Lecture

Stability of a Planet's Orbit

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In course

PHYS-203: Computational physics I

Aborder, formuler et résoudre des problèmes de physique en utilisant des méthodes numériques simples. Comprendre les avantages et les limites de ces méthodes (stabilité, convergence). Illustrer différents sujets de physique traités dans d'autres cours. ...

Description

This lecture covers the examination of the stability of a planet's orbit, focusing on writing code to analyze the orbit's behavior. Topics include the use of Runge-Kutta numerical integration, hierarchical organization of data, and the study of double star systems.

Instructor

Laurent Villard

Teaching & PhD Past EPFL PhD Students Matteo Maccio, Olivier Fischer, Gloria Luisa Falchetto, Paolo Angelino, Sébastien Jolliet, Xavier Lapillonne, Thibaut Vernay, Julien Stanislas Pierre Dominski, Gabriele Merlo, Emmanuel Lanti, Noé Ohana, Moahan Murugappan

Official source

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Verlet integration

Verlet integration (vɛʁˈlɛ) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C.

Planet

A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young protostar orbited by a protoplanetary disk. Planets grow in this disk by the gradual accumulation of material driven by gravity, a process called accretion. The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.

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