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Full-Text Articles in Physical Sciences and Mathematics
On The Motion Of The Nodes Of The Moon And The Variation Of Its Inclination To The Ecliptic (An English Translation Of De Motu Nodorum Lunae Eiusque Inclinationis Ad Eclipticam Variatione), Patrick T. Headley
Euleriana
In this paper Euler attempts to explain some features of the motion of the Moon using Newton’s inverse-square law of gravity. He describes the evidence in favor of Newton’s theory but also the lack of progress in the study of lunar motion due to the difficulty of the three-body problem, arising here since both the Sun and the Earth have large effects on the Moon. He proceeds to investigate the line of intersection between the planes of the Earth's orbit and the Moon's orbit, as well as the angle between the two planes.
Euler And Venus' Suspicious Moon, Michael P. Saclolo
Euler And Venus' Suspicious Moon, Michael P. Saclolo
Euleriana
This is a brief note on Leonhard Euler's published German translation from the French of two memoirs read by Armand Henri Baudouin de Guémadeuc to the Paris Academy of Sciences in 1761 and published the same year. The memoirs report on observations made of the planet Venus, performed in Limoges, France by Jacques Montaigne, where he claimed to have detected a moon orbiting the Morning and Evening Star.
On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa
On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa
Euleriana
This is an annotated translation from Latin of E327 -- De motu rectilineo trium corporum se mutuo attrahentium (“On the rectilinear motion of three bodies mutually attracting each other”). In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Here Euler finds that the parameter that controls the relative distances among the bodies is given by a quintic function.
Euler's Three-Body Problem, Sylvio R. Bistafa
Euler's Three-Body Problem, Sylvio R. Bistafa
Euleriana
In physics and astronomy, Euler's three-body problem is to solve for the motion of a body that is acted upon by the gravitational field of two other bodies. This problem is named after Leonhard Euler (1707-1783), who discussed it in memoirs published in the 1760s. In these publications, Euler found that the parameter that controls the relative distances among three collinear bodies is given by a quintic equation. Later on, in 1772, Lagrange dealt with the same problem, and demonstrated that for any three masses with circular orbits, there are two special constant-pattern solutions, one where the three bodies remain …
Development Of Selected Mathematical Instruments Representing Angular, Logarithmic And Arithmetic Computation, Lillian L. Troxell
Development Of Selected Mathematical Instruments Representing Angular, Logarithmic And Arithmetic Computation, Lillian L. Troxell
University of the Pacific Theses and Dissertations
The Sextant in its earliest known form consisted of divided circles and compasses with simply sights. An early Creek astronomer of the second century after Christ, Claudius Ptolemaeus, or more commonly called Ptolemy, wrote a book entitled Megale Syntaxis tes Astron- omias, also known by the Arabic title Almagest. The instrument described in this book was called the Astrolable and was used to measure the angular distance between stars. It was made of two concentric vertical circles, the largest and outer circle was about sixteen inches in diameter with graduated arc; the central ring was movable and carried the two …