GRAVITATION AND THE RELATIVISTIC DOMAIN D₁

The links below are to the Sections of the paper on a new theory of gravitation within a linear space-time continuum.

This paper published in the online Journal Apeiron Vol.10 (4). See Links page

Introduction - The first section contains a title page, a brief abstract, and the main introduction.

The Relativisic Domain - The second section defines the Relativistic Domain D₁, the space-time contimuum in which the development is accomplished. It establishes the criteria for existence within the Domain, and presents its general characterisation.

Gravitational Planar Motion - The third section deals with Gravitational Planar Motion within D₁. Initially an equation is derived describing the gravitational phenomenon in general, followed by expressions for the equation of motion, mass, energy, and weight within the gravitational Domain D₁.

Correlation with the Solar System - The fourth section derives the necessary relationships to correlate the Relativistic Space-Time Domain D₁ with that of the Solar System.

Planetary Orbits (Part 1) - The first part derives the equation of the orbit and goes on to present a rigorous solution of this equation. This includes full expressions for the basic curve and for the precession of the perihelion of the orbit.

Planetary Orbits (Part 2) - The second part, using a process of logical simplification, then reduces this latter expression for the precession of the apse of the orbit to suitable approximations for comparison with like solutions of the General Theory.

Conclusions - Concluding Remarks.

Appendix A - The first appendix presents a transformation of the equation of planar motion in D₁ to Pseudo-Euclidean Space-Time, (D₀).

Appendix B - The second appendix presents a transformation of the equation of a planetary orbit in D₁ to Pseudo-Euclidean Space-Time, (D₀).

Appendix C - The third appendix presents a conversion of the equation of motion to the proper time of the gravitating mass.

Appendix D - The fourth appendix demonstrates the red shift of atomic spectra in D₁ for comparison with that in the General Theory.

Appendix E - The fifth appendix presents a derivation of the metric of the General Theory from the characteristics of existence within D₁ in support of statements in the concluding remarks.

Appendix F - The sixth appendix presents a mathematical justification for radial and radial-normal unit vector differentials in D₁ used in the main text.

Appendix G - The last appendix presents the reduction of a number of gravitational relativistic expressions to their Special Relativity Theory equavalents, as well as to their classical equivalents.

References