Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory. (arXiv:2012.09620v3 [astro-ph.EP] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Arnas_D/0/1/0/all/0/1">David Arnas</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Linares_R/0/1/0/all/0/1">Richard Linares</a>
This work introduces the use of the Koopman operator theory to generate
approximate analytical solutions for the zonal harmonics problem of a satellite
orbiting a non-spherical celestial body. Particularly, the solution proposed
directly provides the osculating evolution of the system under the effects of
any order of the zonal harmonics, and can be automated to obtain any level of
accuracy in the approximated solution. Moreover, this paper defines a modified
set of orbital elements that can be applied to any kind of orbit and that
allows the Koopman operator to have a fast convergence. In that regard, several
examples of application are included, showing that the proposed methodology can
be used in any kind of orbit, including circular, elliptic, parabolic and
hyperbolic orbits.
This work introduces the use of the Koopman operator theory to generate
approximate analytical solutions for the zonal harmonics problem of a satellite
orbiting a non-spherical celestial body. Particularly, the solution proposed
directly provides the osculating evolution of the system under the effects of
any order of the zonal harmonics, and can be automated to obtain any level of
accuracy in the approximated solution. Moreover, this paper defines a modified
set of orbital elements that can be applied to any kind of orbit and that
allows the Koopman operator to have a fast convergence. In that regard, several
examples of application are included, showing that the proposed methodology can
be used in any kind of orbit, including circular, elliptic, parabolic and
hyperbolic orbits.
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