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In Planetary Systems from the Ancient Greeks, Theodor S. Kepler seeks to present a bird's-eye view of the astronomical nature of the work of Newton's predecessors. Rather than dwelling only on the influence of each thinker's great ideas, Jacobsen tracks the actual details of their development by investigating the various systems involved and how they were used. As such, this book is an attempt to describe the specific processes through which (pre-Newtonian) astronomers derived a knowledge of the cosmos by observing the heavens and trying out detailed models to account for their observations. Planetary Systems from the Ancient Greeks contributes to scholarship on historical astronomy by offering an approach between that of popular, exact astronomical information and formal, fully referenced scholarly investigation. Each chapter is organized around a key astronomer (Eudoxus, Hipparchus, Ptolemy, Copernicus, Tycho Brahe, and Kepler) and offers relevant biographical introduction, exposition of the astronomical system, and assessment of their contributions. As Jacobsen suggests, the present elementary study of these historical astronomical systems also yields valuable insights for visualizing the salient facts of general astronomy.

We prove the existence of an almost full measure set of The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, common tool of previous literature.

Based on scores of medieval manuscript texts and diagrams, the book shows how Roman sources were used in the age of Charlemagne to reintroduce and expand a qualitative picture of articulated geometrical order in the heavens.

Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical insights, the book surveys solid, fluid and gas dynamics. In later review chapters, it explores new aspects of the field emerging from nonlinearity and dynamical complexity and provides a brief introduction to computational modeling. Simple, yet rigorous, derivations are used to review the essential mathematics. The author emphasizes the full three-dimensional geometries of real-world examples, enabling students to apply this in deconstructing solid earth and planet-related problems. Problem sets and worked examples are provided, making this a practical resource for graduate students in geophysics, planetary physics and geology and a beneficial tool for professional scientists seeking a better understanding of the mathematics and physics within Earth sciences.

In Planetary Systems from the Ancient Greeks, Theodor S. Kepler seeks to present a bird’s-eye view of the astronomical nature of the work of Newton’s predecessors. Rather than dwelling only on the influence of each thinker’s great ideas, Jacobsen tracks the actual details of their development by investigating the various systems involved and how they were used. As such, this book is an attempt to describe the specific processes through which (pre-Newtonian) astronomers derived a knowledge of the cosmos by observing the heavens and trying out detailed models to account for their observations. Planetary Systems from the Ancient Greeks contributes to scholarship on historical astronomy by offering an approach between that of popular, exact astronomical information and formal, fully referenced scholarly investigation. Each chapter is organized around a key astronomer (Eudoxus, Hipparchus, Ptolemy, Copernicus, Tycho Brahe, and Kepler) and offers relevant biographical introduction, exposition of the astronomical system, and assessment of their contributions. As Jacobsen suggests, the present elementary study of these historical astronomical systems also yields valuable insights for visualizing the salient facts of general astronomy.

This textbook provides an intuitive yet mathematically rigorous introduction to the thermodynamics and thermal physics of planetary processes. It demonstrates how the workings of planetary bodies can be understood in depth by reducing them to fundamental physics and chemistry. The book is based on two courses taught by the author for many years at the University of Georgia. It includes 'Guided Exercise' boxes; end-of-chapter problems (worked solutions provided online); and software boxes (Maple code provided online). As well as being an ideal textbook on planetary thermodynamics for advanced students in the Earth and planetary sciences, it also provides an innovative and quantitative complement to more traditional courses in geological thermodynamics, petrology, chemical oceanography and planetary science. In addition to its use as a textbook, it is also of great interest to researchers looking for a 'one stop' source of concepts and techniques that they can apply to their research problems.

Urban studies today is marked by many active debates. In an earlier paper, we addressed some of these debates by proposing a foundational concept of urbanisation and urban form as a way of identifying a common language for urban research. In the present paper we provide a brief recapitulation of that framework. We then use this preliminary material as background to a critique of three currently influential versions of urban analysis, namely, postcolonial urban theory, assemblage theoretic approaches and planetary urbanism. We evaluate each of these versions in turn and find them seriously wanting as statements about urban realities. We criticise (a) postcolonial urban theory for its particularism and its insistence on the provincialisation of knowledge, (b) assemblage theoretic approaches for their indeterminacy and eclecticism and (c) planetary urbanism for its radical devaluation of the forces of agglomeration and nodality in urban-economic geography.

The planetary theory in the Great Expansion System (Dayan li 大衍历, 727 CE) is investigated, with a detailed example of Mars. In ancient Chinese astrology, the position of one planet and the relative positions of different planets had important astrological significance. Thus, planetary theory is an important part of Chinese mathematical astronomy. The Great Expansion System, which was compiled by Yixing 一行 of the Tang唐 dynasty (618–907 CE), provided many innovations in planetary theory. Based on the extant Treatises on Mathematical Harmonics and Astronomy (Lü li zhi 律历志) in Chinese official histories, the Great Expansion System was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet. It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet, which was the basis for calculating the true position of the planet. In addition, Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China. The innovations of the Great Expansion System regarding planetary theory established its important position in the history of Chinese astronomical systems. Mars is taken as a case study to investigate the planetary theory in the Great Expansion System, including the astronomical constants related to Mars, two important astronomical tables, namely the table of the equation of center and the table of the phase motion of Mars in one synodic period, and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center. Two questions are addressed. First, how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars? Second, how did Yixing calculate the true position of Mars on any given day? The original text of the Great Expansion System is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.

We present the results of observations of the Galilean moons of Jupiter carried out at the Normal Astrograph of the Pulkovo Observatory in 2018. We obtained 452 positions of the Galilean moons of Jupiter in the Gaia DR1 catalog system (ICRF, J2000.0) and 671 differential coordinates of the satellites relative to each other. The obtained mean errors in the satellites’ normal positions on the right ascension and declination, which demonstrate the intrinsic convergence of the observational results, are εα = 0.003′′ and εδ = 0.003′′, respectively, for the entire observational period. The errors of one difference are σα = 0.070′′, and σδ = 0.067′′, respectively. The equatorial coordinates of the moons were compared to eight motion theories of planets and satellites. On average, the (O–C) residuals in the both coordinates relative to the motion theories are 0.014′′. The best agreement with observations is achieved by combination of all four motion theories of satellites with the planetary theory EPM2017, which yields average (O–C) residuals of approximately 0.01′′ for each of them. The new results were compared to those of the 2016−2017 observational season. As in the past, peculiarities in the behavior of the (O–C) residuals for Io and Ganymede have been noticed.