arenstorf_ode

arenstorf_ode, a Python code which sets up an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.

Although the orbit should be periodic, and repeats after a time interval of a little more than 17 units, most ODE solvers will have difficulty coming close to periodicity.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

arenstorf_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

python_ode, Python codes which sets up various systems of ordinary differential equations (ODE).

References:

1. Richard Arenstorf,
   Periodic solutions of the restricted three body problem representing analytic continuations of Keplerian elliptic motions,
   American Journal of Mathematics,
   Volume 85, Number 1, pages 27-35, January 1963.
2. John D Cook,
   The orbit that put men on the moon,
   https://www.johndcook.com/blog/
   Posted 08 February 2020.
3. Ernst Hairer, Syvert Norsett, Gerhard Wanner,
   Solving Ordinary Differential Equations I: Nonstiff Problems,
   Springer, 1987.

Source Code:

• arenstorf_ode.py, the source code.
• arenstorf_ode.sh, runs all the tests.
• arenstorf_ode.txt, the output file.

• arenstorf_euler_phase.png, a phase plane plot of x versus y, computed by euler().
• arenstorf_solve_ivp_phase.png, a phase plane plot of x versus y, computed by solve_ivp().