# Papers by Dr. Gopi Krishna Vijaya, Ph.D

• Calculus and Geometry

An examination of the relationship of calculus to geometry in the context of the Reciprocal System.

• Celestial Dynamics and Rotational Forces In Circular and Elliptical Motions

The understanding of circular motion as being conditioned by a central force coupled to a tangential velocity is questioned, by analyzing the origins of its derivation, and revising it in the light of rotational kinematics. It is shown that one cannot stop the analysis at a force directed to the center, but has to continue it to include an infinite series of higher order rotational forces in four perpendicular directions. The verification of this in terrestrial dynamics, as well as the consequences of its application in celestial dynamics is presented.

• Charge Field and the Reciprocal System

This paper serves to compare the different approaches to a general theory of physics that has been attempted independently by two researchers, Dewey Larson (Reciprocal System) and Miles Mathis (Charge Field Theory) in order to show the overlapping concepts side by side. It is not intended to do what is traditionally done in science (establishing and fighting over priority) but to show how very similar ideas can be reached by anyone who takes an honest look at current scientific data.

• Gothean Science and the Reciprocal System

The concepts used in the Reciprocal System can be traced back in many ways. One direct line is from phenomenology of Goethe, where he stresses the importance of sticking to the phenomena without any theorizing. This principle-based approach further elaborated by Rudolf Steiner is essentially what the Reciprocal System has independently extended further.

• Importance of Conic Section "size" in the Derivation of Propositions X-XVI in Newton's Principia Book I

The “direct problem” of the inverse-square law is examined, by retracing the derivations of Propositions X-XVI in Newton’s Principia. It is found that transfers of constants of proportionality are inconsistent between the propositions, leading to errors in the derived relations for multiple orbits. Proposition X has to be corrected for the relations of time period to the force law by including the area constants for conic sections.

• Magnetic Moments of Leptons

A comparison of the values of the magnetic moments of leptons derived from the Reciprocal System with the values in conventional Physics theories is presented here. Even though the magnetic moment is touted as one of the most accurate tests of modern quantum electrodynamics, it is normally not noticed that the conventional derivation involves several ad-hoc constants. In contrast, these values arise straightforwardly out of the principles of the Reciprocal system.

• Original Form of Kepler's Third Law and its Misapplication in Propositions XXXII-XXXVII in Newton's Principia (Book I)

The original form of Kepler’s Third Law contains a caveat regarding the requirement of small eccentricities – a fact that has been missed by the traditional Newtonian derivations. This constraint is analyzed, and a re-clarification of the real meaning of “mean distance” in the law is provided, by following up the indications given by Kepler in the Harmonices Mundi. It is shown that the modified expression for the “mean distance” not only clears up conceptual difficulties, but also removes a discrepancy found by Kepler for Mercury.

• Preparing for the Reciprocal System

The purpose of this booklet is to take a look at the theory and its development by approaching the fundamental postulates in a slightly different manner than usually presented, for instance, as in Larson’s careful descriptions of the Outline of the Reciprocal System and Lawrence Denslow’s clarification of the Fundamentals of Scalar Motion. While efforts have so far been made to highlight the development of the theory from the postulates, it appears that a fresh effort, one that leads to the postulates by preparation, is necessary at this point of time.

• Replacing the Foundations of Astronomy

The historical development of astronomy is described, with respect to the derivation of Kepler's Laws and their subsequent application by Newton. It is described how the two-dimensional nature of movement of planetary bodies is transformed into one-dimensional movement by the application of an inverse-square law. It is also shown how the Newtonian method of adding perturbations to the inverse-square law for the purpose of planetary calculations is simply a repetition of the Ptolemaic epicycles in algebraic form.

• The Quaternion Struggle

A brief description of the history of quaternions, and how they got lost for a time in history and came back as Quantum Mechanics.

International Society of  Unified Science
Reciprocal System Research Society

Salt Lake City, UT 84106
USA

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