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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.

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. [ABSTRACT FROM AUTHOR]

This article examines the transformation of the "heart of the world" concept and its influence on the understanding of what causes planetary motion. It begins with Aristotle's conception of the sphere of the fixed stars and that of commentators such as Simplicius, Averroes, and Aquinas. The focus then shifts to the notion of a mobile Sun positioned between the upper and lower planets in the geocentric tradition of Macrobius, medieval, and Renaissance thinkers. We then examine the transition to the Copernican Sun, which is both stationary in terms of its central geometric position but also perceived as the "natural" or vital center of the universe. These ideas are then traced from Copernicus and Rheticus to Kepler and Galileo. We will conclude with some considerations concerning Giordano Bruno and William Harvey, and the intriguing connection between the circulation of the blood and the Sun's role as the heart of the world. [ABSTRACT FROM AUTHOR]

One of the key concepts in modern science is force (F). In present studies on the history of dynamics, Patricius is either completely omitted or only cursorily mentioned. The aim of this text is to show that Patricius's concept of the soul, as he developed it in his Nova de universis philosophia from 1591, comes close to the modern (i.e. Newtonian) understanding of force. This should support the more general position that one of the most intriguing aspects of Patricius's philosophy is his contribution to the emergence of modern science. [ABSTRACT FROM AUTHOR]

Kepler published Mysterium Cosmographicum in 1597 constructing his cosmological model based on the five regular polyhedra. Such a creative but weird idea was almost consistent with empirical evidence. Furthermore, following the Pythagorean belief about the connection between music and astronomy, Kepler delved into looking for what things having to do with the planetary movements have the harmonic consonances. This article claims that Kepler's model is a 3M (mathematical, musical, and metaphysical) model and demonstrates how it had been constructed. Furthermore, I explore the reasons behind Kepler's departure from the 3M model and his subsequent consideration of a non-circular orbit, ultimately presenting the Three Laws of Planetary Motion as a consequential outcome. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Copernican inextricable revolution is scrutinized in the distinctive context of intense interaction and profound interpenetration of Aristotelean and Ptolemaic subtle theoretical languages. It is elicited that already within the Ptolemaic sophisticated research program the mathematical exactness increasingly deviated from the blunt tenets of Aristotelean qualitative physics though well-grounded empirically. Aristotelian - Ptolemaic heathen cosmology could not help but be exposed to repeated severe attacks during the European Middle Ages since it apparently confronted the stout principles of monotheism not admitting the strict demarcation line between the celestial and mundane realms. All seemingly different worlds should have one and the same Creator. Henceforth the Copernican startling breakthrough should be evaluated in the refined scope of further clarification of the tremendous gap between astronomy and physics and the subsequent commencement of effective efforts to eradicate it in the favorable monotheistic social-cultural context of Christian Weltanschauung enforcement. The posterior indispensable contributions of Galileo Galilei, Johann Kepler, René Descartes and Isaac Newton incarnated the stiff milestones of the mathematics descent from sublime Skies to sinful Earth and the reciprocal ascent of Earth physics in comprehending the distinctive Divine phenomena. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

According to selective, retentive, scientific realism, past empirical success may be explained only by the parts of past theories that are responsible of their successful predictions being approximately true, and thus theoretically retained, or approximated, by the parts of posterior theories responsible of the same successful predictions. In this article, we present as case study the transit from Ptolemy's to Kepler's astronomy, and their successful predictions for Mars' orbit. We present an account of Ptolemy's successful prediction of Mars' orbit from Kepler's perspective, and scrutinize whether the theoretical elements responsible for Ptolemy's empirical success are approximately retained in Kepler. In order to give to the realist the best chances, we try different strategies. We conclude that all fail and thereby this case constitutes a prima facie strong anomaly for selective retentive realism. Structural realists may call preservation of structure to the rescue, but the existing notions of structure do not work. In absence of a new notion that works, the burden of the proof lies on the realist side. [ABSTRACT FROM AUTHOR]

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.

Optical Intersatellite Links (OISLs) are being considered for future Global Navigation Satellite System (GNSS) constellations. Thanks to OISLs, the constellation incorporates improved clock synchronization and precise ranging among the satellites, which are essential features to achieve accurate time and orbit determination. High data rate communications within the space segment also reduce ground segment dependency, by means of decentralized access to information. However, the dual optimization of data and navigation performance metrics requires a careful assignment of OISLs to the available laser communication terminals on-board. To this end, we present a contact plan design scheme based on a degree constrained minimum spanning tree heuristic applied to such OISL-enabled GNSS (O-GNSS) constellations. Results on the Kepler system, a novel GNSS proposal, show that a fair distribution of connectivity among the constellation can be ensured while optimizing its range-based position estimation capabilities (PDOP). A PDOP improvement of 85 % is reached on average by the optimized contact plan with respect to a generic scheduler that disregards the geometrical distribution of the chosen links. [ABSTRACT FROM AUTHOR]

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.

In two early unpublished texts (a Disputation in favor of Copernicus of 1593 and the Apologia pro Tychone against Ursus of 1600), Kepler argued with the Pythagoreans that, contrary to Aristotle (De caelo, ii, 13), the geometrical center of the cosmos coincides with its natural center. Since the Sun is the body that occupies this central position, Kepler conceives it as the heart of the world and the principle of planetary motion. In the following study, we examine how Kepler further develops this pivotal theme in a letter to Herwart von Hohenburg of 25 March 1605 and later in the Dissertatio cum nuncio sidereo (Prague, 1610) as well as in a German translation and critical commentary of the Aristotelian chapter, which ultimately remained unpublished as well. [ABSTRACT FROM AUTHOR]

The paper presents results of precise orbit and Earth parameter determination based on full-scale simulations of a potential future GNSS, with the name of Kepler, recently proposed by the German Aerospace Center. The space segment of the system consists of 24 Galileo-like Medium Earth Orbit (MEO) satellites and 6 Low Earth Orbit (LEO) satellites equipped with ultra-stable optical clocks. All spacecraft carry terminals for two-way optical inter-satellite links (ISLs) enabling high-rate data communication, constellation-wide clock synchronization and precise absolute ranging. The clock synchronization is assumed to create an extremely stable reference time scale based on ensemble of the optical clocks. A series of simulation scenarios are defined, starting from the Galileo constellation as benchmark, and gradually incorporating additional features including LEOs, ISLs and synchronized clocks to assess the impact on orbits, singnal-in-space range errors (SiSREs) and a geodetic quality Earth parameters like polar coordinates, length of day (LOD) and geocenter coordinates. Precise orbit determination (POD) is done at the observation level using the same standards and setups as in real data processing with ground network containing up to 18 stations. The MEO SiSRE, the most relevant to navigation applications, obtained for the Kepler constellation with perfect models and 18 ground stations was found to be 0.009 cm, 160 times better than 1.4 cm found for Galileo. It was demonstrated, that for operational POD for the Kepler system the ground network can be significantly reduced to only two stations if Earth rotation parameters are to be estimated, or to just one otherwise. A SiSRE value of 0.037 cm was obtained with two stations, and 0.018 cm with one station. For more realistic results a number of modeling errors are being considered. These concern observations – multipath, GNSS code hardware delays and ISL range biases, the dynamics – solar radiation pressure (SRP), gravity field, air drag, MEO antenna thrust, Earth tide potential, and the geometry – ocean loading and phase center offsets (PCOs) of space GNSS antennas. Any other satellite and station equipment contribution to mismodeling has been disregarded. It is shown, that for the Kepler the modeling errors are clearly visible in ISL observation residuals, in contrast to Galileo case, where they are to a large extent absorbed by the large number of estimated clock parameters. This was exploited to efficiently mitigate the dynamic modeling errors by estimation of empirical accelerations. With this setup the MEO SiSRE of 5 cm was obtained for Galileo and 0.3 cm, 0.4 cm and 0.7 cm for Kepler with 18, two and one ground station, respectively. The key to obtaining such low values are ISLs and synchronized satellite clocks. In the Kepler constellation with a single ground station the ISL range biases (RBs) up to 5 mm and 20 mm increase the SiSRE to 0.74 cm and 1.67 cm. Estimation of the ISL RBs is not recommended in the presence of modeling errors since they are significantly biased, which leads to increase of SiSRE to 2.2 cm. The Earth parameter determination, based on global network of 124 observing IGS stations, also benefits significantly from the Kepler constellation. The initial results show that the impact of modeling errors on Earth parameters can, as with POD, be effectively reduced in the Kepler system. The 30 cm error in integrated LOD, which has an impact on UT1-UTC, obtained for Galileo due to combined modeling errors could be reduced to 0.5 cm for the Kepler system. The same is true for the Z-coordinate of the geocenter, whose 14 mm error in the MEO-only solution could be reduced to 0.2 mm in the Kepler solution. The Earth parameters completely free of bias are obtained when the number of the modeling errors is reduced to only two: MEO SRP and PCOs. The ISL range biases up to 5 mm were found to have negligible impact on the estimated EPs. The largest differences (up to 0.2 mm) are found for UT1-UTC, for all other parameters they do not exceed 0.02 mm. The estimation of PCOs, being an integral part of Earth parameter determination, also benefits enormously from the Kepler design. It was demonstrated, that using only ten days of data they could be estimated with millimeter accuracy for MEOs and sub-millimeter accuracy for LEOs in all three spacial directions even in the presence of ISL range biases of up to 5 mm. Such accuracy of PCOs is not achievable with the Galileo constellation. [ABSTRACT FROM AUTHOR]

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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.

Cosmos has always sparked human curiosity to unveil and speculate its fascinating secrets. This curiosity has ultimately opened a window to other worlds. After years of observation, computation, and data analysis, scientists have revealed the diversity in exoplanets that have been helpful in the characterization and further investigation of biosignatures and technosignatures. This article presents some of the scientific advances made in extraterrestrial planetary science that guarantees to search through the thick clouds of the mysterious planets in the near future. [ABSTRACT FROM AUTHOR]

The article explores Johannes Kepler's abortive attempts to produce an opulent, decorative art object to accompany the publication of his first treatise, Mysterium Cosmographicum (1596). It was Kepler's hope that this Credentzbecher, so-called because it was designed to resemble a large, ceremonial chalice, would valorize the significance of what he believed to be an epoch-defining discovery concerning the proportional nature of the planetary intervals and serve as a personal introduction to his local sovereign, Duke Friedrich I of Württemberg (1557–1608). The correspondences of Kepler and his circle, some of which have been reproduced and translated here for the first time, reveal in excruciating detail the struggles to negotiate the demands, and exacting standards, of the Stuttgart court and Kepler's difficulty working with the local goldsmiths employed by the court to enact his vision. Though met with skepticism and destined for failure, the model, its design, and the misunderstandings its failure revealed, poignantly display the sometimes-insurmountable gap between artisanal knowledge and scientific ambition. [ABSTRACT FROM AUTHOR]

The State Archives of Belgium, in particular, the archives of Archduke Albert VII of Austria, hold a letter which possibly is a copy of the letter, or an excerpt of the letter, of Kepler to Emperor Rudolf II of October 1604 on SN1604, that is, the first letter of Kepler on the subject. Together with this letter, there are other letters on SN1604, written by Johannes Brengger and Michiel Coignet. In one of these letters, the very observation by Brengger which Kepler cites can be found. The letters are in Albert's archive because he asked his Court Mathematician Coignet about the phenomenon. It is less clear why Albert was interested in the phenomenon, given the lack of interest in science at his court. [ABSTRACT FROM AUTHOR]

The application of analytical chemistry to the exploration of the World Cultural Heritage represents a major challenge in that most protocols and strategies are invasive and require micro-sampling. We report a novel methodology for harvesting material deposited on the surface of ancient documents while avoiding their damage or contamination. The technology here described relates to the capture of metals on these specimens. It is based on the use of plastic films (ethylene vinyl acetate, EVA) impregnated with different metal chelators (sodium 2,3-dimercapto-1-propanesulfonate, DMPS, meso-2,3-dimercaptosuccinic acid, DMSA and ethylene diamino tetra acetic acid, EDTA, as calcium salt), for harvesting from surfaces of different supports potential traces of metals therein deposited. The EVA film technology has been used to explore the pages of a manuscript written by Kepler concerning the movements of the moon and catalogued under the title "Hipparchus" at the Archives of the Russian Academy of Sciences (St. Petersburg branch). The EVA-based chelating diskettes were able to capture very significant amounts of different metals, namely: Au, Ag, Hg, As, Pb, suggesting that Kepler, well known as astronomer, astrologist, mathematician and Lutheran theologian, might have started practicing alchemy, a pseudo-chemical science he had learned from his colleague Tycho Brahe in Prague. Image 1 • The EVA film technology for monitoring traces of past life in manuscripts. • An Eva diskette with chelating agents for harvesting metals. • As, Pb, Ag, Au, Hg metal quantitation discovers potential Kepler's work on alchemy. • Four types of EVA films expand our ability of exploring the World Cultural Heritage. [ABSTRACT FROM AUTHOR]

This manuscript reviews recent progress in optical frequency references and optical communication systems and discusses their utilizations in global satellite navigation systems and satellite geodesy. Lasers stabilized with optical cavities or spectroscopy of molecular iodine are analyzed, and a hybrid architecture is proposed to combine both forms of stabilization with the aim of achieving a target frequency stability of 10-15 [s/s] over a wide range of sampling intervals. The synchronization between two optical frequency references in real-time is realized by means of time and frequency transfer on optical carriers. The technologies enabling coherent optical links are reviewed, and the development of an optical communication system for synchronization, ranging and data communication in space is described. An infrastructure exploiting the capabilities of both optical technologies for the realization of a modernized constellation of navigation satellites emitting highly synchronized signals is reviewed. Such infrastructure, named Kepler system, improves satellite navigation in terms intra-system synchronization, orbit determination accuracy, as well as system monitoring and integrity. The potential impact on geodetic key parameters is addressed. [ABSTRACT FROM AUTHOR]

Aristotle held that perception consists in the reception of external sensory qualities (or sensible forms) in the sensorium. This idea is repeated in many forms in contemporary philosophy, including, with regard to vision, in the idea (still not firmly rejected) that the retinal image consists of points of colour. In fact, this is false. Colour is a quality that is constructed by the visual system, and though it is possible to be a realist about colour, it is completely misleading to think of it as received by the retina. Moreover, such supposedly "charitable" interpretations of Aristotle's doctrines, based on misconceptions of perception-science, distort our understanding of his historical context. [ABSTRACT FROM AUTHOR]

• A unique historical approach. • A useful transition technique from Heliocentric to geocentric system and vice versa. • Simulation which could be extended in various celestial objects leading to useful conclusions. • How the free interactive computing tool GeoGebra can be used in astronomical calculations. The word 'Geocentric' comes from the Greek word Γεωκεντρικό which is a compound word composed from two words: "γεω" means Earth and "κεντρικό" means centric. Geocentric aspect, appears for the first time in ancient Greece. Pythagoras had formulated the geocentric system with the Earth at the center of the Universe surrounded by the orbiting planets with Sun included. Later Greek ancient astronomers, trying to explain the weird planetary motion in the sky, introduced the epicyclic theory. 3 3 The epicyclic theory was well formulated by Hipparchus and Apollonius. Using this theory the two famous Greek astronomers managed to explain the weird planetary motion on the sky. This theory states that the geocentric planetary motion could be considered as a combination of circular motions. Today this idea is quite sensible if we consider that the geocentric motion could be perceived as synthesis of two independent motions; one is the rotation of the planet around the Sun and the other is the apparent rotation of the Sun around the Earth. Someone could say that the heliocentric motion is hidden inside the geocentric planetary path as one of two superimposed motions. This logical conclusion is supported by F. Hoyle Hoyle (1975) who states "We know that the difference between a heliocentric theory and a geocentric theory is one of relative motion only, and that such a difference has no physical significance." In other words Geocentrism isn't completely wrong excluding only the arbitrary claim that the Earth is fixed and immobile at the center of the Universe. Geocentrism lasted many years until Nicolaus Copernicus at the middle of 15th century, proposed the heliocentric system by transferring the reference origin from Earth to Sun. Although Copernican model was capable explaining the geocentric orbits of planets with negligible eccentricity, it failed to give a convincing explanation in cases of planets with considerable eccentricity like Mars. The lack of symmetry in Mar's trajectory led Kepler to discover that planet's orbits weren't circular, as it was already believed, but elliptical. According to (Evans, 1998, p.431) Kepler said "I therefore once again think it to have happened by divine arrangement, that I arrived at the same time in which he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy, without which we would remain forever ignorant of those secrets." In this article we are trying to simulate the process followed by Kepler, studying the apparent geocentric Mar's orbit which triggered him to discover elliptical planetary orbits. The relation between heliocentrism and geocentrism is highlighted during this study. Besides, this aspect is mentioned by David R. Topper...But this fact is then sometimes generalized to positing that geocentrism and Heliocentrism are equivalent, that they are the same geometrically or mathematically or even exactly the same; in a phrase, there is an isomorphism between them... Topper (2007) The methodology which was used, in the whole process, relies on mathematical modeling. This approach is based mainly on dynamic position change over time, which the interactive mathematic software GeoGebra can generously provide. The end of this historical approach shows that the heliocentric view was revealed throughout a geocentric model, proving the equivalence of these two different aspects. Finally the theoretical numerical results of this study seem to be in full agreement with the astronomical records of that era with minimal discrepancies. [ABSTRACT FROM AUTHOR]

Johannes Kepler described the Copernican universe as consisting of a central, small, brilliant sun with its planetary system, all surrounded by giant stars. These stars were far larger than, and much dimmer than, the sun - his De Stella Nova shows that every visible star must exceed the size of the Earth's orbit, and the most prominent stars may exceed the size of the entire planetary system. His other writings, including his response to Ingoli, his Dissertatio cum Nuncio Sidereo, and his Epitome Astronomiae Copernicanae, also reflect this Copernican universe. To Kepler, such a universe was an illustration of divine power - and solid evidence against the stars being suns, against the universe of Giordano Bruno. Kepler's starry universe was in fact the Copernican universe supported by observations of the stars, which showed them to have measurable apparent sizes. Not until the later seventeenth century were those apparent sizes shown to be spurious, allowing for a universe in which the stars were suns. [ABSTRACT FROM AUTHOR]

The Kepler spacecraft's imaging photometer monitored the Pluto system from October–December 2015 during Campaign 7 of the K2 extended mission. Kepler obtained an unprecedented and fortuitous nearly continuous 12-Pluto day lightcurve from measurements acquired every 30 min using long cadence sampling. This 3-month-long baseline anchors the Pluto+Charon lightcurve near the time of the New Horizons July 2015 encounter, observing at solar phase angles between 1.16° and 1.74°. Long-term modeling of Pluto's lightcurve will ultimately reveal its long-term seasonal variation. K2’s combined Pluto+Charon lightcurves measured at this epoch have an average total amplitude of 0.120 ± 0.006, 0.07 magnitudes smaller than the amplitude predicted by a static frost model (Buie and Tholen, 1989) projected from Hubble Space Telescope surface maps (Buie et al., 1992). Subtracting a static Charon lightcurve from the Pluto+Charon K2 lightcurve produces the same results. Likewise, we subtract each rotation model from the model for the first full rotation and find that the average difference of all variations is 0.017 ± 0.008 magnitudes. Moreover, the difference between the first and last K2 rotation is 0.005 magnitudes, implying that there are no significant changes in the lightcurve during the 3 months of K2 observations. These results are consistent with seasonal transport on Pluto's surface and the predictions of Buratti et al. (2015a) . However, a detailed understanding of the surface-atmosphere interactions associated with these phenomena requires decades of monitoring. [ABSTRACT FROM AUTHOR]

We revisit the discovery and implications of the first candidate systems to contain multiple transiting exoplanets. These systems were discovered using data from the Kepler space telescope. The initial paper, presenting five systems (Steffen et al., 2010a), was posted online at the time the project released the first catalog of Kepler planet candidates. The first extensive analysis of the observed population of multis was presented in a follow-up paper published the following year (Lissauer et al., 2011b). Multiply-transiting systems allow us to answer a variety of important questions related to the formation and dynamical evolution of planetary systems. These two papers addressed a wide array of topics including: the distribution of orbital period ratios, planet size ratios, system architectures, mean-motion resonance, orbital eccentricities, planet validation and confirmation, and the identification of different planet populations. They set the stage for many subsequent, detailed studies by other groups. Intensive studies of individual multiplanet systems provided some of Kepler 's most important exoplanet discoveries. As we examine the scientific impact of the first of these systems, we also present some history of the people and circumstances surrounding their discoveries. [ABSTRACT FROM AUTHOR]

We describe the circumstances that led to the discovery of Kepler-36b, and the subsequent characterization of its host planetary system. The Kepler-36 system is remarkable for its physical properties: the close separation of the planets, the contrasting densities of the planets despite their proximity, and the short chaotic timescale. Its discovery and characterization was also remarkable for the novelty of the detection technique and for the precise characterization due to the large transit-timing variations caused by the close proximity of the planets, as well as the precise stellar parameters due to asteroseismology. This was the first multi-planet system whose transit data was processed using a fully consistent photometric-dynamical model, using population Markov Chain Monte Carlo techniques to precisely constrain system parameters. Amongst those parameters, the stellar density was found to be consistent with a complementary, concurrent asteroseismic analysis. In a first, the 3D orientation of the planets was constrained from the lack of transit-duration variations. The system yielded insights into the composition and evolution of short-period planet systems. The denser planet appears to have an Earth-like composition, with uncertainties comparable to the highest precision rocky exoplanet measurements, and the planet densities foreshadowed the rocky/gaseous boundary. The formation of this system remains a mystery, but should yield insights into the migration and evolution of compact exoplanet systems. [ABSTRACT FROM AUTHOR]

In the history of warfare various media and technologies have been devised both to enable contingent events in the form of scenarios and simulations and to reign them in and bring the proliferation of possible futures under control. War games, horoscopes, astrolabes, celestial and topographical maps have in different ways served as 'contingency media', i.e. tools that enable strategic thought and action under conditions of uncertainty. Through the prism of Schiller's Wallenstein from 1799, this essay examines the development of military contingency media from the 17th to the early 19th century. Delving into the disagreements between Johannes Kepler and the historical Wallenstein about the reach and power of astrological star charts and horoscopes, the essay analyzes Schiller's late Enlightenment critique of astrological contingency media as well as his transformation of them into productive poetic devices. Finally, it situates the play in the context of military theory around 1800 in which contingency emerged as a central factor of large-scale warfare. A historically complex document, Wallenstein serves as an archive of the shifting conceptions of war and of the media devised to manage its uncertain futures. [ABSTRACT FROM AUTHOR]

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/