Mean Element Propagations Using Numerical Averaging

Ely, Todd A.

doi:10.1007/s40295-014-0020-2

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…The short-term effect of perturbations is eliminated by averaging the variational equations, or the corresponding potential, over one orbit revolution of the small body. Indeed, averaging corresponds to filtering the higher frequencies of the motion (periodic over one orbit revolution), which typically have small amplitudes (Ely, 2014). The resulting system allows a deeper understanding of the dynamics (Shapiro, 1995;Krivov and Getino, 1997).…”

Section: Introductionmentioning

confidence: 99%

Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry

Colombo

2019

Front. Astron. Space Sci.

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This paper investigates the long-term evolution of spacecraft in Highly Elliptical Orbits (HEOs). The single averaged disturbing potential due to luni-solar perturbations, zonal harmonics of the Earth gravity field is written in mean Keplerian elements. The double averaged potential is also derived in the Earth-centered equatorial system. Maps of long-term orbit evolution are constructed by measuring the maximum variation of the orbit eccentricity to identify conditions for quasi-frozen, long-lived libration orbits, or initial orbit conditions that naturally evolve toward re-entry in the Earth's atmosphere. The behavior of these long-term orbit maps is studied for increasing values of the initial orbit inclination and argument of the perigee with respect to the Moon's orbital plane. In addition, to allow meeting specific mission constraints, quasi-frozen orbits can be selected as graveyard orbits for the end-of-life of HEO missions, in the case re-entry option cannot be achieved due to propellant constraints. On the opposite side, unstable conditions can be exploited to target Earth re-entry at the end-of-mission.

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Section: Introductionmentioning

confidence: 99%

Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry

Colombo

2019

Front. Astron. Space Sci.

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“…Dissipative perturbations such as atmospheric drag cannot be expressed as the gradient of a disturbing function. In this case, the rates of change of the osculating elements can be written in Gauss form and the perturbing acceleration can be numerically averaged over one orbital period (Uphoff, 1973;Ely, 2014).…”

Section: Averaging Perturbing Accelerationsmentioning

confidence: 99%

Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

Amato

Bombardelli

Baù

et al. 2019

Celest Mech Dyn Astr

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This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.

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“…In order to study the long-term evolution behavior of the Galilean moon probe, researchers applied the mean element theory to eliminate the short-period variations in the orbital elements [4,5]. It was first employed to construct the secular evolution model with respect to classic orbital elements under the non-spherical gravitation perturbation of the central body such as the zonal terms J2 and J3 [6], the harmonic term C22 [7], and irregular celestial body shapes [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…It was first employed to construct the secular evolution model with respect to classic orbital elements under the non-spherical gravitation perturbation of the central body such as the zonal terms J2 and J3 [6], the harmonic term C22 [7], and irregular celestial body shapes [8,9]. Later, the third-body gravitation perturbation of the planet was taken into account, and the secular evolution behavior was studied in the planetary system exploration mission [5,[10][11][12]. Scheeres et al [11] and Broucke [13] derived the secular Lagrange equations of a Europa probe under Europa's non-spherical gravitation and Jovian third-body gravitation perturbations.…”

Section: Introductionmentioning

confidence: 99%

Design of Ganymede-Synchronous Frozen Orbit around Europa

Huang

Yang

et al. 2022

Mathematics

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A Ganymede-synchronous frozen orbit around Europa provides a stable spatial geometry between a Europa probe and a Ganymede lander, which facilitates the observation of Ganymede and data transmission between probes. However, the third-body gravitation perturbation of Ganymede continues to accumulate and affect the long-term evolution of the Europa probe. In this paper, the relative orbit of Ganymede with respect to Europa is considered to accurately capture the perturbation potential. The orbital evolution behaviors of the Europa probe under the non-spherical gravitation of Europa and the third-body gravitation of Jupiter and Ganymede are studied based on a double-averaging framework. Then, the initial orbital conditions of the Ganymede-synchronous frozen orbit are developed. A station-keeping maneuver was performed to maintain the orbital elements to achieve the Ganymede-synchronous and frozen behaviors. A numerical simulation showed that the consumption for orbital maintenance is acceptable.

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Mean Element Propagations Using Numerical Averaging

Cited by 9 publications

References 21 publications

Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry

Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry

Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

Design of Ganymede-Synchronous Frozen Orbit around Europa

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