PPKBZ9 $$\mathcal{A}, \mathcal{S}\mathcal{A}$$ Two Orbit Propagators Based on an Analytical Theory

San-Juan, Juan F.; Gavín, A.; López, Luis M.; López, Rosa

doi:10.1007/bf03321535

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…In return, the most classical theories (e.g. [5], [1], [3]) for which the whole J 2 perturbation is relegated in H 1 are no longer directly usable. We have to construct another solution taking into account the new sharing of the J 2 disturbing function.…”

Section: Discussionmentioning

confidence: 99%

Towards an analytical theory of the third-body problem for highly elliptical orbits

Lion,

Métris,

Deleflie

2016

Preprint

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When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the altitude of the satellite becomes high, which is the case around the apocentre of this type of orbit. For several reasons, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and therefore limited to quasi-circular orbits [17,25]. On the other hand, the time-dependency due to the motion of the third-body is often neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the disturbing function into a finite polynomial using Fourier expansions of elliptic motion functions in multiple of the satellite's eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, we show how to perform a normalization of the expanded Hamiltonian by means of a time-dependent Lie transformation which aims to eliminate periodic terms. The difficulty lies in the fact that the generator of the transformation must be computed by solving a partial differential equation involving variables which are linear with time and the eccentric anomaly which is not time linear. We propose to solve this equation by means of an iterative process.

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Section: Discussionmentioning

confidence: 99%

Towards an analytical theory of the third-body problem for highly elliptical orbits

Lion,

Métris,

Deleflie

2016

Preprint

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“…the Mars Global Surveyor (i = 93 • , e ≈ 0.008, pericenter altitude 372 km). Analytical approaches to the study of their dynamics have been proposed by San-Juan et al (2011), for an axisymmetric model. Here, we focus on the conditions needed to effectively retain very low altitude, namely a 'circular altitude' a − R ⊗ less than 100 km, where a is the semi-major axis of the satellite and R ⊗ the mean equatorial radius of Mars.…”

Section: Introductionmentioning

confidence: 99%

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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“…In the case of numerical integration, the emphasis has been placed on achieving both a higher accuracy and faster algorithms, which can take advantage of parallel computing [14] in multicore and GPU computational systems. Alternatively, the research activity on analytical and semianalytical techniques has mainly been focused on extending to higher orders the required series expansions [15], as well as on completing their perturbation models.…”

Section: Introductionmentioning

confidence: 99%

Hybrid SGP4 orbit propagator

et al. 2017

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Two-Line Elements (TLEs) continue to be the sole public source of orbiter observations. The accuracy of TLE propagations through the Simplified General Perturbations-4 (SGP4) software decreases dramatically as the propagation horizon increases, and thus the period of validity of TLEs is very limited. As a result, TLEs are gradually becoming insufficient for the growing demands of Space Situational Awareness (SSA). We propose a technique, based on the hybrid propagation methodology, aimed at extending TLE validity with minimal changes to the current TLE-SGP4 system in a non-intrusive way. It requires that the institution in possession of the osculating elements distributes hybrid TLEs, HTLEs, which encapsulate the standard TLE and the model of its propagation error. The validity extension can be accomplished when the end user processes HTLEs through the hybrid SGP4 propagator, HSGP4, which comprises the standard SGP4 and an error corrector.Comment: 18 pages, 4 figure

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PPKBZ9 $$\mathcal{A}, \mathcal{S}\mathcal{A}$$ Two Orbit Propagators Based on an Analytical Theory

Cited by 4 publications

References 18 publications

Towards an analytical theory of the third-body problem for highly elliptical orbits

Towards an analytical theory of the third-body problem for highly elliptical orbits

Design of low-altitude Martian orbits using frequency analysis

Hybrid SGP4 orbit propagator

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