Introduction to the Maths and Physics of the Solar System

This book provides undergraduate students and interested laypeople with an understanding of the basic physics and maths that governs our solar system. It can be used as a companion to all introductory astronomy textbooks.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Piccirillo, Lucio
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Milton : Taylor & Francis Group, 2020.
Temas:
Celestial mechanics.
Mécanique céleste.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Dedication
  • Table of Contents
  • Foreword
  • Preface
  • Chapter 1: Basic Concepts
  • 1.1 Geometry
  • 1.2 Trigonometry
  • 1.3 Calculus
  • 1.3.1 Functions
  • 1.3.2 Infinity in Maths
  • 1.3.3 Derivatives, Integrals and the Fundamental The-orem of Calculus
  • 1.3.4 Inverse Trigonometric Functions
  • 1.4 Eratosthenes's Final Calculation
  • 1.5 Aristarchus's Calculations
  • Chapter 2: Math and Physics Toolkit
  • 2.1 Vectors
  • 2.1.1 Change of Coordinate Systems
  • 2.1.2 Operations with Vectors
  • 2.1.3 Differentials and Derivatives of Vectors
  • 2.1.4 Polar and Cylindrical Coordinates
  • 2.1.5 Vectors in Physics
  • 2.1.6 Polar and Axial Vectors
  • 2.2 Newton's Laws and Gravity
  • 2.3 The Concept of Mass
  • Chapter 3: Celestial Mechanics
  • 3.1 The Principle of Least Action
  • 3.1.1 Conservation Laws
  • 3.1.2 Newtonian and Lagrangian Problem Solving
  • 3.2 Kepler's Laws
  • 3.2.1 Theory of Conic Sections
  • 3.2.2 Kepler's 1st Law as Discovered by Kepler Himself in the Years 1600
  • 1630
  • 3.2.3 Kepler's Problem: Geometrical Solution
  • 3.2.4 Kepler's Problem: Newton's Solution Using Cal-culus
  • 3.2.5 Kepler's Problem: Solution Using Geometric Al-gebra with the Laplace-Runge-Lenz Vector
  • 3.3 Energy and Orbits
  • 3.4 The Universal Law of Gravitation: One Very Famous Apple
  • 3.4.1 Newton's Shell Theorem Using Calculus
  • 3.4.2 Newton's Shell Theorem Using Geometry
  • 3.4.3 Newton's Shell Theorem Using Gauss's Law
  • 3.5 Planet's Motion Using Euler-Lagrange Equations
  • Chapter 4: A Few Facts about the Solar System
  • 4.1 Geocentric Versus Heliocentric
  • 4.2 Motion and Coordinates
  • 4.3 The Analemma
  • 4.4 Tides in the Solar System
  • 4.5 Roche Limit
  • 4.6 Measuring the Speed of Light in the So-Lar System
  • Bibliography
  • Index

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