Applications of Computers to Celestial Mechanics

The Geometry of Celestial Mechanics

10.1017/cbo9781316410486 ◽

2016 ◽

Cited By ~ 3

Author(s):

Hansjorg Geiges

Keyword(s):

Celestial Mechanics

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Modelling Lunar Extremes

Journal of Skyscape Archaeology ◽

10.1558/jsa.34686 ◽

2018 ◽

Vol 3 (2) ◽

pp. 207-216 ◽

Cited By ~ 1

Author(s):

David Fisher ◽

Lionel Sims

Keyword(s):

High Precision ◽

Celestial Mechanics ◽

Computer Modelling ◽

Landscape Context ◽

The Sun ◽

The Moon

Claims first made over half a century ago that certain prehistoric monuments utilised high-precision alignments on the horizon risings and settings of the Sun and the Moon have recently resurfaced. While archaeoastronomy early on retreated from these claims, as a way to preserve the discipline in an academic boundary dispute, it did so without a rigorous examination of Thom’s concept of a “lunar standstill”. Gough’s uncritical resurrection of Thom’s usage of the term provides a long-overdue opportunity for the discipline to correct this slippage. Gough (2013), in keeping with Thom (1971), claims that certain standing stones and short stone rows point to distant horizon features which allow high-precision alignments on the risings and settings of the Sun and the Moon dating from about 1700 BC. To assist archaeoastronomy in breaking out of its interpretive rut and from “going round in circles” (Ruggles 2011), this paper evaluates the validity of this claim. Through computer modelling, the celestial mechanics of horizon alignments are here explored in their landscape context with a view to testing the very possibility of high-precision alignments to the lunar extremes. It is found that, due to the motion of the Moon on the horizon, only low-precision alignments are feasible, which would seem to indicate that the properties of lunar standstills could not have included high-precision markers for prehistoric megalith builders.

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On the matter of proving Euclidean fifth postulate and the origin of non-Euclidean geometries

Geodesy and Cartography ◽

10.22389/0016-7126-2019-950-8-2-11 ◽

2019 ◽

Vol 950 (8) ◽

pp. 2-11

Author(s):

S.A. Tolchelnikova ◽

K.N. Naumov

Keyword(s):

Celestial Mechanics ◽

Natural Philosophy ◽

Relativity Theory ◽

Theory Of Relativity ◽

The Third ◽

Stellar Astronomy ◽

Spherical Surfaces ◽

Mathematical System ◽

Solar System Bodies ◽

The Universe

The Euclidean geometry was developed as a mathematical system due to generalizing thousands years of measurements on the plane and spherical surfaces. The development of celestial mechanics and stellar astronomy confirmed its validity as mathematical principles of natural philosophy, in particular for studying the Solar System bodies’ and Galaxy stars motions. In the non-Euclidean geometries by Lobachevsky and Riemann, the third axiom of modern geometry manuals is substituted. We show that the third axiom of these manuals is a corollary of the Fifth Euclidean postulate. The idea of spherical, Riemannian space of the Universe and local curvatures of space, depending on body mass, was inculcated into celestial mechanics, astronomy and geodesy along with the theory of relativity. The mathematical apparatus of the relativity theory was created from immeasurable quantities

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