This page is being deleted because WEBS.COM wants too much money for it ($179 for two years).  Please download all files today.  This page is under construction...but you can view any pdf  file by clicking its button.  Feel free to comment about the contents of these files (use the Guestbook).  As of 8/27/2017, there has been more than 9000+ hits (recorded by from all over the world and counting (about an average of 7 a day).  There probably is many, tens-of-thousands more not recordable via  The n-Body Problem Closed-form Solution is really a presentation of the generalization of NEWTON's Law of Universal Gravitation.

      N-body Problem Closed-form Solution (first button): As of 9/23/2017, a draft of the 3rd Edition has been uploaded; the update has been completed as of Oct. 2, 2017.   Appreciate readers finding and reporting any errors.  Thank you!   Clarify definition of gravity cause in n-Body Problem monograph 10/18/17,

    On this day, 3/29/2015, in "Planet Forces" section, added reference to LIBESKIND's work, 2nd Edition, has been uploaded -- enjoy.  One suggestion in this article is the electromagnetic energy flux issuing from the atomic nuclei is a cause of gravity.  The link for this phenomena may be van der WAALS (second button) and/or like long-range forces between atoms; and even for those atoms not in direct contact.  See the short "van der WAALS Forces and Gravity" article below (second button).  The n-body Problem closed-form algorithm may be used to determine these interaction forces.

     Astronomy, Part I, (fourth button down) consists of a collection of essays about the Antikythera astronomy machine, Greek astronomy, Aristotle's Physics, Islamic astronomy, Copernicus, Galileo, Bacon versus Descartes, Newton, Celestial Mechanics, and more.  Astronomy, Part II (the fifth button down) consists of a continuation of the technical and historical documentation.  Part III contains WOODARD's paper; and the essential pages from the book, Astronomical Paper..., Vol. XII, Coordinates of the Five Outer Planets, 1653-2060 (and the book's equations for the coordinates too).  Astronomy, Parts I, II, III is a monograph mainly serving as technical background, with some historical background given too, to augment the N-body Problem

     "NASTRAN Integration..." (last button) is a technical paper on integrating the Finite Element method into Aerospace structural analyses.  In includes the definitions of the mass centroidal equations and inertia tensor employed in the n-body Problem Closed-form Solution monograph.  Enjoy.

     Coming soon: NEWTON's Law of Universe Gravitation derived via the Potential Function V = m/r.

     Also coming soon: essay on the "Universe is naught but a series of past eutectic events."

     Free compilers and interpreters for miscellaneous programing languages at

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