Isaac Newton, the motion of the lunar apogee, and the establishment of the inverse square law

The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler's laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravitational attraction of both the Earth and the Sun. Newton discussed this problem at great length, and with mixed success; it was the only testing ground for his Universal Gravitation. This background for today's many-body theory is discussed in some detail because all the guiding principles for our understanding can be traced to the earliest developments of astronomy. They are the oldest results of scientific inquiry, and they were the first ones to be confirmed by the great physicist-mathematicians of the 18th century. By a variety of methods, Laplace was able to claim complete agreement of celestial mechanics with the astronomical observations. Lagrange initiated a new trend wherein the mathematical problems of mechanics could all be solved by the same uniform process; canonical transformations eventually won the field. They were used for the first time on a large scale by Delaunay to find the ultimate solution of the lunar problem by perturbing the solution of the two-body Earth-Moon problem. Hill then treated the lunar trajectory as a displacement from a periodic orbit that is an exact solution of a restricted three-body problem. Newton's difficultly in explaining the motion of the lunar perigee was finally resolved, and the Moon's orbit was computed by a new method that became the universal standard until after WW II. Poincaré opened the 20th century with his analysis of trajectories in phase space, his insistence on investigating periodic orbits even in ergodic systems, and his critique of perturbation theory, particularly in the case of the Moon's motion. Space exploration, astrophysics, and the landing of the astronauts on the Moon led to a new flowering of celestial mechanics. Lunar theory now has to confront many new data beyond the simple three-body problem in order to improve its accuracy below the precision of 1 arcsecond; the computer dominates all the theoretical advances. This review is intended as a case study of the many stages that characterize the slow development of a problem in physics from simple observations through many forms of explanation to a high-precision fit with the data. [S0034-6861(98)00802-2] CONTENTS I. Introduction 590 A. The Moon as the first object of pure science 590 B. Plan of this review 591 II. Coordinates in the Sky 591 A. The geometry of the solar system 591 B. Azimuth and altitude-declination and hour angle 592 C. Right ascension-longitude and latitude 592 D. The vernal equinox 593 E. All kinds of corrections 593 F. The measurement of time 593 G. The Earth's rota...

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“…Notice the marvelous definition of what we would call chaos nowadays! See Cohen (1975), as well as Waff (1976) and(1977).…”

Section: B Philosophiae Naturalis Principia Mathematicamentioning

confidence: 99%

Moon-Earth-Sun: The oldest three-body problem

1998

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“…Particularly, Newton himself understood his scientific undertaking to describe a physical force or interaction (such as the three fundamental ones meant by the Standard model 18 Riemann 1854. 19 Poincaré 1882; 1902 20 Newton's conception of universal gravitation is widely discussed even nowadays: Slavov 2019; Cunha, Tort 2017;Nacer, Eddine 2016;Sim 2015;Lunteren 1993;Ducheyne 2011;2006b;Nauenberg 2005;Tanona 2000;Onofrio 1998;Ihmig 1993;Dieks 1987;Cushing 1982;Waff 1976;Poultney 1971;Wilson 1970;Westfall 1967;etc. nowadays), called by him universal gravitation 21 , thoroughly and perfectly mathematically in the framework of philosophy, "Philosophiae Naturalis" (in English, Natural Philosophy).…”

Section: From Euclid's Geometry To Quantum Information: Via Lobachevs...mentioning

confidence: 99%

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

Penchev

2023

Preprint

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Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

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Section: From Euclid's Geometry To Quantum Information: Via Lobachevs...mentioning

confidence: 99%

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

Penchev

2023

SSRN Journal

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Isaac Newton, the motion of the lunar apogee, and the establishment of the inverse square law

Cited by 7 publications

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Moon-Earth-Sun: The oldest three-body problem

Moon-Earth-Sun: The oldest three-body problem

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

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