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Abstract Distributed Space Systems (DSS) are gaining prominence in the space industry due to their ability to increase mission performance by allowing cooperation and resource sharing between multiple satellites. In DSS where communication between heterogeneous satellites is necessary, achieving autonomous cooperation while minimizing energy consumption is a critical requirement, particularly in sparse constellations with nano-satellites. In order to minimize the functioning time and energy consumed by the Inter-Satellite Links established for satellite-to-satellite communication, their temporal encounters must be anticipated. This work proposes an autonomous solution based on Supervised Learning that allows heterogeneous satellites in circular polar Low-Earth Orbits to predict their close-approach encounters given the Orbital Elements. The model performance is evaluated and compared in two different scenarios: (1) a simplified scenario assuming Kepler orbits and (2) a realistic scenario assuming Simplified General Perturbations 4 orbital model. The obtained results demonstrate a Balanced Accuracy exceeding 95% when compared to realistic data from an available database. This work represents a promising initial stage in developing an alternative approach within the field of DSS.

The article presents the results of the authors’ research on the cosmological views of Johannes Keppler in his Latin treatise Harmonices Mundi. The authors discuss the background of composing the treatise concerning the philosophical, religious, and cultural contexts of that period, and give a brief overview of the structure of the treatise, Kepler’s theory and his third law of harmony. The paper demonstrates the connection and reception of philosophical ideas on the harmony of the world in Kepler’s treatise and ancient philosophers, such as Pythagoras, Plato, and Proclus. This shows that Kepler’s philosophical and scientific views largely depended on his theological background. The authors discuss the perception of ancient cosmological ideas in Kepler’s Harmonices Mundi relating to Pythagorean tetractys, five Platonic solids or regular polyhedral, and cosmic harmony as well as Proclus’ theoretical mathematics.

In this paper, I approach Hegel’s philosophy under the banner of a “Keplerian Revolution”, the implicit reference being, of course, to Kant’s supposed Copernican philosophical revolution. Kepler had been an early supporter of the Copernican paradigm in astronomy, but went well beyond his predecessor, and so is invoked here in an attempt to capture some of the important ways in which Hegel attempted to go beyond the philosophy of Kant. To make these issues more determinate, however, Hegel’s Keplerian orientation will not be presented in its contrast to Kant’s “Copernicanism” as such, but as contrasted with that of another early follower of Copernicus, Giordano Bruno, and this Brunian orientation will be used to characterize Kant’s philosophy as seen from Hegel’s rival Keplerian point of view. Interpreting Hegel as a philosophical Keplerian will require that we broach those worrisome aspects of Kepler’s astronomy, namely his support for Plato’s cosmology and the tradition of the “music of the spheres”, but this will be shown to have connections to Hegel’s own approach to logic. This in turn will help shed light on the meaning of Hegel’s form of idealism and, in particular, on its usually unacknowledged Platonic dimensions.

Planets orbiting binary stars—circumbinary planets—play a paramount role in our understanding of planetary and stellar formation and evolution, dynamical interactions in many-body systems, and the potential for habitable environments beyond the Solar System. Each new discovery holds immense value and inherent fascination both for the astronomical community and for the general public. This is perhaps best demonstrated by the 1500+ citations of the discovery papers for the 14 known transiting circumbinary planets and the dozens of related press-releases in major news outlets. This article reviews the observational and theoretical aspects related to the detection and confirmation of transiting circumbinary planets around main-sequence binaries from space-based surveys, discusses the associated challenges, and highlights some of the recent results.

Este artigo tem por objetivo apresentar um estudo sobre alguns aspectos geométricos e físicos na primeira parte da obra Astronomia Nova de 1609, tendo em vista fornecer subsídios aos professores que queiram abordar a história da astronomia em suas disciplinas de nível básico ou superior. Tendo este foco, veremos como Kepler entendia algumas equivalências entre os sistemas de mundo em discussão em sua época e apresentaremos um estudo de um dos experimentos que Kepler propõe e analisa geometricamente. Neste, percebemos um pequeno erro de cálculo que não foi explorado na literatura pesquisada e, mais que isso, nos permitiu entendermos sobre o uso das construções geométricas em sua época e a ideia de equivalência que Kepler tem em mente.

Kepler’s discoveries were permitted by his remarkable insight to place the Sun at the focus of an elliptical planetary orbit. This coordinate system reduces a 2-dimensional orbit to a single spatial dimension. We consider an alternative coordinate system centered on the “image focus,” which is the symmetrical (mirror) counterpart of the “real focus” occupied by the Sun. Our analytical approach provides new purely geometric formulae and an exact relationship for the dynamic property of orbital time. In addition, considering the mirror symmetry of the ellipse leads to a simple approximation: the radial hand of an orbital clock rotates counterclockwise at a nearly steady angular velocity 2π/T about the “image focus,” where T is the orbital period. This approximation is a useful pedagogic tool and has good accuracy for orbits with low to moderate eccentricities, since the deviation from the exact result goes as eccentricity squared. Planetary comparisons are made. In particular, the angular speeds of Mercury and Jupiter are highly variable in the geocentric and heliocentric reference frames, but are nearly constant in the image focus reference frame. Our findings resolve whether the image focus is the location for observing uniform motion of an elliptical orbit, and pertain to their stability.

Noticias falsas, afirmaciones engañosas, bulos, medias verdades, mentiras… Para vencer al virus de la desconfianza, alimentado por las falsas noticias de salud que circulan por internet -y más en tiempos de coronavirus-, la receta es acudir a los expertos, como son los científicos y los profesores, actividad que comparten Hipócrates, Agustín de Hipona y Kepler. Desde nuestro punto de vista, los tres están entre esas fuentes de prestigio para informarse bien de los acontecimientos y descubrir las falsas noticias (fake news) de las que, por regla general, la gente se entera por un tuit o una notificación que salta de pronto en la pantalla de su smartphone. A nuestro entender, las bases de la información veraz no las ofrece la tecnología como un fin en sí mismo. Es el espíritu de las profundas convicciones lo que define la objetividad subyacente en los hechos comprobables.

This article attempts to understand the extent to which, and the terms in which, it was possible to speak of sensory vision as a psychic representation before Johannes Kepler inaugurated the new optics in his famous Paralipomena ad Vitellionem (1604). The following argument is taken as a starting point: That it is only within this new paradigm, dissociating the physical process of vision from its psychic treatment, one can legitimately speak of vision as a mental construction or a representation. After examining this question in the light of several ancient and medieval theories, the article reaches a different conclusion. The question of vision as a mental representation dates as far back as Aristotle, conferring to the internal senses (phantasia, common sense) the major function in elaborating the content of perception. Additionally, some theories under neo-Platonic influence, such as those of Augustine or Avicenna, clearly conceive direct vision as a psychic representation. In Paralipomena ad Vitellionem, Kepler distinguishes optics as a physical science of light from the psychology of perception; but the latter has already a long history, as does the idea of vision as a mental representation.

Many late-type stars across the Milky Way exhibit observable pulsations similar to our Sun that open up a window into stellar interiors. The NASA Kepler mission, a space-based photometric telescope, measured the micro-magnitude luminosity fluctuations caused by solar-like oscillations of tens of thousands of stars for almost 10 years. Detailed stellar structure, evolution, and oscillation theoretical work established in the decades before, such as predictions about mode mixing in the interior of red-giant stars, among many others, now had voluminous precision data against which it could be tested. The overwhelming result is the general validation of the theory of stellar oscillations as well as stellar-structure models; however, important gaps in our understanding of interior physics was also revealed by Kepler. For example, interior rotation, convection, and mixing processes are complex phenomena not fully captured by standard models. This review explores some of the important impacts Kepler observations of solar-like oscillations across the cool end of the H-R diagram has had on stellar astrophysics through the use of asteroseismology.

Viene esaminato un luogo testuale della Harmonice mundi (III i) in cui Keplero espone la dottrina di contenuto teologico e astrologico del tredicesimo dialogo del Corpus Hermeticum collegandola alla dottrina pitagorica della Tetrade, evidenziandone le affinità convergenti in una concezione della numerologia che risulta essere per Keplero lo strumento più idoneo per la speculazione teologica; a conferma di questo, viene proposta la dottrina procliana degli enti matematici presenti nella mente divina e nella costituzione del cosmo come struttura latente dell'intera realtà, manifestando la concezione di una teologia matematica concepita come strumento conoscitivo che funge da tramite fra l'armonia cosmica e la stessa natura divina attraverso gli archetipi matematici conoscibili e utilizzabili dalla mente umana.

La música como modelo explicativo del universo ha estado presente desde el mismo nacimiento de la reflexión filosófica. En el caso de Kepler, la música y la astronomía quedaban homologadas sobre la base de un único arquetipo geométrico, y por ello podían compartir sus observaciones, teorías e, incluso, emotividades. Las condiciones históricas que posibilitaron esta interconexión están fundamentadas en la sólida formación musical de Kepler, su interés por la polifonía de sus contemporáneos y, en especial, por la música de Orlando di Lasso. Visto así, una experiencia estética musical, permitió a Kepler configurar un marco de verdades sobre el que formuló y contrastó sus teorías; tal como puede leerse – y escucharse – en los mismos textos del Harmonices Mundi. Enlace fundamental para este ensayo: http://www.calderon-online.com/anuariomusical/kepler/

In this paper, a root finding method due to iterative method is used first to thesolution of Kepler's equation for an elliptical orbit. Then the extrapolationtechnique in the form of Aitken D2 - acceleration is applied to improve theconvergence of the iterative method.In addition, by making use a new improvement to Aitken's method enables oneto obtain efficiently the numerical solution of the Kepler's equation. The speed ofthe proposed algorithms is compared using different values of eccentricity( e ) inthe range eÎ( 0,1 ) and for given mean anomaly (M).

Na física celeste apresentada em sua Astronomia nova, Kepler explica os movimentos planetários através da ação de uma certa força ou potência motriz solar. Em vista da aproximação feita no livro entre física celeste e explicações baseadas em "causas corpóreas", chamam a atenção as numerosas passagens onde Kepler refere-se às noções de alma e mente planetária. No presente artigo discutimos esses trechos pouco comentados da Astronomia nova. Com o objetivo de iluminar a discussão, abordamos na segunda seção a definição de alma terrestre delineada por Kepler no opúsculo Da neve hexagonal, escrito logo após a publicação da Astronomia nova. Kepler atribui a forma hexagonal dos flocos de neve a uma certa faculdade formadora da alma da Terra, que agiria como uma potência geometrizante com a finalidade de otimizar a saída do calor no processo de congelamento.In the celestial physics presented in his New Astronomy, Kepler explains the planetary motions through the action of the solar motive force or power. In regard of the approximation, performed in the book, between celestial physics and explanations grounded upon "corporeal forces", the numerous moments when Kepler resources to the notions of planetary souls and minds are somehow striking. In the present article we discuss these underestimated extracts from the New Astronomy, where Kepler employs the notions of planetary minds and souls. Intending to enlighten the subject, we have dealt in the second section with the definition of Earth's soul drawn by Kepler in his work on the regular shape of snowflakes, written right after the publication of the New Astronomy. Kepler ascribes the hexagonal shape of snowflakes to a certain forming faculty of the Earth's soul, which would act as a geometrizing power with the aim of optimizing the heat's departure during the freezing process.

The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While the Kepler Space Telescope mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve the characterization of exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling and originally designed to analyze archived Kepler Space Telescope and CoRoT (Convection Rotation et Transits planétaires) exoplanet mission data. We discuss the EXONEST software package and describe how it accommodates plug-and-play models of exoplanet-associated photometric effects for the purpose of exoplanet detection, characterization and scientific hypothesis testing. The current suite of models allows for both circular and eccentric orbits in conjunction with photometric effects, such as the primary transit and secondary eclipse, reflected light, thermal emissions, ellipsoidal variations, Doppler beaming and superrotation. We discuss our new efforts to expand the capabilities of the software to include more subtle photometric effects involving reflected and refracted light. We discuss the EXONEST inference engine design and introduce our plans to port the current MATLAB-based EXONEST software package over to the next generation Exoplanetary Explorer, which will be a Python-based open source project with the capability to employ third-party plug-and-play models of exoplanet-related photometric effects.

One of the remarkable features of blazars is violent variability over a wide wavelength range. The variation mechanism causing the observed complex behavior is still under debate. The variability timescales range from less than a day to decades. Variation on timescales less than a day is known as “microvariability.” Such short-term variations can provide insights regarding the origin of the variability after they are distinguished from longer-term variational components. We select about 195 microvariability events from the continuous light curve of blazar W2R 1926+42 with 1-min time resolution obtained by the Kepler spacecraft, and estimate the timescale and amplitude of each event. The rise and decay timescales of the events reveal random variations over short timescales less than a day, but they indicate systematic variations on timescales longer than several days. This result implies that the events are not independent, but rather mutually correlated.

Será apresentado um método alternativo para se ensinar as duas primeiras leis de Kepler, usando conceitos básicos de geometria, procurando-se chegar à importante noção de sistemas de referência e à equivalência entre o heliocentrismo (sistema Copernicano-Kepleriano) e o geocentrismo (sistema Ptolomaico). O método foi utilizado para estudantes de Ensino Fundamental (último ano), Ensino Médio e em cursos de graduação (Física e Matemática).

Será apresentado um método alternativo para se ensinar as duas primeiras leis de Kepler, usando conceitos básicos de geometria, procurando-se chegar à importante noção de sistemas de referência e à equivalência entre o heliocentrismo (sistema Copernicano-Kepleriano) e o geocentrismo (sistema Ptolomaico). O método foi utilizado para estudantes de Ensino Fundamental (último ano), Ensino Médio e em cursos de graduação (Física e Matemática).In this work we will present an alternative method to teach the first two Kepler's laws, using basic concepts of geometry, but achieving conclusions in the important notions of reference systems and the equivalence between heliocentrism (Copernican-Keplerian system) and geocentrism (Ptolemaic system). We used this method for students of junior (last year), high school and for undergraduate courses (Physics and Mathematics).

A revolução científica pode ter datado seu início com o trabalho de Copérnico e o seu ápice ocorreu com Isaac Newton. Porém, muito tem sido discutido de forma imprecisa a respeito da motivação de Copérnico e Kepler para que desenvolvessem seus trabalhos. Neste artigo será descrito questões acerca da versão corrente de que a complexidade dos epiciclos do sistema ptolomaico seria a motivação principal para a revolução copernicana. Ainda é discutida a possibilidade de que na formulação por Kepler de sua primeira lei tenha havido inspiração em ideia de outra pessoa.

Desde la más remota antigüedad, al hombre le ha preocupado el poder establecer una medición válida del tiempo. Ha sido una constante a través de la Historia. El problema es, que hasta hoy, no se ha podido determinar exactamente, esa magnitud. Pero se han logrado, fórmulas aleatorias bastante aproximadas.Since the remotest antiquity, mankind has been trying to establish an accurate measurement of time. It has been a constant aspiration throughout the History. The problem is that, up to now, this division has not been exactly determined. But quite approximate random formulae have been achieved.

L'article analitza el contingut de dues obres de Kepler, Mysterium Cosmographicum i Harmonice Mundi amb el propòsit d'esbrinar la qüestió del platonisme de Kepler, una qüestió que, d'acord amb el punt de vista d'aquest treball, necessita qualificació. És cert que Kepler adopta mètodes de recerca suggerits per Plató en el Timeu i que accepta llurs conseqüències epistemològiques. Però és obvi tambe que rebutja elements essencials de La física que hi ha exposada en ei Timeu. L'estudi suggereix que el resultat de totes aquestes anàisis podria ser que separar el platonisme de Kepler del seu realisme perilla d'esdevenir una tasca impossible.

Nesse trabalho apresentamos uma visão panorâmica da obra astronômica de Johannes Kepler. Tratamos, em ordem cronológica, dos quatro principais livros relacionados ao tema por ele escritos, a saber, Mistério Cosmográfico, Astronomia Nova, Harmonia dos Mundos e Epitome de Astronomia Copernicana, a fim de evidenciar as etapas históricas do desenvolvimento do pensamento científico do autor. Procuramos ressaltar a presença nesse pensamento de um elemento filosófico-teológico e de uma concepção física fortemente determinantes, paralelamente a um orientação metodológica já significativamente típica da ciência moderna, então nascente.