Tables for the trigonometric series representations of the orbital inclination function

Image registration is important in geostationary weather satellites. Achieving consistent registration of the images with respect to the geographical locations on the Earth is here of interest. The consistency in the registration between the images is affected whenever the orbital inclination and eccentricity are not zero. The imaging payload has a two-axis scanning mirror to capture the Earth image. The above orbital effects together with scan mirror pointing direction are the factors that cause the misregistration. This paper presents an onboard algorithm that provides the scan compensation angles due to the above factors and achieves consistent registration. The compensation varies every second, which is the time taken for each scan. Hence it is preferred to have computations onboard than to have ground based bulk uplinks for the scan compensation. The paper presents an algorithm that is useful, say, when (i) the onboard computing capabilities are limited, (ii) the navigation accuracies are coarse and (iii) the image resampling is not preferred on the ground and the payload data are directly used for weather applications. The paper also discusses the tests that were carried on the onboard software in order to validate its performance in achieving the consistent registration before launch. This is done by using another independent software tool which is also described in detail. Image motion algorithm was invoked for a couple of days in INSAT 3DR. The atmospheric wind vector deduced directly from the satellite images is given at the end.

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Galileo L10 Satellites: Orbit, Clock and Signal-in-Space Performance Analysis

Sensors ◽

10.3390/s21051695 ◽

2021 ◽

Vol 21 (5) ◽

pp. 1695

Author(s):

Constantin-Octavian Andrei ◽

Sonja Lahtinen ◽

Markku Poutanen ◽

Hannu Koivula ◽

Jan Johansson

Keyword(s):

Performance Indicators ◽

Satellite System ◽

Short Term ◽

Orbital Inclination ◽

Navigation Data ◽

Periodic Signals ◽

Global Navigation Satellite ◽

Minor Correction ◽

Very High

The tenth launch (L10) of the European Global Navigation Satellite System Galileo filled in all orbital slots in the constellation. The launch carried four Galileo satellites and took place in July 2018. The satellites were declared operational in February 2019. In this study, we report on the performance of the Galileo L10 satellites in terms of orbital inclination and repeat period parameters, broadcast satellite clocks and signal in space (SiS) performance indicators. We used all available broadcast navigation data from the IGS consolidated navigation files. These satellites have not been reported in the previous studies. First, the orbital inclination (56.7±0.15°) and repeat period (50680.7±0.22 s) for all four satellites are within the nominal values. The data analysis reveals also 13.5-, 27-, 177- and 354-days periodic signals. Second, the broadcast satellite clocks show different correction magnitude due to different trends in the bias component. One clock switch and several other minor correction jumps have occurred since the satellites were declared operational. Short-term discontinuities are within ±1 ps/s, whereas clock accuracy values are constantly below 0.20 m (root-mean-square—rms). Finally, the SiS performance has been very high in terms of availability and accuracy. Monthly SiS availability has been constantly above the target value of 87% and much higher in 2020 as compared to 2019. Monthly SiS accuracy has been below 0.20 m (95th percentile) and below 0.40 m (99th percentile). The performance figures depend on the content and quality of the consolidated navigation files as well as the precise reference products. Nevertheless, these levels of accuracy are well below the 7 m threshold (95th percentile) specified in the Galileo service definition document.

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A general inverse matrix series relation and associated polynomials – II

Mathematica Slovaca ◽

10.1515/ms-2017-0469 ◽

2021 ◽

Vol 71 (2) ◽

pp. 301-316

Author(s):

Reshma Sanjhira

Keyword(s):

Matrix Polynomial ◽

Combinatorial Identities ◽

Inverse Matrix ◽

Matrix Polynomials ◽

Special Cases ◽

Series Representations ◽

The Matrix ◽

Associated Polynomials ◽

Matrix Pair ◽

Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

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DESTINY: Database for the Effects of STellar encounters on dIsks and plaNetary sYstems

Computational Astrophysics and Cosmology ◽

10.1186/s40668-019-0030-3 ◽

2019 ◽

Vol 6 (1) ◽

Cited By ~ 2

Author(s):

Asmita Bhandare ◽

Susanne Pfalzner

Keyword(s):

Planetary System ◽

Planetary Systems ◽

Gravitational Effect ◽

Parameter Study ◽

Orbital Inclination ◽

Particle Properties ◽

Disk Size ◽

Stellar Group ◽

Cluster Environment ◽

Parabolic Orbits

Abstract Most stars form as part of a stellar group. These young stars are mostly surrounded by a disk from which potentially a planetary system might form. Both, the disk and later on the planetary system, may be affected by the cluster environment due to close fly-bys. The here presented database can be used to determine the gravitational effect of such fly-bys on non-viscous disks and planetary systems. The database contains data for fly-by scenarios spanning mass ratios between the perturber and host star from 0.3 to 50.0, periastron distances from 30 au to 1000 au, orbital inclination from 0∘ to 180∘ and angle of periastron of 0∘, 45∘ and 90∘. Thus covering a wide parameter space relevant for fly-bys in stellar clusters. The data can either be downloaded to perform one’s own diagnostics like for e.g. determining disk size, disk mass, etc. after specific encounters, obtain parameter dependencies or the different particle properties can be visualized interactively. Currently the database is restricted to fly-bys on parabolic orbits, but it will be extended to hyperbolic orbits in the future. All of the data from this extensive parameter study is now publicly available as DESTINY.

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Trigonometric Series after 1830

Series and Products in the Development of Mathematics ◽

10.1017/9781108709453.023 ◽

2021 ◽

pp. 639-656

Keyword(s):

Trigonometric Series

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A dominated convergence theorem for Eisenstein series

Annales mathématiques du Québec ◽

10.1007/s40316-021-00157-7 ◽

2021 ◽

Author(s):

Johann Franke

Keyword(s):

Fourier Series ◽

Dirichlet Series ◽

Eisenstein Series ◽

Modular Forms ◽

Convergence Theorem ◽

Rational Functions ◽

New Approach ◽

Series Representations ◽

Dominated Convergence ◽

Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

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