arenstorf_ode

arenstorf_ode, an Octave code which describes 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 information on this web page is 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

octave_ode, an Octave code which sets 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.

Source Code:

• arenstorf_deriv.m, dxydt=arenstorf_deriv(t,xy) returns the right hand side of the Arenstorf ODE.
• arenstorf_parameters.m, returns parameters of the Arenstorf ODE.
• timestamp.m, prints the YMDHMS date as a timestamp.