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E-grāmata: Moving Planets Around

  • Formāts: EPUB+DRM
  • Izdošanas datums: 01-Sep-2020
  • Izdevniecība: MIT Press
  • Valoda: eng
  • ISBN-13: 9780262359610
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  • Formāts: EPUB+DRM
  • Izdošanas datums: 01-Sep-2020
  • Izdevniecība: MIT Press
  • Valoda: eng
  • ISBN-13: 9780262359610
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An introduction to the laws of celestial mechanics and a step-by-step guide to developing software for direct use in astrophysics research.

This book offers both an introduction to the laws of celestial mechanics and a step-by-step guide to developing software for direct use in astrophysics research. It bridges the gap between conventional textbooks, which present a rigorous and exhaustive exposition of theoretical concepts, and applying the theory to tackle real experiments. The text is written engagingly in dialogue form, presenting the research journey of the fictional Alice, Bob, and Professor Starmover. Moving Planets Around not only educates students on the laws of Newtonian gravity, it also provides all that they need to start writing their own software, from scratch, for simulating the dynamical evolution of planets and exoplanets, stars, or other heavenly bodies.

The first half of the book develops a fully functional N-body integrator, using state-of-the art integration techniques, explaining both the techniques and the reasons that they are useful. The second half of the book focuses on using an advanced integration scheme to conduct real research, leading students in an investigation of the long-term dynamical stability of extrasolar circumbinary planets. At the end of the journey, students will be ready to design, conduct, and publish peer-review quality research.

List of Code Snippets
xi
Acknowledgments xv
Foreword xvii
Prologue xxiii
1 A Bestiary Of Planets
1(6)
1.1 Many Moons
1(1)
1.2 Multiple Star Systems
2(1)
1.3 Dead Stars
2(1)
1.4 Supermassive Black Holes
3(1)
1.5 The Cast of Characters
4(3)
2 Physics Background
7(28)
2.1 Newton's Laws
7(3)
2.2 Coordinate Systems
10(4)
2.3 The Two-Body Problem
14(9)
2.4 The General N-Body Problem
23(2)
2.5 Multiplanet Systems
25(10)
3 First Two-Body Code
35(12)
3.1 Choosing a Programming Language
35(4)
3.2 Forward Euler Integrator
39(8)
4 Accuracy And Performance Of The Integration
47(16)
4.1 Structuring the Code
48(5)
4.2 Speeding Up the Code: Allocating Arrays
53(4)
4.3 Checking the Conservation Laws
57(6)
5 Fixed Step-Size Integration
63(22)
5.1 Truncation and Round-Off Errors
63(3)
5.2 Runge-Kutta Methods
66(5)
5.3 Multistep Methods
71(2)
5.4 Leapfrog Integrator
73(3)
5.5 Symplectic Integrators
76(4)
5.6 Numerical Performance
80(5)
6 Variable Step-Size Integration
85(20)
6.1 Estimating the Local Truncation Error
86(3)
6.2 Step-Size Control
89(3)
6.3 Initial Step Size
92(2)
6.4 Implementing Flexibility
94(2)
6.5 Numerical Performance
96(3)
6.6 Thoughts on Choosing the Integration Method
99(1)
6.7 Code Review
100(5)
7 The Three- And N-Body Problems
105(18)
7.1 From the Two-Body to the Three-Body Problem
105(8)
7.2 The N-Body Problem
113(10)
8 Gauss--Radau Integrator Of The Fifteenth Order
123(40)
8.1 Preparing the Second-Order System
124(1)
8.2 Numerical Quadratures: Choosing the Right Sequence
125(5)
8.3 Approximating the Integrand Using a Polynomial
130(2)
8.4 Approximating the Force Function
132(2)
8.5 Computing the Coefficients
134(3)
8.6 Radau Sequence and Integration Order
137(2)
8.7 Coding the Main Components of the Integrator
139(3)
8.8 Advancing One Integration Step
142(5)
8.9 The Complete Integrator
147(4)
8.10 Testing the Integrator
151(4)
8.11 Code Review
155(8)
9 Symplectic Map For Long-Term Integration
163(32)
9.1 Understanding Time Scales
164(2)
9.2 Long-Term Evolution
166(4)
9.3 Wisdom--Holman Integrator
170(16)
9.4 Propagating the Solar System for a Million Years
186(5)
9.5 Code Review
191(4)
10 Building A Production Code
195(46)
10.1 An Object-Oriented Discussion
195(2)
10.2 Requirement Analysis: What Do We Want Our Code to Be?
197(2)
10.3 Constructing the Software Framework
199(19)
10.4 Accelerating the Code Using Native C
218(23)
11 Defining The Project
241(6)
11.1 What Project to Tackle?
241(2)
11.2 Circumbinary Planets
243(4)
12 Setting Up The Project
247(16)
12.1 Initial Conditions
247(8)
12.2 The First Simulation
255(3)
12.3 Running on a Cluster
258(5)
13 Running And Analyzing The Simulations
263(22)
13.1 Problems with the Simulations
263(8)
13.2 A Suite of Integrations for Kepler-16
271(7)
13.3 The Other Kepler Systems
278(7)
14 How To Write A Publishable Research Paper
285(10)
14.1 Abstract
286(1)
14.2 Introduction
286(2)
14.3 Methods
288(2)
14.4 Results
290(2)
14.5 Discussion
292(1)
14.6 Summary
293(2)
15 Conclusions
295(4)
15.1 Physics of the N-Body Problem
295(1)
15.2 Programming Languages
296(1)
15.3 Numerical Integrators
297(1)
15.4 Research Project
297(1)
15.5 Publishing the Results
298(1)
APPENDICES
299(46)
A Derivation of Kepler's Third Law and the Kepler Equation
301(6)
A.1 The Kepler Equation
301(3)
A.2 Conserved Quantities in the N-Body Problem
304(3)
B Keplerian Propagator in Universal Variables
307(8)
B.1 Stumpff Functions
308(1)
B.2 Solving the Universal Kepler Equation
309(1)
B.3 Two-Body Propagator
310(5)
C Introduction to Matrices
315(4)
D Derivations in the Lidov--Kozai Problem
319(26)
D.1 The Three-Body Hamiltonian
319(4)
D.2 Averaging the Hamiltonian
323(8)
D.3 The Equations of Motion
331(7)
D.4 Analytic Solutions in the Test Particle Quadrupole-Order Limit
338(7)
Bibliography 345(4)
Index 349