modified_equinoctial_module Module

Modified equinoctial elements routines.

The modified equinoctial elements are applicable to all orbits and have non-singular equations of motion (except for a singularity at $i = \pi$ ). They are defined as:

$$\begin{array}{rcl} p & = & a (1 - e^2) \\ f & = & e \cos (\omega + \Omega) \\ g & = & e \sin (\omega + \Omega) \\ h & = & \tan (i/2) \cos \Omega \\ k & = & \tan (i/2) \sin \Omega \\ L & = & \Omega + \omega + \nu \\ \end{array}$$

Where $L$ is the true longitude, $p$ is the semi-latus rectum, and $\nu$ is the true anomaly.

References

• Broucke, R. A. & Cefola, P. J., "On the Equinoctial Orbit Elements" Celestial Mechanics, Volume 5, Issue 3, p 303-310. (1972)
• M. J. H. Walker, B. Ireland, Joyce Owens, "A Set of Modified Equinoctial Orbit Elements" Celestial Mechanics, Volume 36, Issue 4, p 409-419. (1985)
• Walker, M. J. H, "Erratum - a Set of Modified Equinoctial Orbit Elements" Celestial Mechanics, Volume 38, Issue 4, p 391-392. (1986)