arenstorf_ode

arenstorf_ode, a MATLAB 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:

arenstorf_ode_test

matlab_ode, MATLAB codes which set up various 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,
   ISBN: 3540566708,
   LC: QA372.H16.

Source Code:

• arenstorf_conserved.m, evaluates a conserved quantity of the ODE.
• arenstorf_deriv.m, returns the right hand side of the ODE.
• arenstorf_parameters.m, returns parameters of the ODE.