“A former consulting engineer proposes a geometric alternative to Einstein’s Relativity, derived entirely from the classical Two Body Problem of orbital mechanics — challenging modern physics to return to its geometric roots. Essential reading for physicists and mathematicians who question scientific orthodoxy.”
KEYWORDS: astronomy, celestial mechanics, relativity, orbital mechanics
134 pages 6x9 Trade book Available as a Paperback or PDF book Read a 15-page preview at Blurb.com
About the Book
What if Einstein’s Relativity could be derived not from electromagnetic theory — but from the ancient geometry of planetary orbits? In A Geometric Derivation of Relativity From the Two Body Problem, engineer and orbital mechanist William H. Clark II makes a bold case that the foundations of modern physics are best understood through classical geometry, not calculus, statistics, or computer simulation.
Beginning with Kepler and Newton, Clark methodically constructs the mathematical architecture of the Two Body Problem — angular momentum, conic sections, trajectory equations, and orbital elements — before introducing two entirely new force equations that he argues emerge naturally from orbital geometry. These forces, he contends, provide a simpler and more intuitive explanation for Relativity’s three classical proofs: the bending of light, the precession of Mercury, and gravitational time dilation.
Clark also challenges the scientific establishment’s over-reliance on complex gravity models, arguing that a return to geometric first principles reveals a unified “system wave” governing planetary motion — and that the same mathematics may unlock new understanding in quantum chemistry and atomic physics. Rigorous yet accessible, this work is an essential provocation for physicists, mathematicians, and independent thinkers willing to question the foundations of modern science.
Target Audience:
- Advanced undergraduate and graduate students in physics, mathematics, and aerospace engineering
- Professional physicists, astronomers, and orbital mechanists
- Independent researchers and theorists skeptical of mainstream scientific consensus
- Readers with prior exposure to classical mechanics, conic sections, and Keplerian orbital theory
- Academics interested in the history and philosophy of physics (Kepler, Newton, Poincaré, Einstein)
Key Themes:
- Geometric derivation of Relativity as an alternative to Einstein’s electromagnetic framework
- The Two Body Problem as the foundational structure of all orbital and physical motion
- Introduction of two novel force equations (F- and F-equations) emerging from orbital geometry
- Critique of modern physics’ over-reliance on statistical models and computer simulation
- The “System Wave” and “Symmetric Plane” as a unified geometric model of Solar System structure
- Poincaré’s Relativity revisited as a celestial-mechanics-based alternative to Einstein
- Interdisciplinary bridges between celestial mechanics, quantum chemistry, and atomic physics
Detailed Table of Contents
Chapter 0 — Front Matter Introduces the author’s thesis, motivations, and acknowledgments, framing the geometric critique of modern Relativity theory.
Chapter 1 — Gravity Establishes the classical foundations: Kepler’s Laws, Newton’s Laws of Motion, the Two Body Equation, and gravitational field force as the starting point for all derivations.
Chapter 2 — Unknown Variables Derives the key conserved quantities of orbital motion — angular momentum, the energy integral, center of mass, and the barycenter — essential building blocks for the trajectory model.
Chapter 3 — Geometry of Conic Sections Develops the full geometric toolkit: the ellipse, flight path angle, the Vis-Viva equation, the hyperbola, and orbital velocity relationships.
Chapter 4 — The Trajectory Equation Unifies conic sections, simple harmonic motion, and the argument of periapse into a single trajectory equation, introducing Poincaré’s Relativity as a geometric precursor to Einstein.
Chapter 5 — 2nd Body in Motion Extends the model to a moving second body, covering the Law of Equal Areas, Kepler’s Third Law, orbital elements, and rotation matrices for three-dimensional orbital geometry.
Chapter 6 — Kepler’s Equation Presents both graphical and rigorous derivations of Kepler’s Equation, with methods for solving Kepler’s Problem in practical orbital mechanics applications.
Chapter 7 — Applications Applies the geometric framework to real-world problems, including ballistic trajectories and Lambert’s Problem for orbital transfer calculations.
Chapter 8 — Two New Forces Introduces the author’s original contribution: the F- and F-equations, two novel force relationships derived geometrically from the Two Body Problem.
Chapter 9 — Relativity Theory Presents the book’s central argument — that Relativity’s three classical proofs (light bending, Mercury’s precession, time dilation) can be explained by a new 1/r force at a geometric “virtual center” or event horizon, without electromagnetic assumptions.
Chapter 10 — Appendix Extends the theory into the frequency domain, analyzing orbital motion as a wave phenomenon and further developing the new 1/r force model in the context of the Solar System’s “system wave.”
Purchase the Book
Please visit the book’s landing page on Blurb.com for a 15-page preview and options to purchase the paperback or PDF.
Further Reading
Visit the author’s website 4 Theory.org for more extreme technology ideas + his latest tech papers in celestial mechanics.
Visit WH Clark.net for complete details of his dismissal from graduate school, where this book was a draft PhD dissertation.