# 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 below 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 gravitational 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 rudy.k.mckee@gmail.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 principal **Monograph** 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 effecting other atom's electrons, is gravity**. **

Premise**:** a mechanism of gravity is *assumed* to be the result of **van der WAALS** like forces**.** That is, all the Earth's atom's nuclei radiate electromagnetic energy – is the energy which holds their electrons in orbit, including the outer-most valance electrons**.** These *nuclei forces don't stop at the valance electrons*, but continue weakly, spreading on outward like **van der WAALS** forces**.** This gives rise to gravity**.** Hence it is assumed *Earth's mechanism of gravity is via the resulting manifestation of all Earth's nuclei's attractive, diffused electromagnetic flux, by-passing forces, which gives rise to gravity***.**

** **As a result, Earth's smeared gravitational field pulls on all the electrons attached to all the nuclei of every body equally, regardless of mass, weight, shape, etc.**;** so (**Galil****e****o**'s *Law*) all bodies are pulled down to Earth equally at the same rate**.** Experimental evidence via **ROTHEN**'s experiments, coupled with the observations of **van der WAALS**' forces, does provide more than a sufficient reason for the above conjecture; i.e., for the *mechanism of gravity***. ** See**: **the **n****-Body Problem Closed-form Solution** for further discussion below. It's *algorithm* may be used to determine those gravitational 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* (now 4th)**. ****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, P**art 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 are available at https://www.thefreecountry.com/compilers/miscellaneous.shtml , which can be used to

*the included computer programs in*

**RUN****The**

**n****-body Problem**

**.**

On this day, 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*” buttons**.**

** **Added an extract, 10/06/2021, from** ****Report from Iron Mountain on the Possibility and Desirability of Peace**** **, by Leonard C. **LEWIS**, is a political satire; will be completed shortly. Also added is a page on "**Shear Flow****.**" Currently adding **A Principia Mathematica** free ebook, see below**.**