Origin Of The Solar System

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The Origin And Evolution Of The Solar System

Abstract
M Woolfson discusses theories of how the Sun and the planets began.

The heliocentric nature of the solar system with its major components — the Sun, planets and satellites — was firmly established well before the end of the 17th century. After the publication of Newton's Principia in 1687 it became possible to apply scientific principles to the problem of its origin.

Most theories that have been advanced in the last 300 years are obviously untenable, but some contain the germs of what might be part of a viable theory. It would not be practical to attempt to deal with all theories in detail in a short review article. Here we shall mention five theories, recently developed or still in the process of development, that have a reasonable scientific basis. Two of them, the Solar Nebula Theory and the Capture Theory, will be described in more detail, emphasizing what they have and have not explained and what their remaining difficulties are. Two early theories will be described first, chosen because they relate closely to the extant ones and illustrate the major problems for theories.

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A History of the Solar System

About this book:

This well illustrated book presents a compact history of the Solar System from its dusty origins 4,600,000 years ago to the present day. Its primary aim is to show how the planets and their satellites, comets, meteors, interplanetary dust, solar radiation and cosmic rays continually interact, sometimes violently, and it reflects humanity's progress in exploring and interpreting this history. The book is intended for a general readership at a time when human and robotic exploration of space is often in the news and should also appeal to students at all levels. It covers the essentials but refers to a large literature which can be accessed via the internet. 

About the authors:

Claudio Vita-Finzi was born in Australia and educated in Argentina and the UK, with BA, PhD and ScD degrees from Cambridge University. He has taught Earth and planetary sciences at University College London for many years and is now a Scientific Associate at the Natural History Museum, London. He has been a member of the American Philosophical Society since 1991, received the GK Warren Prize of the US Academy of Sciences in 1994 and was elected a Fellow of the British Academy in 2012. He has published numerous papers on geology and planetary science and several books including Planetary Geology (Terra 2005), The Sun – a User’s Guide (Springer 2008) and Solar History, an Introduction (Springer 2012). 

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Measure, Integration & Real Analysis

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.

Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.

Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.

Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.

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