Satellite orbits design using frequency analysis

Noullez, A.; Tsiganis, K.; Tzirti, S.

doi:10.1016/j.asr.2015.03.031

Cited by 5 publications

(17 citation statements)

References 24 publications

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“…The frequency analysis algorithm I use is based on NAFF (see (Laskar 1993) for the method, and (Laskar 2005) for the convergence proofs), with a refinement suggested by (Champenois 1998) consisting in iterating the process to improve the accuracy of the determination. Correcting the initial condition to remove free oscillations has been used in different contexts these last years (Locatelli & Giorgili 2000;Noyelles 2009;Couetdic et al 2010;Robutel et al 2011;Delsate 2011;Hou et al 2014), and the convergence of this algorithm is addressed in (Noyelles et al 2011). Noullez et al (2015 propose a similar algorithm for the computation of periodic orbits of artificial satellites of the Earth, but in using de Prony's frequency analysis (de Prony 1795; Tzirti et al 2014).…”

Section: An Iterative Algorithmmentioning

confidence: 99%

Rotation of a synchronous viscoelastic shell

Noyelles

2017

Monthly Notices of the Royal Astronomical Society

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Several natural satellites of the giant planets have shown evidence of a global internal ocean, coated by a thin, icy crust. This crust is probably viscoelastic, which would alter its rotational response. This response would translate into several rotational quantities, i.e. the obliquity, and the librations at different frequencies, for which the crustal elasticity reacts differently.This study aims at modelling the global response of the viscoelastic crust. For that, I derive the time-dependency of the tensor of inertia, which I combine with the time evolution of the rotational quantities, thanks to an iterative algorithm. This algorithm combines numerical simulations of the rotation with a digital filtering of the resulting tensor of inertia.The algorithm works very well in the elastic case, provided the problem is not resonant. However, considering tidal dissipation adds different phase lags to the oscillating contributions, which challenge the convergence of the algorithm.

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Section: An Iterative Algorithmmentioning

confidence: 99%

Rotation of a synchronous viscoelastic shell

Noyelles

2017

Monthly Notices of the Royal Astronomical Society

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“…Recently, in (Tzirti et al, 2014) and (Noullez et al, 2015), we studied low-altitude satellite orbits around the Moon, using a novel frequency analysis (FA) algorithmthat we called Prony's method -as a tool for obtaining a global view of the secular dynamics, in arbitrary lunar gravity models. Our numerical FA method is quite efficient, as only short trajectory arcs are necessary for deriving an accurate quasi-periodic decomposition of the orbit; thus it can be applied to large sets of initial conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In (Noullez et al, 2015) we also presented an iterative filtering algorithm, as a tool that allows efficient computation of the families of POs of the 2-d.o.f problem. The algorithm is not really 'new'; it has been 'rediscovered' many times in celestial mechanics, for example by Couetdic et al (2010), who used it to locate stable, resonant periodic orbits in two-planet systems, Noyelles (2009) and Robutel et al (2011) who studied the 3:2 spin-orbit resonance problem and 1:1 resonant coorbital rotation, Dufey et al (2009) who analyzed the libration of Mercury, or Delsate (2011) who studied ground-track resonances around Vesta.…”

Section: Introductionmentioning

confidence: 99%

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Design of low-altitude Martian orbits using frequency analysis

Noullez

Tsiganis²

2021

Advances in Space Research

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Nearly-circular Frozen Orbits (FOs) around axisymmetric bodies -or, quasi-circular Periodic Orbits (POs) around non-axisymmetric bodies -are of primary concern in the design of low-altitude survey missions. Here, we study very low-altitude orbits (down to 50 km) in a high-degree and order model of the Martian gravity field. We apply Prony's Frequency Analysis (FA) to characterize the time variation of their orbital elements by computing accurate quasi-periodic decompositions of the eccentricity and inclination vectors. An efficient, iterative filtering algorithm, previously applied to lunar orbiters, complements the method and is used to accurately compute the locations of POs/FOs, for a wide range of initial conditions. By defining the 'distance' of any orbit from the family of POs and using the relative amplitudes of the different components of the motion, we can build 'dynamical fate maps' that graphically depict the survivability of low-eccentricity, low-altitude orbits at every inclination, and can be used for efficient mission planning. While lowering the altitude generally enhances the effect of tesseral and sectorial gravity harmonics, we find this to have less consequence for low altitude Martian satellites, in contrast with the Lunar case. Hence, a high-degree ( 20 th ) axisymmetric model is adequate for preliminary mission design at moderate altitudes, but should be complemented at low altitudes by the methods described here. All families of POs and their spectral decompositions can be accurately and effectively computed by continuation in arbitrarily complex Martian gravity models, as our filtering algorithm requires only short integration arcs.

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“…Indeed the effect of the function f 0 is reduced to a small contribution, i.e., relegated. The relegation algorithm has been successfully used in celestial mechanics [18][2] [4] and artificial satellite theory [12] [13] , with a particular focus on the dynamics close to asteroids (the so-called fast-rotating case) [3][19][6] [16] . Let us remark that a similar normal form approach has also been introduced in [1], where the authors studied the problem of the energy exchanges between a system of uncoupled harmonic oscillators and a generic other dynamical system, playing the role of the functions h 0 and f 0 of the relegation algorithm, respectively.…”

Section: Introductionmentioning

confidence: 99%

Rigorous estimates for the relegation algorithm

Sansottera

Ceccaroni

2016

Celest Mech Dyn Astr

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Abstract. We revisit the relegation algorithm by Deprit et al. (2001) in the light of the rigorous Nekhoroshev's like theory. This relatively recent algorithm is nowadays widely used for implementing closed form analytic perturbation theories, as it generalises the classical Birkhoff normalisation algorithm. The algorithm, here briefly explained by means of Lie transformations, has been so far introduced and used in a formal way, i.e. without providing any rigorous convergence or asymptotic estimates. The overall aim of this paper is to find such quantitative estimates and to show how the results about stability over exponentially long times can be recovered in a simple and effective way, at least in the non-resonant case.

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Satellite orbits design using frequency analysis

Cited by 5 publications

References 24 publications

Rotation of a synchronous viscoelastic shell

Rotation of a synchronous viscoelastic shell

Design of low-altitude Martian orbits using frequency analysis

Rigorous estimates for the relegation algorithm

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