Celestial Mechanics

Homework of Fundamental Celestial Mechanics Class. This is a project of source codes and some pictures I wrote to solve the problems in the textbook.

The textbook is written by Jilin Zhou @ NJU.

Requirement

In case someone wants to use my code:

This project need the static library of another project of mine : MyRecipes

Besides of this, you need those programs/modules installed in your computer:

• gcc
• make
• python
  • numpy
  • matplotlib

Chapter 2

Problem 2.6

Transformation between orbital elements and coordinate-velocity of a celestial body.

related files:

transform.c

Problem 2.7

Use RKF7(8) method to integrate the two-body motion's differential equation for more than two periods. Check the conservation of energy.

related files:

OrbitEvaluation.c

plotorbit.py

Chapter 3

Problem 3.2

Find circular restricted three-body problem orbit using RKF7(8) method. Check the conservation of C_J.

Plot the contour map of C_J in z=0 plane.

Find at least three kinds of motions.

related files:

CircularRTB.c

orbitplot.py

plotcontour.py

Problem 3.4

Use numerical method to plot the Poincare section among the five Lagrangian points in circular restricted 3-body problem.

related files

CircularRTB.c

PoincareMapRTB.py

Problem 3.6

Plot the phase diagram of circular and elliptic Sitnikov problem.

related files

CircularSitnikov.c

EllipticSitnikov.c

plotcontour.py

Chapter 4

Problem 4.1

The perturbation potential of two body system is U = - c / r^2, solve the perturbation equations using numerical method.

related files

Perturbation.c

plotperturbation.py

Problem 4.3

Calculate the Laplace coefficient. Refer to the values in equation (4.163) in the textbook.

related files

LaplaceCoefficient.c