Analysis of the TOPEX/Poseidon Operational Orbit: Observed Variations and Why

Frauenholz, R. B.; Bhat, R. S.; Shapiro, Bruce E.; Leavitt, R. K.

doi:10.2514/2.3312

Cited by 14 publications

(4 citation statements)

References 7 publications

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“…The mild behavior of the mean anomaly is due to the additional term in (40) for the secular part of mean motion n ˚when compared with the usual secular rate in (42). We checked that if the later is used instead of the former, the error in the mean anomaly grows by about two orders of magnitude at the end of the one-day interval in the current example, reaching an amplitude close to one degree, which translates into about two hundred km along-track as opposed to the km level obtained when using n For a second example we take a low-eccentricity orbit with the initial conditions a " 7707.27 km, e " 0.01, I " 63.4 ˝, Ω " 180 ˝, ω " 270 ˝, M " 0, (58) corresponding to the configuration of the popular Topex orbit [44], and the propagation is likewise carried out up to one day, which now amounts to about 13 orbits. We checked that the agreement between the mean elements dynamics and the average dynamics of the true orbit preserves in each case an analogous number of digits to the previous example.…”

Section: Examplesmentioning

confidence: 99%

Earth satellite dynamics by Picard iterations

Lara¹

2022

Preprint

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The main effects of the Earth's oblateness on the motion of artificial satellites are usually derived from the variation of parameters equations of an average representation of the oblateness disturbing function. Rather, we approach their solution under the strict mathematical assumptions of Picard's iterative method. Our approach recovers the known linear trends of the right ascension of the ascending node and the argument of the perigee, but differs from the accepted solution in the value of the mean motion. This amended rate radically improves the in-track errors of typical orbit propagations. In addition, our truncation of the Picard iterations solution to its secular terms includes the corrections that must be applied to the osculating initial conditions in the right propagation of the mean dynamics.

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Section: Examplesmentioning

confidence: 99%

Earth satellite dynamics by Picard iterations

Lara¹

2022

Preprint

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“…The third test has been specifically carried out to check the behavior of the analytical solution when approaching the critical inclination resonance. For this last case we selected an orbit with orbital parameters similar to the TOPEX orbit, which departs only ∼ 3 • from the inclination resonance condition [20]. Orbital elements corresponding to these three cases are presented in Table 12.…”

Section: Performance Of the Solutionmentioning

confidence: 99%

Solution to the main problem of the artificial satellite by reverse normalization

Lara

2020

Preprint

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The non-linearities of the dynamics of Earth artificial satellites are encapsulated by two formal integrals that are customarily computed by perturbation methods. Standard procedures begin with a Hamiltonian simplification that removes non-essential short-period terms from the Geopotential, and follow with the removal of both short-and longperiod terms by means of two different canonical transformations that can be carried out in either order. We depart from the tradition and proceed by standard normalization to show that the Hamiltonian simplification part is dispensable. Decoupling first the motion of the orbital plane from the inplane motion reveals as a feasible strategy to reach higher orders of the perturbation solution, which, besides, permits an efficient evaluation of the long series that comprise the analytical solution.

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“…This paper seeks to provide study of a potential solution to impose safe segregation between orbital shells while improving orbital capacity relative to these alternatives by relying on the use of frozen orbits and taking advantage of the approximate latitude-based altitude dependency that these shells exhibit. Many Earth-observing missions have used frozen orbits to minimize radial orbit variation, beginning with Seasat [2], ERS-1 and ERS-2 [3], and TOPEX/Poseidon [4], and continuing to more modern Earth observation missions that are required to maintain a near fixed radial distance to a ground site [5,880]. Reference [6] suggested using frozen orbits and specifically optimizing for minimum radial distance variation as a function of latitude in order to avoid cross-shell collision risk.…”

Section: Introductionmentioning

confidence: 99%

A Method for Generating Closely Packed Orbital Shells and the Implication on Orbital Capacity

Lifson¹,

Arnas²,

Avendaño³

et al. 2022

Preprint

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Shell-wise orbital slotting in Low EarthOrbit (LEO) can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This paper describes two methods to generate 2D Lattice Flower Constellations (2D-LFCs) that are defined with respect to either an arbitrary degree or an arbitrary degree and order Earth geopotential. By generating shells that are quasi-periodic and frozen with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semi-major axis of each shell or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. This helps mitigate the single inclination per shell requirement in prior work by admitting more shells for a given orbital volume while retaining self-safe phasing in each shell. These methods exploit previous work on the Time Distribution Constellation formulation and designs of closed 2D-LFCs under arbitrary Earth geopotentials using RGT orbits. Factors that influence the widths and shapes of these frozen shells are identified. Simplified formulas for estimating shell geometry and thickness are presented. It is shown that sequencing shells to group similar or ascending inclinations improves capacity versus arbitrary inclination ordering.

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Analysis of the TOPEX/Poseidon Operational Orbit: Observed Variations and Why

Cited by 14 publications

References 7 publications

Earth satellite dynamics by Picard iterations

Earth satellite dynamics by Picard iterations

Solution to the main problem of the artificial satellite by reverse normalization

A Method for Generating Closely Packed Orbital Shells and the Implication on Orbital Capacity

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