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Three-body gravitational problem and its bigger brother n-body
gravitational problem were possibly the most celebrated unsolved problems
in physics. Until now.
Introducing new
book:
N-Body
Gravitational Problem
Unrestricted Solution
The title is stocked by The Distributors, 702
S. Michigan, South Bend, IN 46601, USA
tel.
219-232-8500
Available at your favorite local Barnes & Noble
bookstore.
Get Your Copy at BarnesandNoble.com for $12.78
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It all started in the year 1687 when Isaac Newton published his
Law of Gravitation for two bodies. He stated at that time that he
was unable to promote it to three bodies and that he did not believe
a brain existed that could solve a three-body gravitational problem.
That was a challenge that no mathematician could ignore.
Ever since, the most famous mathematicians in the history have
tried their hands at the unrestricted solution of the three-body
gravitational problem. In the process they made great advances and
important contributions to the celestial mechanics and to the theory
of planetary orbits. However, surprisingly, the greatest discovery,
the general unrestricted solution of the three-body or n-body
gravitational problem, eluded them.
Having unsuccessfully
wrestled for several hundred years with a general problem of
three bodies moving under mutual gravitation, the mathematicians
resorted to the next best thing: a restricted solution. Few
restricted solutions of a multi-body gravitational problem have been
published since, but no unrestricted solution appeared yet.
In 1885 King Olaf II od
Sweden and Norway, to celebrate his 60th birthday, declared a
contest for general solution of the three-body gravitational
problem. So great was the prestige of the prize that all
mathematicians in the world immediately went to work. Surprisingly,
even the greatest concentration of mathematical talent produced no
general solution of the problem. The King's prize was
eventually awarded to French mathematician Henri Poincaré for
his impressive effort, even though he did not solve the problem.
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Dear Reader,
Let me get
to the point. There are two ways of looking at the n-body gravitational
problem. The first one is from the position of professional
mathematicians, who unanimously agree that the unrestricted solution is
impossible. The second way of looking at it is from the perspective of the
rocks out there in space, which have no difficulty of flying under the
influence of gravitation. Every speck of dust knows what to do under
gravitation. They always do it right. None of them complains that it is
impossible. So we can say that the rocks and dust disagree with the
mathematicians.
Accordingly, I decided to attack the n-body
gravitational problem not from the position of the mathematicians, but
from the position of the rocks flying in space. I sought the solution in
two steps: first I tried to figure out in detail how the rocks in space
are physically flying under the influence of gravitation. The physical
solution turned out to be extremely simple. Then I converted the
physical solution to a mathematical model. The result was the unrestricted
analytical solution valid for any number of bodies of unequal masses. You
will find the resulting equations and all details of the conversion to the
mathematical model in this book . Even though it is considerably more
complex than the physical solution, the mathematical model is surprisingly
simple. Who can now say that the unrestricted solution is impossible?
This is believed to be the first
practical unrestricted analytical solution of
the n-body gravitational problem, for unequal masses. Only trivial
limitations apply to the values of the variables in the equations
disclosed in the book: the masses of all bodies must be positive (and, of
course, they may be respectively different); the bodies must be initially
placed in respectively different positions (no two bodies are allowed in
the same position).
CONSIDER THESE REVIEWS OF THE BOOK:
There are some concepts that are so
complex that even the most learned of minds fail to grasp them.
"N-Body Gravitational Problem: Unrestricted Solution" attempts to
solve the unsolvable by offering a possible solution to one of the most
controversial and debated topics in modern physics – the N-body
gravitational problem. Claimed by Isaac Newton as simply incomprehensible
to the human mind, this problem has baffled the world for over three
centuries. Offering a new way of exploring the problem, "N-Body
Gravitational Problem: Unrestricted Solution " is highly recommended
for community library physics collections.
Midwest Book Review, by
James A. Cox. Reprinted with permission.
Whereas in Gravitation: Master
Key to the Universe the author sets out his basic theory; N-Body
Gravitational Problem: Unrestricted Solution looks at the actual
workings of gravitation in a variety of differing circumstances. The first
portion of this second book analyses how bodies actually react under the
effects of gravitation. In this, the author is very thorough. His
explorations do not simply reflect the findings of a single body being
influenced by gravitation but also reflect various scenarios where the
bodies vary in size or are being reacted upon by multiple gravitational
carriers.
After methodically setting out all of the potential
influences and creating a model, the second part of this book seeks to
create a working set of formulas for any number of bodies. Although quite
heady material, all of these calculations are intuitively presented with
plenty of figures to illustrate each situation. The author is meticulous
when it comes to defining and presenting each step so that his work can
easily be understood and then replicated by the reader. In all cases, the
work is well thought out and scientifically presented.
From TCM
Reviews, by Dr. Tami Brady. Reprinted with permission.
The book N-Body Gravitational Problem: Unrestricted Solution
(ISBN 978-0-9689120-5-8) is a 6" x 9" trade paperback that has 96
pages and includes extensive bibliography and index. Since the book
is mostly about mathematics, it expects from the reader the basic
knowledge of calculus. However, the mathematics in the book is rather
light when compared to typical scientific literature.
Just look
at the Table of Contents:
- Chapter 1 - Philosophy of Solution
- Chapter 2 - Gravitation
- Chapter 3 - Geometry
- Chapter 4 - Mathematical Model
- Chapter 5 - Two-Body Problem
- Chapter 6 - Three-Body Problem
- Chapter 7 - N-Body Problem
- Chapter 8 - Unrestricted Numerical Solution
- Chapter 9 - Restricted vs. Unrestricted
Grevyt Press
704 - 15 Kensington Road
Brampton,
ON
Canada L6T 3W2
Tel./FAX 905-791-2102
The title is stocked by The Distributors, 702 S.
Michigan, South Bend, IN 46601, USA
tel.
219-232-8500
Available at your favorite local Barnes & Noble
bookstore.
Get Your Copy at BarnesandNoble.com for $12.78
|