. this is possible with precisely any two objects because their orbital periods are known. the public parsec list is also used.


transits are calculated with the range-2 algorithm. the standard algorithm will not be able to handle a transit of any of the five major planets and it is not being used. nevertheless, it is also possible to compute the transit of the four gas giants using a range-2 algorithm. the author of beth's calendar program also has done this and has posted a code release to the web.


we take a look at the world of astrometry in general, and the earliest work on the subject of positional astronomy in particular. we find that not only is astronomy always the most ancient field of human knowledge, but also that there are hints in the history of the field that much of the oldest planetary theory was based on a cyclical theory of the solstices, not unlike pre-christian gnostic ideas in other fields such as alchemy, but also drawing on egyptian ideas such as that of the hathor cycle. 84d34552a1