What is SOLEX and what does SOLEX do?

    The name comes from “SOLar system integration by a fast EXtrapolation method”, and, indeed, SOLEX computes the positions of solar system bodies (planets, asteroids and comets) by a method which is entirely based on the numerical integration of the Newton equation of motion.

<>    This means that, once the position and velocity of each body is known at a given starting instanct, the acceleration arising from the mutual gravitational forces is computed, and then the new position and velocity after a suitably short time interval (the stepsize) can be predicted. The procedure can be iterated, so that the whole orbits are generated. A beautiful and simple description of the general idea was given by Feynmann in its famous Physics textbook. The more sophisticated integration technique actually implemented by Solex, as well as the Solar System model adopted, have been described by the author (Download reprint).
    On one hand the numerical integration approach introduces a limitation for the user: it is not possible to feed a date to the program and to get the planetary configuration in response. If the date were to be changed, the planets would still travel following their original clock. Planets must instead travel from the initial starting epoch to the desired epoch, and the time required depends on the time interval between the two epochs and on the machine speed. On my 2.0 GHz Pentium M760 notebook, hundred years orbiting of the Solar System (including the three major asteroids Ceres, Pallas and Vesta) takes less than 5 seconds. Still, if we were interested in the Christmas night sky of year 1 BC (astronomical year 0), starting from the present epoch (say January 1st, 2009), one and a half minute would be needed to reach the desired epoch. This limitation is overcome by Solex by using a database of precalculated starting conditions, among which the program will chose the one which is closest in time to the target epoch. Therefore the initial “go to epoch” waiting time is reduced to not more than a few seconds (if the target epoch is within the time span covered by the library). After this affordable cost is payed, the reward comes back: whatsoever astronomical phenomenon is always dynamically reproduced. The Solar System is "alive", and the moving bodies can be seen from any point of view, static or dynamic, according to various coordinate systems and at variable speed, forward or backward in time. Everything combined with an unmatched precision, fully comparable to that given by the Astronomical Almanac or by the JPL "on-line" Horizon ephemerides,  and generally superior to that given by computer programs implementing analytical methods. Libraries containing starting condition for ca. 130000 numbered asteroids and ca. 600 comets are available to the program, which can then integrate the “expanded” solar system up to any desired epoch (at a rate of up to 35s/millennium on a Pentium 3 GHz machine). Besides the library objects Solex can easily handle custom bodies and also Earth’s satellites. Moreover, a fictitious Solar System can easily be loaded to the program, to model the gravitational dynamics of N-body systems and to get insights on aspects such chaos, perturbing effects of heavy planets, relativistic effects of a very massive star and so on ...
    The new  version 10 keeps the planetary libraries (matching either the JPL DE406 or DE421 ephemerides) extended to epochs as far as +/- 150000 years.  It takes just a few seconds to experience the virtual emotion of the simultaneous transit of Mercury and Venus on the solar disk, which will take place on  July 26 (Dynamical Time) 69163 !  (Download reprint)    
The star library now includes stars up to magnitude 12.0 from the NOMAD1 catalog and a number of NGC objects up to magnitude 13.5. Aesthetically pleasant sky views can be displayed, statically or dynamically, at any desired magnification and in any direction, in either equatorial, ecliptic or horizontal coordinate frame and from any terrestrial or extra-terrestrial point of view. A further  feature is the ability to handle as many body as desired all together and to run a systematic search for the prediction of close approaches between bodies, both in space (close encounters) and angular (close conjunctions, eclipses or mutual occultations, including star occultations and multiple conjunctions). The path of an occultation or that of a central solar eclipse on the Earth’s surface can also be mapped. An important feature is also that of giving  uncertainty estimates along with the prediction of asteroidal occultations.
    For people interested in programming, the source code to Solex 10 is written in BASIC for the PowerBasic Console Compiler 3.0. Graphic functions are implemented through the Console Tools + Graphics addon to the PowerBasic compiler.  
Solex  10 implements the Extended Precision arithmetics, so that the numerical integration is done with an arithmetical precision equivalent to 19 significant decimal digits.<>
    In conclusion, Solex 10 is a very precise ephemeris generator, a Planetarium, an advanced Celestial Mechanics' device and a serious research tool. Above all, it can be a self-instruction tool to be explored and enjoied.

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Page update: June  2008