Book contents
- Frontmatter
- Contents
- Preface
- How to Use the Book
- First Steps
- Project 1: Rectangular Finite Quantum Well – Stationary Schrödinger Equation in 1D
- Project 2: Diffraction of Light on a Slit
- Project 3: Pendulum as a Standard of the Unit of Time
- Project 4: Planetary System
- Project 5: Gravitation inside a Star
- Project 6: Normal Modes in a Cylindrical Waveguide
- Project 7: Thermal Insulation Properties of a Wall
- Project 8: Cylindrical Capacitor
- Advanced Projects
- Project 9: Coupled Harmonic Oscillators
- Project 10: The Fermi–Pasta–Ulam–Tsingou Problem
- Project 11: Hydrogen Star
- Project 12: Rectangular Quantum Well Filled with Electrons – The Idea of Self-Consistent Calculations
- Project 13: Time Dependent Schrödinger Equation
- Project 14: Poisson’s Equation in 2D
- Appendix A: Supplementary Materials
- Further Reading
- Index
Project 4: - Planetary System
Published online by Cambridge University Press: 01 February 2024
- Frontmatter
- Contents
- Preface
- How to Use the Book
- First Steps
- Project 1: Rectangular Finite Quantum Well – Stationary Schrödinger Equation in 1D
- Project 2: Diffraction of Light on a Slit
- Project 3: Pendulum as a Standard of the Unit of Time
- Project 4: Planetary System
- Project 5: Gravitation inside a Star
- Project 6: Normal Modes in a Cylindrical Waveguide
- Project 7: Thermal Insulation Properties of a Wall
- Project 8: Cylindrical Capacitor
- Advanced Projects
- Project 9: Coupled Harmonic Oscillators
- Project 10: The Fermi–Pasta–Ulam–Tsingou Problem
- Project 11: Hydrogen Star
- Project 12: Rectangular Quantum Well Filled with Electrons – The Idea of Self-Consistent Calculations
- Project 13: Time Dependent Schrödinger Equation
- Project 14: Poisson’s Equation in 2D
- Appendix A: Supplementary Materials
- Further Reading
- Index
Summary
This project involves the application of molecular dynamics (MD) to a simple two-dimensional planetary system consisting of two planets and a fixed star. The primary focus is to construct a MD code using Newton’s law of universal gravitation as the interaction law and the Verlet algorithm for solving the initial value problem. The project examines the gravitational interaction described by Newton’s laws, focusing on the law of universal gravitation and its application to the planetary system. It further explores the principle of equivalence, the concept of conservative force, and the effective potential energy of the system. The discussion also covers the reduction of a single planet motion to one dimension, which offers insights into the trajectory of the planetary system. Finally, the project outlines the numerical approach using the Verlet algorithm for simulating the motion of the planets. The comprehensive understanding of the gravitational interactions and the computational techniques provide a solid foundation for the study of complex dynamical systems.
Keywords
- Type
- Chapter
- Information
- A First Guide to Computational Modelling in Physics , pp. 26 - 33Publisher: Cambridge University PressPrint publication year: 2024