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This paper discusses measurements of the apparent diameter and parallax of the star Sirius, made in the early 18th century by Jacques Cassini, and how those measurements were discussed by other writers. Of particular interest is how other writers accepted Cassini’s measurements, but then discussed Sirius and other stars as though they were all the same size as the sun. Cassini’s measurements, by contrast, required Sirius and other stars to dwarf the sun—something Cassini explicitly noted, and something that echoed the ideas of Johannes Kepler more than a century earlier.

In the present work, in order to estimate the semi-amplitude of the radial velocity, we evaluate the contribution of the Doppler beaming effect to the phase curves of the all confirmed extrasolar planets (2776, September 2019), observed so far by the Kepler telescope. By modeling the tiny photometric variations (reflection, ellipsoidal and Doppler beaming effects) of the light curves, we found that the best observational data are in close agreement with the theoretical and published values of the amplitudes only for exoplanets: KOI-13b and TrES-2b. The derived values for the radial velocity also are in good agreement with those published by some authors. Furthermore, we found it necessary to introduce a third harmonic (3Φ) contribution into the KOI-13b and HAT-P7b light curve models, in order to decrease the residuals.

Johannes Kepler is considered to be the first scholar to have offered an adequate description of heavenly phenomena observed on the Moon's sky. Kepler outlined his ideas in his Somnium ( The Dream ), written originally in 1609, and subsequently printed in the years 1630/34. Kepler's lunar astronomy was to expose the absurdity of the arguments that the geocentric theatre of heavenly phenomena proves that the Earth remains motionless. In this paper, I argue that at the turn of the seventeenth century the idea of the sky observed from the Moon's surface was explored in cosmological discourse far more often than it has been assumed so far. My argument derives from the manuscript treatise Astrostereon (1603) authored by an English astrologer and physician, Edward Gresham. Writing for the same purpose as Kepler but several years earlier, Gresham laid down the foundation of lunar astronomy. I also demonstrate the uses of lunar astronomy in astrological almanacs printed in London at the time when Kepler's ideas were not widely known.

An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an expression for the planetary orbit, which is then compared against an equation for the ellipse. However, we derive the equation that we match against, using trigonometry, from two well-known properties of the ellipse. Calculus is avoided altogether., Comment: 7 pages, 2 figures

Kepler’s Laws of planetary motion (following the Copernican revolution in cosmology), according to Leibniz and his follower Hegel, for the first-time in history discovered the keys to what Hegel called the absolute mechanics mediated by dialectical laws, which drives the celestial bodies, in opposition to finite mechanics in terrestrial Nature developed by mathematical and empirical sciences, but that are of very limited scope. Newton wrongly extended and imposed finite mechanics on the absolute mechanics of the cosmic bodies in the form of his Law of one-sided Universal Gravitational Attraction, by distorting and misrepresenting Kepler’s profound laws and in opposition to Leibniz’s more appropriate “Radial Planetary Orbital Equation”. The still-prevailing error by Newton (notwithstanding his well known manipulation of science for selfish ends), not only shows the limitation of mathematical idealism and prejudice driven modern cosmology in the form of Einstein’s theories of relativity; but also, have made gaining positive knowledge of the cosmos an impossibility and has impaired social/historical development of humanity by reinforcing decadent ruling ideas. Hegel’s Naturphilosophie is not only a protest against the misrepresentation of Kepler’s Laws in particular; his Enzyklopädie der Philosophischem Wissenschaften is the negation and the direct rebuttal of Newtonian physics and Philosophiæ Naturalis Principia Mathematica, in general. Modern natural science ignores Leibniz and Hegel at its own peril! Kepler’s phenomenological laws of planetary motion and the dialectical insights of Leibnitz and Hegel opens the way for gaining positive knowledge of the dynamics, structure and the evolution of the cosmic bodies and other cosmic phenomena; without invoking mysteries and dark/black cosmic entities, which has been the pabulum of official astrophysics and cosmology so far.

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.

This paper deals with the integrations of homogeneous quasi-Keplerian Hamiltonians, that is, perturbed Kepler Hamiltonians which perturbation is of the form ∑ j = 2 N A j ∕ r j with A j constant. Although there are many applications of these Hamiltonians in Physics, Astronomy and Astrodynamics, we focus our interest on a particular case in the core of Artificial Satellite Theory, the Cid’s radial intermediary. For this problem, we integrate the equations of motion in two different ways, by means of the elliptic P -Weierstrass function and by using the Krylov–Bogoliubov averaging method to integrate a perturbed harmonic oscillator. In this case, the resulting solution is given in terms of the classical Kepler’s equation, with no need of introducing more complex generalized Kepler’s equation.

When our school implemented AP Physics 1, I wanted to include a project that would extend over time, use more advanced data analysis, and teach students about handling experimental error. Using a donated 5-inch Newtonian telescope and an entry-level digital camera, the students gathered data from digital images of the four Galilean moons, Io, Europa, Ganymede, and Callisto (see Fig. 1), to verify Kepler’s third law of planetary motion (T2=Kr3). Simulation software could have been used. Among others, Project CLEA (Contemporary Laboratory Experiences in Astronomy) seems to be a favorite that includes verifying Kepler’s third law using the orbits of the Galilean moons. Galileo measured the moons’ periods with his telescope. My students could do the same with modern equipment. The investigation started with a purely Keplerian analysis of the data, then to a Newtonian analysis leading to accurate orbital properties of the Galilean moons and Jupiter’s mass. Once the images have been obtained, they can be used each year.

Promises and disappointments of artificial intelligence for scientific discovery Recent successes within Artificial Intelligence with deep learning techniques in board games gave rise to the ambition to apply these learning methods to scientific discovery. This model for discovering new scientific laws is based on data-driven generalization in large databases with observational data using neural networks. In this study we want to review and critical assess an earlier research programme by the name of BACON. Though BACON was based on different AI technology, we can learn from its limitations and thus adjust our expectations. The BACON program had two ambitions, one descriptive and one normative. On the one hand, it wanted to provide an explanation how philosophers of nature in history arrived at general laws from observational data and on the other hand it also aimed to reconstruct historical discoveries and realize new ones. We will assess the claims of the BACON program by means of two historical cases studies: the discovery of the sine law of refraction in optics and the discovery of Kepler’s third law of planetary motion. I will demonstrate that, despite the formulated claims, BACON did not use the same historical data available to its discoverers and, more importantly, that the model of inductive generalization of observational data does not correspond with the historical methods. Finally I will question the value of data-driven induction for scientific discovery in general.

We present the results of a search for stellar flares from stars neighbouring the target sources in the Kepler short cadence data. These flares have been discarded as contaminants in previous surveys and therefore provide an unexplored resource of flare events, in particular high energy events from faint stars. We have measured M dwarf flare energies up to 1.5$\times$10^35 erg, pushing the limit for flare energies measured using Kepler data. We have used our sample to study theflaring activity of wide binaries, finding that the lower mass counterpart in a wide binary flares more often at a given energy. Of the 4430 flares detected in our original search, 298 came from a neighbouring star, a rate of 6.7$\pm$0.4 per cent for the Kepler short cadence lightcurves. We have used our sample to estimate a 5.8$\pm$0.1 per cent rate of false positive flare events in studies using TESS short cadence data., 10 pages, 2 figures, 2 tables. Accepted for publication in the Monthly Notices of the Royal Astronomical Society

Reports on the Chair for Intelligent Transportation Systems (ITS)–Sustainable Transport Logistics 4.0 at Johannes Kepler University Linz (JKU).

In [4], the following problem is solved. Imagine that you are standing in the middle of a road. Suddenly, you see a truck coming towards you. The driver is distracted and cannot see you. Your first...

We examine the origins of the Kepler 36 planetary system, which features two very different planets: Kepler 36b ($\rm \rho = 7.46$ $\rm g$ $\rm cm^{-3}$) and Kepler 36c ($\rm \rho = 0.89$ $\rm g$ $\rm cm^{-3}$). The planets lie extremely close to one another, separated by just 0.01 au, and they orbit just a tenth of an au from the host star. In our origin scenario, Kepler 36b starts with far less mass than Kepler 36c, a gaseous giant planet that forms outside the ice line and quickly migrates inwards, capturing its neighbour into its 2:1 mean-motion resonance while continuing to move inwards through a swarm of planetesimals and protoplanets. Subsequent collisions with these smaller bodies knock Kepler 36b out of resonance and raise its mass and density (via self-compression). We find that our scenario can yield planets whose period ratio matches that of Kepler 36b and c, although these successes are rare, occurring in just 1.2 per cent of cases. However, since systems like Kepler 36 are themselves rare, this is not necessarily a drawback.

Neste trabalho apresentaremos um pequeno estudo sobre a astrologia de Kepler e algumas reflexões sobre a prática em suas concepções. O escrito que norteou nossa pesquisa foi De fundamentis astrologiae certioribus (1602), um trabalho em que temos uma preocupação com os fundamentos da astrologia, além das previsões para o referido ano. Nossa análise se voltou, principalmente, nas características dos planetas que nos levou a iniciar uma reflexão sobre o papel da luz. A partir desse estudo acreditamos ser possível, de fato, atribuir uma fundamental importância da astrologia em sua cosmologia

Cet article a pour objet la réinterprétation, dans le sillage de la rénovation keplérienne de l’optique, de la fonction de l’image rétinienne pour la vision par Gassendi et Descartes. Une comparaison de leurs approches montre qu’elles reposent sur une interprétation différente du modèle iconique de la perception. S’ils attribuent un rôle crucial à l’imagination pour la perception visuelle, leurs positions philosophiques font jouer un rôle différent à l’image dans la perception visuelle et les amènent à concevoir de façon divergente l’imagination et son rapport aux autres pouvoirs de l’esprit. This article focuses on the reinterpretation, in the wake of the Keplerian renovation of optics, of the function of the retinal image for vision by Gassendi and Descartes. A comparison of their approaches shows that they are based on a different interpretation of the iconic model of perception. While they attribute a crucial role to the imagination for visual perception, their philosophical positions make the image play a different role in visual perception and lead them to divergent conceptions of imagination and its relationship to other powers of the mind.

If a transiting exoplanet has a moon, that moon could be detected directly from the transit it produces itself, or indirectly via the transit timing variations it produces in its parent planet. There is a range of parameter space where the Kepler Space Telescope is sensitive to the TTVs exomoons might produce, though the moons themselves would be too small to detect photometrically via their own transits. The Earth's Moon, for example, produces TTVs of 2.6 minutes amplitude by causing our planet to move around their mutual centre of mass. This is more than Kepler's short-cadence interval of 1 minute and so nominally detectable (if transit timings can be measured with comparable accuracy), even though the Moon's transit signature is only 7% that of Earth's, well below Kepler's nominal photometric threshold. Here we examine several Kepler systems, exploring the hypothesis that an exomoon could be detected solely from the TTVs it induces on its host planet. We compare this with the alternate hypothesis that the TTVs are caused by an non-transiting planet in the system. We examine 13 Kepler systems and find 8 where both hypotheses explain the observed TTVs equally well. Though no definitive exomoon detection can be claimed on this basis, the observations are nevertheless completely consistent with a dynamically stable moon small enough to fall below Kepler's photometric threshold for transit detection, and these systems warrant further observation and analysis., 17 pages. 15 figures. Accepted for publication on November 26, 2020, by the Monthly Notices of the Royal Astronomical Society

An algorithm for the numerical solution of Kepler’s equation with machine precision is presented. The convergence of the iterative sequence of Newton’s method is proved for the indicated initial approximation. The problem of finding a numerical solution to Kepler’s equation as a floating point number is formulated. Aspects related to computations near machine zero are taken into account. We analyzed the accuracy of the possible result. A problem is identified that arises when tending for the highest possible accuracy and a solution is proposed. An estimate is given of the computer time required to solve Kepler’s equation by this method.

High-precision photometric data from space missions have improved our understanding of stellar granulation. These observations have shown with precision the stochastic brightness fluctuations of stars across the HR diagram, allowing us to better understand how stellar surface convection reacts to a change in stellar parameters. These fluctuations need to be understood and quantified in order to improve the detection and characterization of exoplanets. In this work, we provide new scaling relations of two characteristic properties of the brightness fluctuations time series, the standard deviation ($\sigma$) and the auto-correlation time ($\tau\rm_{eff}$). This was done by using long time series of 3D stellar atmosphere models at different metallicities and across the HR diagram, generated with a 3D radiative hydrodynamical code: the STAGGER code. We compared our synthetic granulation properties with the values of a large sample of Kepler stars, and analyzed selected stars with accurate stellar parameters from the Kepler LEGACY sample. Our 3D models showed that $\sigma\propto\nu\rm_{max}^{-0.567\pm0.012}$ and $\tau\rm_{eff}\propto\nu\rm_{max}^{-0.997\pm0.018}$ for stars at solar metallicity. We showed that both $\sigma$ and $\tau\rm_{eff}$ decrease with metallicity, although the metallicity dependence is more significant on $\sigma$. Unlike previous studies, we found very good agreement between $\sigma$ from Kepler targets and the 3D models at $\log{g}\leq3.5$, and a good correlation between the stars and models with $\log{g}\geq3.5$. For $\tau\rm_{eff}$, we found that the 3D models reproduced well the Kepler LEGACY star values. Overall, this study shows that 3D stellar atmosphere models reproduce the granulation properties of stars across the HR diagram., Comment: Accepted for publication in MNRAS

La question posée dans cet article est de savoir dans quelle mesure et selon quels schémas il est possible de parler de la vision sensible comme d’une représentation psychique avant la nouvelle optique inaugurée par Johannes Kepler dans ses célèbres Paralipomena ad Vitellionem (1604). L’article part du point de vue suivant : c’est seulement à l’intérieur de ce nouveau paradigme, qui dissocie le processus physique de la vision de son traitement psychique, qu’il serait légitime de parler de la vision comme une construction mentale, comme une représentation. En examinant cette question à la lumière de plusieurs théories anciennes et médiévales, l’article aboutit à une conclusion différente. C’est depuis Aristote que la question de la vision comme représentation mentale est posée, du fait de la fonction majeure qui est conférée aux sens internes (phantasia, sens commun) dans l’élaboration du contenu de perception, et certaines théories sous influence néo-platonicienne, comme celles d’Augustin ou Avicenne, conçoivent clairement la vision directe comme une représentation psychique. Dans les Paralipomena ad Vitellionem, Kepler sépare l’optique comme science physique de la lumière de la psychologie de la perception ; mais cette dernière a déjà une longue histoire, tout comme l’idée de la vision comme représentation mentale. 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.

Numerous early modern experimentalists, including Galileo Galilei, Francis Bacon and Thomas Harriot, viewed one seemingly humble principle – that at a given volume, different substances can be identified by their particular weight, or specific gravity – as a fundamental key to the understanding of nature in general. Johannes Kepler’s Messekunst Archimedis of 1616 contains a striking summary of the experimental research on specific gravities in the long sixteenth-century. Counting himself amongst an extensive list of authors interested in this problem, Kepler mentions not only natural philosophers or mathematicians interested in Archimedes. His account surprisingly includes humanists, instrument makers, antiquarians and assayers. Received histories of specific gravities often focus on antecedents of modern disciplinary concepts and methodologies, where instead, Kepler’s account suggests the existence of a heterogeneous group of early modern experts involved in experiments on the quantification of matter, at the intersection between the history of science, practical mathematics and the humanities.

We discuss the current state of problems associated with the discovery and study of exocomets, i.e objects of extrasolar systems, that are in many aspects similar to the solar system comets. Thus far, more than 4,300 exoplanetary systems have been discovered, but little is known about the populations of subplanetary bodies in these systems, in particular comets. Existing theories of planet formation suggest that populations of small bodies in the planetary systems should be numerous, especially at the early stages of their formation. Currently, most of the stars observed with the confirmed transit exoplanets and candidate stars with exoplanetary systems have been collected in the Kepler and TESS space mi- ssion databases. These databases can be used for a search and study of the exocomet transit signatures in extrasolar systems. So far, the number of observed cases of exocomet transits has been small, only about 20 events. Due to the rapid accumulation of data, new researches aimed to identify the specific transit events and study the physical characteristics of small bodies in the extrasolar systems are of great importance.Worth considering is the concept of “falling evaporating bodies”, massive enough bodies surrounded by mini- atmospheres, which fall on the parent star. The events might produce the variable, short-time red-shifts of some spectral features in their spectra. Alternative evidence of exocomet transits can be obtained by detection of the cometary emissions in CO, C, and O lines in the millimeter region of the spectra of debris disks by the ALMA and APEX telescopes. We discuss the known detection methods based on the analysis of the photometric and spectral series of observational data of space missions and ground- based complexes. Some results of experimental studi- es of the exocometary transit signatures obtained by other authors are presented and discussed.

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

Dedicated transiting surveys, such as the Kepler space telescope, have provided the astronomy community with a rich data set resulting in many new discoveries. In this paper, we look at eight Kepler objects identified by Wheeler & Kipping with a periodic, broad increase in flux, that look distinctly different from intrinsic star variability. We consider two physical phenomena as explanations for these observed Kepler light curves; the first being the classical explanation while the second being an alternative scenario: (i) tidal interactions in a binary star system, and (ii) forward scattering from an optically thin cloud around an exoplanet. We investigate the likelihood of each model by modelling and fitting to the observed data. The binary system qualitatively does a good job of reproducing the shape of the observed light curves due to the tidal interaction of the two stars. We do, however, see a mismatch in flux right before or after the peak brightness. We find that six out of the eight systems require an F-type primary star with a K-type companion with large eccentricities. At the same time, we find that optically thin discs, modelled using a Henyey–Greenstein phase function are also able to generate these broad brightening events. Five of the eight observed objects can be described with this new hypothesis in the absence of RV observations. As the other three are not well-described by the disc model, we conclude that they are indeed heartbeat stars.

Johannes Kepler’s little book on the snowflake anticipates one direction of twenty-first-century science. Why do snowflakes all have six corners? Kepler searches for a geometry inscribed in nature, a “formative faculty” that shapes the dynamic patterns of both inorganic and organic forms. A similar search drives modern biotechnology. Twentieth-century science, exemplified by Wolfgang Pauli, had built on principles in tune with those of Kepler’s rival, the hermeticist Robert Fludd. Quantum physics is invested in archetypal numbers (such as 137, the fine-structure constant), in unobjectifiability (the impossibility of viewing a world unaffected by the observer), and in action-at-a-distance (effects that can be calculated but whose cause remains unknown). Kepler scorns such principles. Instead he looks for patterns of organization that account for the real world, whether in snowflakes, the heavens, or living bodies. Today that project has been revived in the life sciences, in ecology and ecosystems, in fractal geometry, in nanotech and biotech. Perhaps Kepler’s vision of science has come into its own.

In his Della Pittura, Leon Battista Alberti initiated what I call a “utopian moment,” a philosophical and practical disposition fusing human ingenuity, geometry, and political harmony. This paper follows these notions as they evolved over the course of the sixteenth century and were embraced by the new science of Johannes Kepler and René Descartes, who reshaped these utopian dispositions with their new geometrical analyses of sight and light. In his Dioptrice, Kepler suggests a new science of refractions produced and manipulated artificially through lenses, their physical properties analyzed geometrically; in analyzing the rainbow, Descartes artificially reproduces it, initially through a glass flask filled with water, and then through a prism, thus giving a geometrical causal account of its colors. In both cases these analyses are entwined with subtle political metaphors, transforming the technical scientific issues into key features of a “utopian moment.”

Approximately half of the planets discovered by NASA's Kepler mission are in systems where just a single planet transits its host star, and the remaining planets are observed to be in multi-planet systems. Recent analyses have reported a dichotomy in the eccentricity distribution displayed by systems where a single planet transits compared with that displayed by the multi-planet systems. Using $N$-body simulations, we examine the hypothesis that this dichotomy has arisen because inner systems of super-Earths are frequently accompanied by outer systems of giant planets that can become dynamically unstable and perturb the inner systems. Our initial conditions are constructed using a subset of the known Kepler five-planet systems as templates for the inner systems, and systems of outer giant planets with masses between those of Neptune and Saturn that are centred on orbital radii $2 \le a_{\rm p} \le 10$ au. The parameters of the outer systems are chosen so that they are always below an assumed radial velocity detection threshold of 3 ms$^{-1}$. The results show an inverse relation between the mean eccentricities and the multiplicites of the systems. Performing synthetic transit observation of the final systems reveals dichotomies in both the eccentricity and multiplicity distributions that are close to being in agreement with the Kepler data. Hence, understanding the observed orbital and physical properties of the compact systems of super-Earths discovered by Kepler may require holistic modelling that couples the dynamics of both inner and outer systems of planets during and after the epoch of formation., 19 pages, 24 figures, accepted to MNRAS

The ratio of small-to-large separations r010 has been widely used in helioseismology and asteroseismology to investigate the internal structure of a star, as it is approximately independent of the structure of the outer layers. Several studies have used this tool to constrain the convective-core overshooting of main-sequence stars (i.e. 0.0 ≤ δov ≤ 0.2). This is consistent with the generally accepted values. However, Yang et al. have proposed that there is large convective-core overshooting in the Kepler targets KIC 2837475 and 11081729: 1.2 ≤ δov ≤ 1.6 and 1.7 ≤ δov ≤ 1.8, respectively. These are much larger than the normal values. Thus, the aim of this study is to re-investigate the ratios of the two stars using a model-independent method with the latest p-mode observations. Our results indicate that there is no robustness for including such a large convective-core overshooting while modelling these two stars. In fact, this leads to over-fitting, and the observational constraints of r010 prefer models with a normal convective-core overshooting (i.e. 0.0 ≤ δov ≤ 0.2) as the candidates for the best-fitting model of KIC 2837475 and 11081729.

The K2 mission of the Kepler Space Telescope offers a unique possibility to examine sources of both Galactic and Extra-galactic origin with high cadence photometry. Alongside the multitude of supernovae and quasars detected within targeted galaxies, it is likely that Kepler has serendipitously observed many transients throughout K2. Such events will likely have occurred in background pixels, coincidentally surrounding science targets. Analysing the background pixels presents the possibility to conduct a high cadence survey with areas of a few square degrees per campaign. We demonstrate the capacity to independently recover key K2 transients such as KSN 2015K and SN 2018oh. With this survey, we expect to detect numerous transients and determine the first comprehensive rates for transients with lifetimes $\leq1$ day., 13 pages, 10 figures, 4 tables

Tycho Brahe was not just an observer; he was a skilled theoretical astronomer, as his lunar and solar models show. Still, even if he is recognized for proposing the Geoheliocentric system, little do we know of the technical details of his planetary models, probably because he died before publishing the last two volumes of his Astronomiae Instaurandae Progymnasmata, which he planned to devote to the planets. As it happens, however, there are some extant drafts of his calculations in Dreyer’s edition of Tycho’s Opera Omnia under the name Calculi ad Corrigenda Elementa orbitae Saturni, which, to the best of my knowledge, have not yet been analyzed before. In these manuscripts, Tycho starts with calculations based on the Prutenic Tables and makes a series of adjustments to the mean longitude, the longitude of the apogee, and the eccentricity to fit a series of observations of oppositions. In doing that, Tycho (1) describes and applies a new method for obtaining accurate values for the parameters of the superior planets, he (2) develops a divided eccentricity (not bisected) model of Saturn, similar to the one we know Longomontanus and Kepler applied to Mars, and finally (3) he realizes that the true position of the Sun somehow affects the motion of Saturn around the zodiac and develops a method to correct the position of Saturn as a function of solar equation of anomaly. So, a close analysis of the calculations reveals details of the Tychonic planetary models unknown until now. The present study analyzes these drafts.

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.

The eclipsing binary system EPIC 201826968 was imaged using the Las Cumbres Observatory Global Telescope Network with Bessel-B, Bessel-V, SDSS-r0 and SDSS-i0 filters. AstroImageJ was used to determine the optimal exposure time for the images. We coded a phase-dispersion minimization (PDM) algorithm and compared its result to PyAstronomy’s PDM algorithm and both PyAstronomy’s and Astropy’s Lomb-Scargle algorithms. Our distance PDM algorithm gave a period of 0.3617673 days, while the PyAstronomy PDM gave 0.3617724 days. The Lomb-Scargle algorithms both gave very different periods of near 1.83 days, possibly due to Lomb-Scargle’s reliance on a sinusoidal fit. Since Kepler measured a period of 0.3617589 days, and the average period from the Python-coded and PyAstronomy PDM algorithms deviated from it by less than a second, we concluded that the period of eclipsing binary system EPIC 201826968 hasnot changed since Kepler’s observations.

In this study we observed and determined the period of the eclipsing binary star EPIC 201458798, finding that its period has not changed since it was last measured and published in the Kepler catalog in 2014. We did this by developing Python code to determine the period using two independent algorithms and partially automating the search for suitable comparison stars. Our system was imaged by the 0.4m Las Cumbres Observatory telescopes in four filters. We analyzed six photometry types returned for each image from the Our Solar Siblings pipeline. Of these photometries, we found source extractor kron (sek) to be the most appropriate type for our 2x2 binned images of EPIC 201458798. Both of the period-finding algorithms we developed gave results that were not statistically different from the Kepler catalog period for the infrared, red, and visual filter images. The blue filter images were statistically different fromthe Kepler catalog period for one of our algorithms but not the other.

In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant planet revolves the central star with an eccentric orbit, which is similar to the observed configuration of Kepler-68. Moreover, we find that the eccentricity of the middle planet can be excited to roughly 0.2 if the giant planet is more massive than 5 $M_J$,otherwise the terrestrial planets are inclined to remain near-circular orbits. Our study may provide a likely formation scenario for the planetary systems that harbor several terrestrial planets near MMRs inside and one gas-giant exterior to them., Comment: 13 pages, 8 figures, accepted for publication in MNRAS

When at the beginning of 1600, Kepler arrived to work with Tycho Brahe, Longomontanus, Tycho’s principal assistant, who was working with a model for Mars that predicted with remarkable accuracy its longitudes at oppositions. According to Kepler, this hypothesis “represented all these oppositions within a distance of two minutes in longitude.” The model, however, was unsuccessful in predicting longitudes at other elongations from the Sun, and latitudes even at opposition. Much has been said on how Kepler developed his model after this meeting, arriving finally at the so-called first two laws published in his Astronomia Nova in 1609. By contrast, Longomontanus’ attempt, published as a final model in his Astronomia Danica, has received little scholarly attention. In this paper, I will systematically analyse and explain this model. Even if Longomontanus’ solution is not as elegant as Kepler’s, it deserves scholarly attention, both because it solves the problems posed by the model that he and Tycho were working on when Kepler arrived and because it offers an interesting though heterodox solution that, by contrast, helps to highlight the elegance and simplicity of Kepler’s own solution.

Based on many years of experience in the organization of the third stage of Ukrainian National Astronomy Olympiad, the authors of the article attempt to formulate general principles for the selection and compilation of astronomy olympiad problems, as well as to demonstrate the application of the described principles on the example of astronomy olympiads in Ivano-Frankivsk region. The peculiarities of school Olympiad in astronomy, the purpose of their conduct, the specificity of task packages, including necessity for differentiation by complexity and topics, were analyzed. A characteristic feature of the Olympiad tasks is their non-standard nature, necessity to use methods that are unusual for students to solve problems. On the other hand, such tasks should match intellectual development of the competition participants, and the course of the solution should be accessible to understanding and should not require knowledge of a university program. In particular, on the basis of the analysis by the authors of the process of compiling astronomy Olympiad tasks, which were offered to students in the past years at the regional stage of the student Olympiads, were identified, the methods of their creation were systematized and characterized. Each method contains a detailed explanation, justification for its use and examples, both analytical and practical. For the sake of clarity, the topic “Kepler Laws” was choosen for Olympiad problems, which were analyzed and methods used to create them were described. This topic is one of the fundamental in the schoolar astronomy, which determines both the need to include such tasks in the Olympiad program and the complexity of their choice, and creation, because the topic is narrow enough and is qualitatively covered in various textbooks and collections of problems.

The Timaeus is the dialogue that was for many centuries the most influential of Plato’s works. Among its readers we find Descartes, Boyle, Kepler and Heisenberg. In the first division of Timaeus Plato deals with the theory of celestial motion, in the second he presents us with the first mathematical theory of the structure of matter. Here, in a gigantic step forward with respect to the preceding Democritean atomistic theory with its unalterable micro-entities, he introduces the intertransformability of elementary corpuscles and with that the first “chemical” reactions in history. Plato’s geometrical interpretation of Empedocles’ elements and his geometrical atomism is described at the molecular, atomic and sub-atomic level. The “chemical” reactions reported in Timaeus are written in the enlightening chemical symbolism, analogies with modern chemistry are noticed throughout.

According to statistics of planetary period ratios in multi-planet extrasolar systems, evident excesses appear just over the exact integral ratios 2 : 1 and 3 : 2 , while deficits exist on the near left side. There are various dynamical explanations for the phenomenon. For three observed planets in Kepler-9 system, the period ratio of the planet b and c approximately equals to 2.03, which cause this planet pair as a typical sample close to the 2:1 resonance. For two situations where secular interactions are considered only and resonance perturbations are added in, we applied Hamiltonian functions with second-order eccentricity terms to provide positions of current orbital configurations located in the level curves of energy as well as surfaces of section, then discussed the probable near resonance configurations of the two planets.

The motion of a particle moving under the influence of a central force is a fundamental paradigm in dynamics. The problem of planetary motion, specifically the derivation of Kepler’s laws motivated Newton’s monumental work, Principia Mathematica, effectively signalling the start of modern physics. Today, the central force problem stands as a basic lesson in dynamics. In this article, we discuss the classical central force problem in a general number of spatial dimensions n, as an instructive illustration of important aspects such as integrability, super-integrability and dynamical symmetry. The investigation is also in line with the realisation that it is useful to treat the number of dimensions as a variable parameter in physical problems. The dependence of various quantities on the spatial dimensionality leads to a proper perspective of the problems concerned. We consider, first, the orbital angular momentum (AM) in n dimensions, and discuss in some detail the role it plays in the integrability of the central force problem. We then consider an important super-integrable case, the Kepler problem, in n dimensions. The existence of an additional vector constant of the motion (COM) over and above the AM makes this problem maximally super-integrable. We discuss the significance of these COMs as generators of the dynamical symmetry group of the Hamiltonian. This group, the rotation group in n + 1 dimensions, is larger than the kinematical symmetry group for a general central force, namely, the rotation group in n dimensions.