Analytical orbit predictions with air drag using KS uniformly regular canonical elements

Raj, Mamata; Sharma, Ram Krishan

doi:10.1016/j.pss.2005.12.006

Cited by 6 publications

(2 citation statements)

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“…Analytical formulations, such as the one derived by D. King-Hele more than half a century ago (King-Hele, 1964) require the density to be evaluated only once per iteration in correspondence of the perigee altitude. Other examples of analytical formulations are the ones derived by Vinh et al (1979), Sharma (1999) and Xavier James Raj and Sharma (2006). While offering improvements to the classical formulation of KH, such as being mathematically more rigorous and non-singular, they still suffer from the same assumption of a fixed scale height.…”

Section: Background On Semi-analytical Orbit Contraction Methodsmentioning

confidence: 99%

“…Vinh et al (1979) improved the theory by removing the ambiguity arising from the regions of validity in eccentricity and by applying the more mathematically rigorous Poincaré method for integration. The classical theory was adapted to non-singular elements, mitigating the problems that theories formulated in Keplerian elements have with vanishing eccentricities (Sharma, 1999;Xavier James Raj and Sharma, 2006).…”

Section: Introductionmentioning

confidence: 99%

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Extension of the King-Hele orbit contraction method for accurate, semi-analytical propagation of non-circular orbits

Frey

Colombo

Lemmens

2019

Advances in Space Research

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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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Section: Background On Semi-analytical Orbit Contraction Methodsmentioning

confidence: 99%