Newton generalized Kepler's laws of planetary motion when he developed his laws of universal gravitation. Modifications to Newton's generalizations are submitted which offer a novel solution for the galaxy rotation problem and a unified model of the Universe. Observable evidence and experimental predictions are also submitted which can prove the unified model.
Table of Contents
1. Introduction
2. A Generalized 2nd Law of Planetary Motion (GKD2)
3. A Generalized 3rd Law of Planetary Motion (GKD3)
Objectives and Topics
The paper aims to introduce General Keplerian Dynamics (GKD) as a unified model of the universe that provides testable predictions. It seeks to resolve anomalies like the galaxy rotation problem without requiring dark matter by generalizing Kepler's laws of planetary motion within a fractal electrodynamic framework.
- Theoretical development of a unified model (FLAME)
- Generalization of Keplerian laws for orbital dynamics
- Application of fractal electrodynamics to celestial mechanics
- Proposed solutions for the galaxy rotation problem
- Mathematical derivation of angular momentum and wave velocity in orbital systems
Excerpt from the Book
A Generalized 2nd Law of Planetary Motion (GKD2)
Kepler's second law of planetary motion can be stated as: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
GKD2(a) can be stated as: The radii of a secondary's major (r1), minor (r2), and torque (r3) axes, joining the major, minor, and torque points respectively, individually sweep out equal sectors during equal intervals of time (GKD2(a) will be expanded upon).
GKD2(b) can be stated as: The radius of a secondary's major axis (r1) is equivalent to the semi-minor axis of its Keplerian ellipse when unperturbed by outside forces, or [2] r1 = b = a sqrt(1-e^2), where b is the semi-minor axis, a is the semi-major axis, and e is the eccentricity of the ellipse. The radius (r1) is also equivalent to the geometric mean of the secondary's apoapsis and periapsis distances relative to the major point (barycenter), or [3] r1 = sqrt(rmin * rmax).
GKD2(c) can be stated as: The angle of the secondary's toroidal major axis, relative to any other plane of reference, can be determined from the angle of r1, relative to the plane of reference when the secondary is at crest or trough (when r2 is perpendicular to r1, and the hypotenuse is joined by the major and torque points).
GKD2(d) can be stated as: The relationship between the major axis revolution period, the minor axis revolution period, and the polar frequency of a secondary's orbit is: J = Pm / Pm.
Summary of Chapters
Introduction: This chapter outlines the foundation of General Keplerian Dynamics and introduces the Lorentz-Mandelbrot Fractal Electrodynamic Astronomical Model (FLAME) as a testable alternative to existing theoretical frameworks.
A Generalized 2nd Law of Planetary Motion (GKD2): The chapter provides a mathematical expansion of Kepler's second law, introducing the concepts of major, minor, and torque axes, and defining the gyrograph as a tool to calculate orbital positions and angular momentum.
A Generalized 3rd Law of Planetary Motion (GKD3): The chapter modifies Newton's version of Kepler's third law to include mass and polar frequency, demonstrating how this approach can potentially eliminate the necessity for dark matter in explaining galaxy rotation curves.
Keywords
General Keplerian Dynamics, GKD, FLAME, Kepler's Laws, Planetary Motion, Fractal Electrodynamics, Galaxy Rotation Problem, Dark Matter, Angular Momentum, Gyrograph, Toroidal Reference Frame, Orbital Dynamics, Polar Frequency, Celestial Mechanics, Wave Function
Frequently Asked Questions
What is the core focus of this research paper?
The paper proposes a unified model of the universe called General Keplerian Dynamics (GKD), which provides an alternative explanation for celestial mechanics and cosmic phenomena.
Which theoretical frameworks are used to develop the model?
The author utilizes the Lorentz-Mandelbrot Fractal Electrodynamic Astronomical Model (FLAME) to integrate classical planetary motion with fractal electrodynamic principles.
What is the primary objective of the work?
The primary objective is to offer a testable model that solves the galaxy rotation problem and provides a unified description of the universe, distinguishing it from untestable string theories.
What scientific methodology is employed?
The author applies mathematical generalizations to Kepler's three laws of planetary motion, incorporating relativistic and fractal concepts to describe orbital paths and angular momentum.
What topics are covered in the main body?
The main body covers the theoretical framework of GKD, the definition of orbital axes (major, minor, and torque), the use of the gyrograph for motion tracking, and the mathematical modification of Kepler's third law.
Which keywords best describe this study?
The most important keywords include General Keplerian Dynamics, fractal electrodynamics, galaxy rotation, dark matter, and planetary orbital motion.
How does this model address the galaxy rotation problem?
By introducing a polar frequency term into the formula for orbital motion, the model suggests that star rotation speeds are determined by factors that negate the need for dark matter.
What is a gyrograph?
A gyrograph is a consolidation of the Generalized 2nd Law definitions created by the author to simplify the calculation of position and momentum of a secondary object in its orbit.
How is the relationship between the major, minor, and torque axes defined?
These axes are defined as radii that sweep out equal sectors, with their specific lengths and orientations providing a precise geometric mapping of the planetary orbit within a toroidal reference frame.
- Citar trabajo
- Brent Jarvis (Autor), 2014, General Keplerian Dynamics (GKD). 2nd Edition, Múnich, GRIN Verlag, https://www.grin.com/document/271676
