9772

Sensitive Dependence on Initial Conditions in a Simple Three-Body Problem

A planet moves under the gravitational influence of two stars of equal mass (very large compared with the planet), in orbits with eccentricity around their center of gravity. The planet moves in a plane perpendicular to the plane of the stars, passing through their center of gravity. The differential equation is solved for initial position in the range and velocity . The system shows sensitive dependence on initial conditions, despite the simplicity of the equation of motion. This problem was studied by the Soviet mathematician Kirill Sitnikov.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The differential equation describing the system is
.
References
[1] K. Sitnikov, "The Existence of Oscillatory Motions in the Three-Body Problem," Doklady Akademii Nauk SSSR (Physics), 133, 1960 pp. 303–306.
[2] B. Casselman, "What Is the Length of a Year on Planet Sitnikov?" (Dec 26, 2012) www.ams.org/samplings/feature-column/fcarc-sitnikov.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+