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E-raamat: Introduction to the Maths and Physics of the Solar System

(University of Manchester, UK)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 19-Mar-2020
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429682803
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Introduction to the Maths and Physics of the Solar SystemSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 19-Mar-2020
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429682803
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This book provides readers with an understanding of the basic physics and mathematics that governs our solar system. It explores the mechanics of our Sun and planets; their orbits, tides, eclipses and many other fascinating phenomena. This book is a valuable resource for undergraduate students studying astronomy and should be used in conjunction with other introductory astronomy textbooks in the field to provide additional learning opportunities.

Features:











Written in an engaging and approachable manner, with fully explained mathematics and physics concepts





Suitable as a companion to all introductory astronomy textbooks Accessible to a general audience
Foreword ix
Preface xi
Chapter 1 Basic Concepts
1(48)
1.1 Geometry
2(4)
1.2 Trigonometry
6(9)
1.3 Calculus
15(24)
1.3.1 Functions
20(1)
1.3.2 Infinity in Maths
20(4)
1.3.3 Derivatives, Integrals and the Fundamental Theorem of Calculus
24(13)
1.3.4 Inverse Trigonometric Functions
37(2)
1.4 Eratosthenes's Final Calculation
39(1)
1.5 Aristarchus's Calculations
40(9)
Chapter 2 Math and Physics Toolkit
49(34)
2.1 Vectors
49(25)
2.1.1 Change of Coordinate Systems
52(4)
2.1.2 Operations with Vectors
56(7)
2.1.3 Differentials and Derivatives of Vectors
63(4)
2.1.4 Polar and Cylindrical Coordinates
67(3)
2.1.5 Vectors in Physics
70(1)
2.1.6 Polar and Axial Vectors
70(4)
2.2 Newton's Laws And Gravity
74(5)
2.3 The Concept Of Mass
79(4)
Chapter 3 Celestial Mechanics
83(94)
3.1 The Principle Of Least Action
84(14)
3.1.1 Conservation Laws
89(5)
3.1.2 Newtonian and Lagrangian Problem Solving
94(4)
3.2 Kepler's Laws
98(47)
3.2.1 Theory of Conic Sections
100(11)
3.2.2 Kepler's 1st Law as Discovered by Kepler Himself in the Years 1600 - 1630
111(4)
3.2.3 Kepler's Problem: Geometrical Solution
115(17)
3.2.4 Kepler's Problem: Newton's Solution Using Calculus
132(8)
3.2.5 Kepler's Problem: Solution Using Geometric Algebra with the Laplace-Runge-Lenz Vector
140(5)
3.3 Energy And Orbits
145(3)
3.4 The Universal Law Of Gravitation: One Very Famous Apple
148(25)
3.4.1 Newton's Shell Theorem Using Calculus
152(6)
3.4.2 Newton's Shell Theorem Using Geometry
158(7)
3.4.3 Newton's Shell Theorem Using Gauss's Law
165(8)
3.5 Planet's Motion Using Euler-Lagrange Equations
173(4)
Chapter 4 A Few Facts about the Solar System
177(44)
4.1 Geocentric Versus Heliocentric
177(8)
4.2 Motion And Coordinates
185(11)
4.3 The Analemma
196(4)
4.4 Tides In The Solar System
200(12)
4.5 Roche Limit
212(1)
4.6 Measuring The Speed Of Light In The Solar System
213(8)
Bibliography 221(2)
Index 223
Lucio Piccirillo is a Professor of Radio Astronomy Technology at the University of Manchester, UK, with extensive experience in designing and building cryogenic systems primarily used to cool astrophysical detectors. He has written more than 100 publications in international journals. He has written more than 100 publications in international journals and is the author of Miniature Sorption Coolers: Theory and Applications (CRC Press, 2018).
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