Towards a General Theory of Orbital Motion: the Thermo-Gravitational Oscillator (original) (raw)
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Milanković and the Planetary Orbital Mechanics/Dynamics
First International Conference on Milankovic, 2019
Based on the list of research topics that Milanković had conceived for the Mathematical and Astronomical institutes (one plus two), as well as for the aspirants’ and doctoral theses (eight plus fifteen) – as found out by mathematician and science-historian Dragan Trifunović back in 1978, in this article is made an attempt to establish the reasons of those which relate to the need of re-examining and further developing the very theory of gravity and the traditional formulation of the natural orbital motion, having in mind that – through the secular changes of eccentricities and other parameters of planetary trajectories – they are in direct connection with the methodology and results of his “Solar Cannon”. In the anticipation of the geologically and otherwise experimentally estblished need for the fundamental modification of the Newtonian orbital mechanics/dynamics, it is brought-up and reaffirmed – starting from as early as the Kepler’s physical considerations - the Leibniz’s two-components central acceleration, which is shown to be arrivable at by using the Milanković’s distance inverse squared dependence of planets’ temperatures within the context of Gordić’s differential formulation of orbital motion as dynamic equilibrium between the gravitational (attractive) and thermal (repulsive) components of central ‘force’. It is hinted to the important correspondence with the somewhat more than one and the half century old formulation through the Kepler-Ermakov non-linear differential equation and the relevance of its application in the context of the “archeological astronomy” and asteroids dynamics modeling, as well as on the astrophysical, astronomic and cosmogony plans, through essentially obsoleting the “dark matter” and “dark energy” problems/issues. The additional support for adequacy of the formulation of the planetary orbital motion as the Thermo-Gravitational Oscillator has been found in the foundation and implications of the Atsukovsky’s Etherodynamics.
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.
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.
Novel Theory Leads to the Classical Outcome for the Precession of The Perihelion of a Planet due to Gravity, 2013
We offer a novel method which lets us derive the same classical result for the precession of the perihelion of a planet due to the gravitational effects of the host star. The theoretical approach suggested earlier by the first author is erected upon just the energy conservation law, which consequently yields the weak equivalence principle. The precession outcome is exactly the same as that formulated by the General Theory of Relativity (GTR) for Mercurial orbit eccentricities, but the methodology used is totally different. In our approach, there is no need to make any categorical distinction between luminal and sub-luminal matter, since, as we have previously demonstrated, our theory of gravity is fully compatible with the foundations of quantum mechanics. Our approach can immediately be generalized to the many-body problem, which is otherwise practically impossible within the framework of GTR. Our approach thus leads to a unified description of the micro and macro world physics.
An unusual approach to Kepler’s first law
American Journal of Physics, 2001
Kepler's first law of planetary motion states that the orbits of planets are elliptical, with the sun at one focus. We present an unusual verification of this law for use in classes in mechanics. It has the advantages of resembling the simple verification of circular orbits, and stressing the importance of Kepler's equation.
Notes on the Motion of Celestial Bodies
JAMP, 2020
A novel method for the computation of the motion of multi-body systems is proposed against the traditional one, based on the dynamic exchange of attraction forces or using complex field equations, that hardly face two-body problems. The Newton gravitational model is interpreted as the emission of neutrino/gravitons from celestial bodies that combine to yield a cumulative flux that interacts with single bodies through a momentum balance. The neu-trino was first found by Fermi to justify the energy conservation in β decay and, using his model; we found that the emission of neutrino from matter is almost constant independently from the nuclides involved. This flux can be correlated to Gauss constant G, allowing the rebuilding of Newton law on the basis of nuclear data, the neutrino weight and the speed of light. Similarly to nature, we can therefore separate in the calculations the neutrino flux, that represents the gravitational field, is dependent on masses and is not bound to the number of bodies involved, from the motion of each body that, given the field, is independent of the mass of bodies themselves. The conflict between exchanges of forces is avoided, the mathematics is simplified, the computational time is reduced to seconds and the stability of result is guaranteed. The example of computation of the solar system including the Sun and eight planets over a period of one to one hundred years is reported, together with the evolution of the shape of the orbits.
A New Physical Description of Planetary Motion-Spinvector Motion I
International Journal of Physics, 2022
A new planetary motion theory, spin-vector motion is developed, based on Kepler's second laws of planetary motion that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The planetary motion follows the same Schrodinger wave equation as quantum particles. The planets have same particle-wave duality, wave length and momentum relation, energy and wave frequency relation as quantum particles too. Based on our deduction we conclude that the Schrodinger equation can be applied successfully to photons, quantum particles, and celestial bodies, but with different energy constant for celestial bodies. Even though these objects are with different masses, sizes and with different wave speeds. And we predict that the wave speed exceeding light speed will not have any impacts on the wave equation form. This spin-vector in motion theory or Spin-vector Mechanics will be a candidate theory leading to the theory of everything.
Mathematics of a new theory for celestial orbits
Since Kepler time (1609) we are educated to believe : "Orbits of the planets are elliptical, with the Sun at one focus of this trajectory; that the ray Planet-Sun sweeps out equal area in equal interval of time; that a period law is valid". I claim the contrary. According Newton's laws the orbits of celestial bodies are not elliptical but spiraled, as discovered by Newton himself ;no area law, no period law. In these papers mathematical proofs are presented in order to change the 400 years wrong trend of Keplerian mathematics.
Azimuthally Symmetric Theory of Gravitation I On the Perihelion Precession of Planetary Orbits
From a purely none-general relativistic standpoint, we solve the empty space Poisson equation, i.e. ∇ 2 Φ = 0, for an azimuthally symmetric setting, i.e., for a spinning gravitational system like the Sun. We seek the general solution of the form Φ = Φ(r, θ). This general solution is constrained such that in the zeroth order approximation it reduces to Newton's well known inverse square law of gravitation. For this general solution, it is seen that it has implications on the orbits of test bodies in the gravitational field of this spinning body. We show that to second order approximation, this azimuthally symmetric gravitational field is capable of explaining at least two things (1) the observed perihelion shift of solar planets (2) that the Astronomical Unit must be increasing -this resonates with the observations of two independent groups of astronomers who have measured that the Astronomical Unit must be increasing at a rate of about 7.0±0.2 m/cy (Standish 2005) to 15.0±0.3 m/cy . In-principle, we are able to explain this result as a consequence of loss of orbital angular momentum -this loss of orbital angular momentum is a direct prediction of the theory. Further, we show that the theory is able to explain at a satisfactory level the observed secular increase Earth Year (1.70 ± 0.05 ms/yr; ). Furthermore, we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least 8.00 ± 2.00 s/cy.
The postulates of gravitational thermodynamics
Physical Review D, 1996
The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.