Paper00-Kepler-Laws.html (original) (raw)
Related papers
Heliyon, 2019
The original form of Kepler's Third Law contains a caveat regarding the requirement of small eccentricitiesa 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. Based on this re-evaluation, the result of ignoring the small-eccentricity constraint is analyzed in the Propositions XXXII-XXXVII in the Principia. It is seen that there are several conceptual and mathematical mistakes that are inevitable with the Newtonian form of Kepler's Third Law. * Nam in Commentarijs Martis cap. XLVIII. fol. 232. probavi Medium hoc arithmeticum vel ipsam. Esse diametrum circuli qui longitudine aequat ellipticam orbitam veleá proximè minus.
The New Physics Kepler's Refutation of Aristotle's Concept of Motion
The main object of this thesis is to expose arguments defending the view according to which Kepler emerged as a modern physicist by refuting the Aristotelian worldview as metaphysics. A key concept in this quest will be that of motion. A comparison of Aristotle’s concept of motion with “Kepler motion” will be an instrument to reveal Kepler’s worldview. To conclude, another key concept will be used: that of falsification as formulated by Karl Raymund Popper. Kepler’s rejection of Aristotle’s worldview is based on Kepler’s refusal of considering the validity of a theory when the theory in question is proven to be pure metaphysics. A metaphysical hypothesis has no alternative, it cannot be refuted or denied by any other hypothesis, least by scientific ones. A metaphysical hypothesis (theory) requires belief while scientific hypotheses (theories) require scientific proof. Therefore, the Aristotelian worldview cannot be, in Kepler’s eyes, falsified by a scientific theory as the two belong to different categories. A theory that is proven unfalsifiable is automatically being refuted.
CPMMI (to be significantly shortened for), 2020
After 412 years of the formulation and publication (in Astronomia Nova, 1609) of the Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativeness, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the fictitious one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), the incomplete congruence among his physical considerations and the ultimately formulated laws, and also of the non-existent transverse acceleration ‘implied’ by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General Aetherodynamics” of V.A. Atsukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, and P, Savić. Certain implications to the Elliptic Integration, the Symplectic Integration, Symplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics and/or dynamics - will be briefly mentioned.
After 412 years of the formulation and publication (in Astronomia Nova, 1609) of the Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativeness, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the fictitious one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), the incomplete congruence among his physical considerations and the ultimately formulated laws, and also of the non-existent transverse acceleration ‘implied’ by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General Aetherodynamics” of V.A. Atsukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, and P. Savić. Certain implications to the Elliptic Integration, the Simplectic Integration, Simplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics and/or dynamics - will be briefly mentioned.
A Short History of 'Definition'
Pending, 2024
A short history of 'definition' in recent philosophy is presented. The views presented here are in approximate chronological historical order and revolve around discussion of 'real' and 'nominal' definitions. Under the tripartite theory, a 'real' definition is approximately identified as a 'theoretic' definition. A 'nominal' definition is understood to be identified as 'reportive' or 'stipulative.' The conclusion of this history is that the quoted texts support the idea that mathematical definitions are typically (3b) stipulative abbreviations or (3c) stipulative formalizations of fixed definiens concepts.
2023
To demonstrate the law of universal gravitation, Newton started from a system of two bodies, the sun and a planet. In addition, he considered the sun to be at rest, and yet, according to the third law, it must be accelerated by the force exerted on it by the planet. In this article, the acceleration of the planet is recalculated, considering the center of mass of the two bodies at rest, using today's math tools. Warning: Contrary to the prediction of the deduction, the relation of Kepler's third law does not vary with eccentricity. Being so constant, τ follows the eccentricity function, a result that is inconsistent with the determination made. It appears that the supposition that the Sun is at rest is more correct than the one that can be considered that each orbit of the solar system's planets can be isolated from each other. This means that the article has lost interest. Updated information of this article: https://vixra.org/abs/2302.0047