Extension of the King-Hele orbit contraction method for accurate, semi-analytical propagation of non-circular orbits. (arXiv:1905.07972v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Frey_S/0/1/0/all/0/1">Stefan Frey</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Colombo_C/0/1/0/all/0/1">Camilla Colombo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lemmens_S/0/1/0/all/0/1">Stijn Lemmens</a>
Numerical integration of orbit trajectories for a large number of initial
conditions and for long time spans is computationally expensive.
Semi-analytical methods were developed to reduce the computational burden. An
elegant and widely used method of semi-analytically integrating trajectories of
objects subject to atmospheric drag was proposed by King-Hele (KH). However,
the analytical KH contraction method relies on the assumption that the
atmosphere density decays strictly exponentially with altitude. If the actual
density profile does not satisfy the assumption of a fixed scale height, as is
the case for Earth’s atmosphere, the KH method introduces potentially large
errors for non-circular orbit configurations.
In this work, the KH method is extended to account for such errors by using a
newly introduced atmosphere model derivative. By superimposing exponentially
decaying partial atmospheres, the superimposed KH method can be applied
accurately while considering more complex density profiles. The KH method is
further refined by deriving higher order terms during the series expansion. A
variable boundary condition to choose the appropriate eccentricity regime,
based on the series truncation errors, is introduced. The accuracy of the
extended analytical contraction method is shown to be comparable to numerical
Gauss-Legendre quadrature. Propagation using the proposed method compares well
against non-averaged integration of the dynamics, while the computational load
remains very low.
Numerical integration of orbit trajectories for a large number of initial
conditions and for long time spans is computationally expensive.
Semi-analytical methods were developed to reduce the computational burden. An
elegant and widely used method of semi-analytically integrating trajectories of
objects subject to atmospheric drag was proposed by King-Hele (KH). However,
the analytical KH contraction method relies on the assumption that the
atmosphere density decays strictly exponentially with altitude. If the actual
density profile does not satisfy the assumption of a fixed scale height, as is
the case for Earth’s atmosphere, the KH method introduces potentially large
errors for non-circular orbit configurations.
In this work, the KH method is extended to account for such errors by using a
newly introduced atmosphere model derivative. By superimposing exponentially
decaying partial atmospheres, the superimposed KH method can be applied
accurately while considering more complex density profiles. The KH method is
further refined by deriving higher order terms during the series expansion. A
variable boundary condition to choose the appropriate eccentricity regime,
based on the series truncation errors, is introduced. The accuracy of the
extended analytical contraction method is shown to be comparable to numerical
Gauss-Legendre quadrature. Propagation using the proposed method compares well
against non-averaged integration of the dynamics, while the computational load
remains very low.
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