Lesson 5 - Kepler’s Planets, Orbits in 3D & Other Python Solvers: Choose your own adventure

Main Lecture Materials

Today we’ll continue our simulations in 2D and we’ll start thinking in 3D as well. There are links to other solvers as well, but they are not required if you like the Hermite one!

Motivation: Online 3D solar system interactive animation - https://theskylive.com/3dsolarsystem

Notes:

• Part1_programming_readWriteData_keplersData_lesson05.pdf
• Part2_planetsIn3D_lesson05.pdf

Python Libraries

Note: put these in the same directory as your .pynb notebooks.

• hermite_library.py
• convert_kepler_data.py
• convert_galaxy_data.py

Data

• Kepler 11 System Data
• Kepler 101 System Data

Galaxy snapshot files - different resolutions

• low res - galaxySnaps/snap_001_fac1n3.txt
• mid res - galaxySnaps/snap_001_fac1n2.txt
• high res - galaxySnaps/snap_001_fac1n1.txt

Reading

• This paper by Piet Hut talks about the evolution of numerical simulations in science.

Other Python Solvers

You can check out these other solvers either now or come back to later in your life. Order is in order of decreasing documentation/increasing difficulty.

Rebound

Rebound has both C and Python implementations to solve N-body equations with a variety of solvers. There are other examples that include comments on the Rebound examples page if you find something of interest to explore there (make sure you use only the Python ones).

• The Rebound Solar System Project: uses the Rebound Python package to calculate up-to-date orbits of our own solar system. Extension question deals with adding more planets.

• The Rebound Galaxies Project: uses Rebound to integrate the motion of the galaxies presented in Lesson 4. Extensions include generating your own initial conditions with pyICs.

SciPy

SciPy is a package that does all kinds of neat scientific calculation stuffs. Check out this example of how to use it to make your own 2D N-body integrator. How would you extend this to 3D?

Others

There are many GitHub repos for N-body Solvers in Python and other languages that you may want to check out.

Materials

• Lecture 5, Part 1 - Kepler's Orbits: (view, source, present)
• Lecture 5, Part 2 - Multibody Motion in 3D: (view, source, present)
• Optional - Galaxy Multibody Motion in 3D: (view, source, present)
• Rebound Galaxies: (view, source)
• Rebound Solar System: (view, source)
• Notebook Optional_animations_lesson05: (view, download)
• Notebook Optional_galaxySimulations_3d_lesson05: (view, download)
• Notebook Part1_programming_readWriteData_keplersData_lesson05: (view, download)
• Notebook Part2_planetsIn3D_lesson05: (view, download)
• Notebook Untitled: (view, download)
• Notebook inClass_lesson05: (view, download)