# n-Body Problem Closed-Form Solution

The n-Body Problem Closed-form Solution monograph (is a freebie ebook), now the 4th Edition, is the principal pdf file and its thrust is the presentation of the generalization of NEWTON's Law of Universal Gravitation -- in the form of an easy to use algorithm for calculating the interacting forces for any number of isolated bodies.

This page is under construction (since 2013)...but you can view or download any pdf file by clicking that file. Feel free to comment at rudrene@yahoo.com about the contents of any of these files; and please report any errors too (thank you).

Added to the principal Monograph, 2nd Edition, was the "Planet Forces" section which refers to LIBESKIND's work. One suggestion in this article is the electromagnetic energy flux issuing from the atomic nuclei is a cause of gravity (the flux however weak doesn't stop at the valence electron, but travels on). The link for this phenomena may be van der WAALS, 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. The n-Body Problem Closed-form Solution's algorithm may be used to determine those interaction forces.

Astronomy, Parts 1, 2, 3, and 4 is a single monograph (divided up into four Sections), mainly serving as technical background, with some historical background given too, to augment the n-body Problem ebook. It has been completely rewritten and now identified as the 2nd Edition. Astronomy, Part 1 and 2, 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. Specifically, in the Second section of Part 1 it explains how the Sun's wobble creates by gravitational forces a planetoid's translation acceleration. And further, it hypothesized in this same section that the Sun's powerful Eddy currents are responsible for effecting the Sun's electromagnetic nodal rings, the gravitational force field (potential) wells encircling the Sun the planets and planetoid are embedded (trapped) in, which, when combined with the Sun's forces of these nodal ring gravitational wells, the planets and planetoids natural gravitational forces and their centrifugal forces, cause orbital stability to be maintained for all the orbiting bodies orbiting the Sun. This phenomenological scenario is described step-by-step in much more detail in the Second section of Part 1. More astronomical history, followed by more celestial mechanics, is presented in Part 2.

See Part 3 and 4 Prefaces for their contents. These Parts contains considerably more technical papers then Parts 1 and 2. For example, Part 4 contains WOODARD's paper on calculating orbits; and gives 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).

On this day, 1/21/2019, added HERGET's "Computation of Orbits" out-of-print textbook, Part I, Chapters 1 through 5; and Part II (a separate document), Chapters 6 through 8, plus some more references (contained in the Main References section).

All pdf files are free to download for private use. Also, free compilers and interpreters for miscellaneous programming languages is at https://www.thefreecountry.com/compilers/miscellaneous.shtml , which can be used to RUN the included computer programs.

As of 8/27/2017, there has been more than 10000+ hits on this webpage from all over the world; and counting (about an average of 7 a day). There probably are many, tens-of-thousands, more not recordable because they have turned on their “do not track” button.

n-body_Problem_4thEd.pdf
Ancient_Astronomy_Pt_1.pdf
Ancient_Astronomy_Pt_2.pdf
Ancient_Astronomy_Pt_3.pdf
Ancient_Astronomy_Pt_4.pdf
Van_Der_WAALS_Forces.pdf
Planetary_Motion_in_Rectrangular_Coord.pdf
HERGET_Master - a.pdf
HERGET_Master - b.pdf

FOX_Mechanics.pdf
NASTRAN_Integration.pdf
Vagabond _Moons.pdf