Dynamics of artificial satellite orbits with tesseral resonances including the effects of luni- solar perturbations

Ely, Todd A.; Howell, Kathleen C.

doi:10.1080/02681119708806247

Cited by 43 publications

(57 citation statements)

References 5 publications

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“…Unless the satellite is in a state of orbital resonance, where the satellite's mean motion is commensurable with the rotational motion of the Earth, the longitude-dependent tesseral terms of the geopotential have, generally, very little effect on the orbit and can be ignored (or, averaged) when looking on timescales much longer than one orbital period. Under resonance conditions, however, the longitudinal forces from the tesseral harmonics induce long-term changes in the semimajor axis and mean motion, leading to a libration in longitude (Ely and Howell, 1997). Contrary to higher-order zonal harmonics that essentially decay at high altitudes, tesseral resonances may become important, as the orbital period approaches commensurability with the Earth's rotation.…”

Section: Dynamical Modelmentioning

confidence: 99%

Dynamical cartography of Earth satellite orbits

Rosengren

Skoulidou

Tsiganis

et al. 2019

Advances in Space Research

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We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term (120 years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes (400 km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded ''ReDSHIFT" project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an ''atlas" of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth's oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest ''delta-v" (DV ) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth's atmosphere within reasonable timescales (50 years).

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Section: Dynamical Modelmentioning

confidence: 99%

Dynamical cartography of Earth satellite orbits

Rosengren

Skoulidou

Tsiganis

et al. 2019

Advances in Space Research

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“…In the present work, we perform the study of the effects of the gravitational resonances (also called tesseral resonances, see Gedeon (1969); Ely & Howell (1997)), within the LEO region. The precise definition of resonance is given as follows.…”

Section: The Geopotential Hamiltonianmentioning

confidence: 99%

“…This work extends the research performed in Celletti & Galeş (2014, 2015a, where analytical and numerical methods, mostly adopting Hamiltonian formalism, have been used to study the dynamics of objects within resonances located at large distances from the Earth (the so-called geostationary and GPS regions at distances, respectively, equal to 42 164 km and 26 560 km). We also mention Ely & Howell (1997); Formiga & Vilhena del Moraes (2011); ; for accurate modeling and analytical studies of space debris dynamics. With respect to Celletti & Galeş (2014, 2015a, the current work presents the novelty that, dealing with LEO, the model becomes more complicated, due to the effect of the geopotential, being the Earth very close, and moreover the dynamics is dissipative because of the air drag.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Resonances and Equilibria of Low Earth Objects

Celletti¹,

Galeş²

2018

SIAM J. Appl. Dyn. Syst.

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The nearby space surrounding the Earth is densely populated by artificial satellites and instruments, whose orbits are distributed within the Low-Earth-Orbit region (LEO), ranging between 90 and 2 000 km of altitude. As a consequence of collisions and fragmentations, many space debris of different sizes are left in the LEO region. Given the threat raised by the possible damages which a collision of debris can provoke with operational or manned satellites, the study of their dynamics is nowadays mandatory. This work is focused on the existence of equilibria and the dynamics of resonances in LEO. We base our results on a simplified model which includes the geopotential and the atmospheric drag. Using such model, we make a qualitative study of the resonances and the equilibrium positions, including their location and stability. The dissipative effect due to the atmosphere provokes a tidal decay, but we give examples of different behaviors, precisely a straightforward passage through the resonance or rather a temporary capture. We also investigate the effect of the solar cycle which is responsible of fluctuations of the atmospheric density and we analyze the influence of Sun and Moon on LEO objects.2010 Mathematics Subject Classification. 70F15, 37N05, 34D08.

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“…Often semi-analytical techniques are employed to obtain Poincaré or stroboscopic maps. For example, Ely and Howell (1997) apply averaging and Lie perturbation techniques to generate Poincaré plots for studying the stability of near-Earth orbits. Roth (1978Roth ( , 1979 uses semi-analytical techniques to stroboscopically map a perturbed orbit from pericenter to pericenter to achieve efficient propagation.…”

Section: Introductionmentioning

confidence: 99%

Element sets for high-order Poincaré mapping of perturbed Keplerian motion

Gondelach

Armellín

2018

Celest Mech Dyn Astr

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The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in celestial mechanics and astrodynamics, e.g. to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits over many revolutions. For this, the method uses the highorder Taylor expansion of a Poincaré or stroboscopic map, which is accurate close to the expansion point. In this paper, we investigate the performance of the HOTM method using different element sets for building the high-order map. The element sets investigated are the classical orbital elements, modified equinoctial elements, Hill variables, cylindrical coordinates and Deprit's ideal elements. The performances of the different coordinate sets are tested by comparing the accuracy and efficiency of mapping low-Earth and highly-elliptical orbits perturbed by J 2 with numerical propagation. The accuracy of HOTM depends strongly on the choice of elements and type of orbit. A new set of elements is introduced that enables extremely accurate mapping of the state, even for high eccentricities and higher-order zonal perturbations. Finally, the high-order map is shown to be very useful for the determination and study of fixed points and centre manifolds of Poincaré maps.

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Dynamics of artificial satellite orbits with tesseral resonances including the effects of luni- solar perturbations

Cited by 43 publications

References 5 publications

Dynamical cartography of Earth satellite orbits

Dynamical cartography of Earth satellite orbits

Dynamics of Resonances and Equilibria of Low Earth Objects

Element sets for high-order Poincaré mapping of perturbed Keplerian motion

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