samson-mano / lagrange_points

Numerical solution of Circular restricted three-body problem in which the mass of one of the bodies is negligible, as well as the interaction forces between it and the other two bodies.

Lagrange Points of Circular resticted three-body problem

Numerical solution of Circular restricted three-body problem in which the mass of one of the bodies is negligible, as well as the interaction forces between it and the other two bodies. The problem is solved by considering the effective potential. For circular restricted three-body problem there are five Lagrangian points which are the five particular solutions for this problem. Using Lagrangian mechanics (principle of least action), Lagrange solved the way in which the lightest body would orbit around the two heavy bodies in a circular orbit. In the rotating frame, he found the five specific points where no net force is working on the lightest body. The numerical expression of this problem is presented in this project.

Lagrange Points

Example: Lagrange Points with Mass ratio 0.03

References

• Lecture L18 - Exploring the Neighborhood: the Restricted Three-Body Problem
https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec18.pdf
• CHAPTER 16 - THE RESTRICTED THREE-BODY PROBLEM
http://astrowww.phys.uvic.ca/~tatum/celmechs/celm16.pdf