Moving Planets Around, An Introduction to N-Body Simulations Applied to Exoplanetary Systems by Roa, Javier -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Table of Contents List of Code Snippets Acknowledgments Foreword Prologue 1. A Bestiary of Planets

1.1. Many Moons 1.2. Multiple Star Systems 1.3. Dead Stars 1.4. Supermassive Black Holes 1.5. The Cast of Characters

2. Physics Background

2.1. Newton’s Laws 2.2. Coordinate Systems 2.3. The Two-Body Problem 2.4. The General N-Body Problem 2.5. Multiplanet Systems

3. First Two-Body Code

3.1. Choosing a Programming Language 3.2. Forward Euler Integrator

4. Accuracy and Performance of the Integration

4.1. Structuring the Code 4.2. Speeding Up the Code: Allocating Arrays 4.3. Checking the Conservation Laws

5. Fixed Step-Size Integration

5.1. Truncation and Round-Off Errors 5.2. Runge–Kutta Methods 5.3. Multistep Methods 5.4. Leapfrog Integrator 5.5. Symplectic Integrators 5.6. Numerical Performance

6. Variable Step-Size Integration

6.1. Estimating the Local Truncation Error 6.2. Step-Size Control 6.3. Initial Step Size 6.4. Implementing Flexibility 6.5. Numerical Performance 6.6. Thoughts on Choosing the Integration Method 6.7. Code Review

7. The Three- and N-Body Problems

7.1. From the Two-Body to the Three-Body Problem 7.2. The N-Body Problem

8. Gauss–Radau Integrator of the Fifteenth Order

8.1. Preparing the Second-Order System 8.2. Numerical Quadratures: Choosing the Right Sequence 8.3. Approximating the Integrand Using a Polynomial 8.4. Approximating the Force Function 8.5. Computing the Coefficients 8.6. Radau Sequence and Integration Order 8.7. Coding the Main Components of the Integrator 8.8. Advancing One Integration Step 8.9. The Complete Integrator 8.10. Testing the Integrator 8.11. Code Review

9. Symplectic Map for Long-Term Integration

9.1. Understanding Time Scales 9.2. Long-Term Evolution 9.3. Wisdom–Holman Integrator 9.4. Propagating the Solar System for a Million Years 9.5. Code Review

10. Building a Production Code

10.1. An Object-Oriented Discussion 10.2. Requirement Analysis: What Do We Want Our Code to Be? 10.3. Constructing the Software Framework 10.4. Accelerating the Code Using Native C

11. Defining the Project

11.1. What Project to Tackle? 11.2. Circumbinary Planets

12. Setting Up the Project

12.1. Initial Conditions 12.2. The First Simulation 12.3. Running on a Cluster

13. Running and Analyzing the Simulations

13.1. Problems with the Simulations 13.2. A Suite of Integrations for Kepler-16 13.3. The Other Kepler Systems

14. How to Write a Publishable Research Paper

14.1. Abstract 14.2. Introduction 14.3. Methods 14.4. Results 14.5. Discussion 14.6. Summary

15. Conclusions

15.1. Physics of the N-Body Problem 15.2. Programming Languages 15.3. Numerical Integrators 15.4. Research Project 15.5. Publishing the Results

Appendices

A. Derivation of Kepler’s Third Law and the Kepler Equation

A.1. The Kepler Equation A.2. Conserved Quantities in the N-Body Problem

B. Keplerian Propagator in Universal Variables

B.1. Stumpff Functions B.2. Solving the Universal Kepler Equation B.3. Two-Body Propagator

C. Introduction to Matrices D. Derivations in the Lidov–Kozai Problem

D.1. The Three-Body Hamiltonian D.2. Averaging the Hamiltonian D.3. The Equations of Motion D.4. Analytic Solutions in the Test Particle Quadrupole-Order Limit

Bibliography Index