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Journal articles on the topic 'Kepler's Algorithm'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Mahmoud, Shakir Wahab. "Wireless Sensor Network (WSN) Energy-Efficient Clustering and Routing: Evaluating Kepler's Algorithm Alongside K-Means." Engineering and Technology Journal 10, no. 05 (2025): 4855–64. https://doi.org/10.5281/zenodo.15349846.

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Wireless Sensor Networks (WSNs) find applications in a broad spectrum of fields, including but not limited to military surveillance and environmental monitoring, where energy efficiency is a key performance indicator because of sensor node power constraint. Implementation of low energy-consumption clustering and routing protocols is pivotal in optimizing network life by minimizing energy consumption. This paper discusses the collaboration of Kepler's Algorithm with the K-means clustering algorithm for improving energy efficiency in WSNs. Kepler's Algorithm, which is planetary motion dynamics-b

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Conway, Bruce A. "An improved algorithm due to laguerre for the solution of Kepler's equation." Celestial Mechanics 39, no. 2 (1986): 199–211. http://dx.doi.org/10.1007/bf01230852.

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CHIPADE, Radhika A., and Thekke Variyam RAMANATHAN. "Extended Kalman filter based statistical orbit determination for geostationary and geosynchronous satellite orbits in BeiDou constellation." Contributions to Geophysics and Geodesy 51, no. 1 (2021): 25–46. http://dx.doi.org/10.31577/congeo.2021.51.1.2.

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BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right asce

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Chen, Xiao Liang, Jian Xun Chen, and Hao Liu. "Large-Scale Virtual Simulation of the Solar System Based on Java3D." Applied Mechanics and Materials 721 (December 2014): 459–63. http://dx.doi.org/10.4028/www.scientific.net/amm.721.459.

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As the modeling of the solar system is difficult and inaccurate, the 3D modeling of the planets in the solar system is studied by using Java3D technology. To make the revolution of simulated planets meet Kepler's laws while traveling around the sun, an improved approximate algorithm to calculate the optimum angle and the vertex coordinates of each planet is proposed. Using java3D perspective projection technique, the observation coordinate system is determined, and real-time viewpoint setting as well as roaming processing is realized. Through multiple view technique, we can observe the movemen

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Sharaf, M. A., A. S. Saad, and H. H. Selim. "Analytical formulations to the method of variation of parameters in terms of universal Y's functions." Serbian Astronomical Journal, no. 190 (2015): 33–40. http://dx.doi.org/10.2298/saj1590033s.

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The method of variation of parameters still has a great interest and wide applications in mathematics, physics and astrodynamics. In this paper, universal functions (the Y's functions) based on Goodyear's time transformation formula were used to establish a variation of parameters method which is useful in slightly perturbed two-body initial value problem. Moreover due to its universality, the method avoids the switching among different conic orbits which are commonly occurring in space missions. The position and velocity vectors are written in terms of f and g series. The method is developed

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Matesic, Michael R. B., Jason F. Rowe, John H. Livingston, Shishir Dholakia, Daniel Jontof-Hutter, and Jack J. Lissauer. "Gaussian Processes and Nested Sampling Applied to Kepler's Small Long-period Exoplanet Candidates." Astronomical Journal 167, no. 2 (2024): 68. http://dx.doi.org/10.3847/1538-3881/ad0fe9.

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Abstract There are more than 5000 confirmed and validated planets beyond the solar system to date, more than half of which were discovered by NASA’s Kepler mission. The catalog of Kepler’s exoplanet candidates has only been extensively analyzed under the assumption of white noise (i.i.d. Gaussian), which breaks down on timescales longer than a day due to correlated noise (point-to-point correlation) from stellar variability and instrumental effects. Statistical validation of candidate transit events becomes increasingly difficult when they are contaminated by this form of correlated noise, esp

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Qian, Zhenghong, Yaming Zhang, Dongqi Pu, Gaoyuan Xie, Die Pu, and Mingjun Ye. "A New Hybrid Improved Kepler Optimization Algorithm Based on Multi-Strategy Fusion and Its Applications." Mathematics 13, no. 3 (2025): 405. https://doi.org/10.3390/math13030405.

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The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak global search ability, and slow convergence speed. To address these deficiencies, this paper presents a multi-strategy fusion Kepler optimization algorithm (MKOA). Firstly, the algorithm initializes the population using Good Point Set, enhancing population diversity. Secondly, Dynamic Opposit

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Claytor, Zachary R., and Jamie Tayar. "New Rotation Periods from the Kepler Bonus Background Light Curves." Astrophysical Journal 987, no. 1 (2025): 8. https://doi.org/10.3847/1538-4357/add5f0.

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Abstract The Kepler field hosts the best-studied sample of field star rotation periods. However, due to Kepler’s large 4″ pixels, many of its light curves are at high risk of contamination from background sources. The new Kepler Bonus Background light curves are deblended using a point-spread function algorithm, providing light curves of over 400,000 new background sources in addition to over 200,000 reanalyzed Kepler prime targets. These light curves provide the opportunity to search for new rotation periods. Here we apply a convolutional neural network trained on synthetic spot-modulated lig

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Zechmeister, M. "CORDIC-like method for solving Kepler’s equation." Astronomy & Astrophysics 619 (November 2018): A128. http://dx.doi.org/10.1051/0004-6361/201833162.

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Context. Many algorithms to solve Kepler’s equations require the evaluation of trigonometric or root functions. Aims. We present an algorithm to compute the eccentric anomaly and even its cosine and sine terms without usage of other transcendental functions at run-time. With slight modifications it is also applicable for the hyperbolic case. Methods. Based on the idea of CORDIC, our method requires only additions and multiplications and a short table. The table is independent of eccentricity and can be hardcoded. Its length depends on the desired precision. Results. The code is short. The conv

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Zechmeister, M. "Solving Kepler’s equation with CORDIC double iterations." Monthly Notices of the Royal Astronomical Society 500, no. 1 (2020): 109–17. http://dx.doi.org/10.1093/mnras/staa2441.

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ABSTRACT In previous work, we developed the idea to solve Kepler’s equation with a CORDIC-like algorithm, which does not require any division, but still requires multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler’s equation using only bitshifts, additions and one initial multiplication. We prescale the initial vector with the eccentricity and the scale correction factor. The rotation direction is decided without correction for the changing scale. We find that double CORDIC iterations are self-correcting and compensate for possible wrong rotations in sub

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Tommasini, D., and D. N. Olivieri. "Comment on ‘An efficient code to solve the Kepler equation: elliptic case’." Monthly Notices of the Royal Astronomical Society 506, no. 2 (2021): 1889–95. http://dx.doi.org/10.1093/mnras/stab1790.

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ABSTRACT In a recent MNRAS article, Raposo-Pulido and Pelaez (RPP) designed a scheme for obtaining very close seeds for solving the elliptic Kepler equation with the classical and modified Newton–Raphson methods. This implied an important reduction in the number of iterations needed to reach a given accuracy. However, RPP also made strong claims about the errors of their method that are incorrect. In particular, they claim that their accuracy can always reach the level of ∼5ε, where ε is the machine epsilon (e.g. ε = 2.2 × 10−16 in double precision), and that this result is attained for all va

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Martínez-Palomera, Jorge, Christina Hedges, and Jessie Dotson. "Kepler Bonus: Light Curves of Kepler Background Sources." Astronomical Journal 166, no. 6 (2023): 265. http://dx.doi.org/10.3847/1538-3881/ad0727.

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Abstract NASA’s Kepler primary mission observed about 116 deg2 in the sky for 3.5 consecutive years to discover Earth-like exoplanets. This mission recorded pixel cutouts, known as target pixel files (TPFs), of over 200,000 targets that were selected to maximize the scientific yield. The Kepler pipeline performed aperture photometry for these primary targets to create light curves. However, hundreds of thousands of background sources were recorded in the TPFs and have never been systematically analyzed. This work uses the linearized field deblending (LFD) method, a point-spread function (PSF)

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Hakmi, Sultan Hassan, Abdullah M. Shaheen, Hashim Alnami, Ghareeb Moustafa, and Ahmed Ginidi. "Kepler Algorithm for Large-Scale Systems of Economic Dispatch with Heat Optimization." Biomimetics 8, no. 8 (2023): 608. http://dx.doi.org/10.3390/biomimetics8080608.

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Combined Heat and Power Units Economic Dispatch (CHPUED) is a challenging non-convex optimization challenge in the power system that aims at decreasing the production cost by scheduling the heat and power generation outputs to dedicated units. In this article, a Kepler optimization algorithm (KOA) is designed and employed to handle the CHPUED issue under valve points impacts in large-scale systems. The proposed KOA is used to forecast the position and motion of planets at any given time based on Kepler’s principles of planetary motion. The large 48-unit, 96-unit, and 192-unit systems are consi

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Tommasini, Daniele. "Bivariate Infinite Series Solution of Kepler’s Equations." Mathematics 9, no. 7 (2021): 785. http://dx.doi.org/10.3390/math9070785.

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A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries. This result is based on an iterative procedure for the analytical computation of all the higher-order partial derivatives of the eccentric anomaly with respect to the eccentricity e and mean anomaly M in a given base point (ec,Mc) of the (e,M) plane. Explicit examples of such bivariate infinite series are provided, corresponding to different choices of (ec,Mc), and their convergence is studied numerically

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Windemuth, Diana, Eric Agol, Josh Carter, et al. "An automated method to detect transiting circumbinary planets." Monthly Notices of the Royal Astronomical Society 490, no. 1 (2019): 1313–24. http://dx.doi.org/10.1093/mnras/stz2637.

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ABSTRACT To date a dozen transiting ‘Tatooines’ or circumbinary planets (CBPs) have been discovered, by eye, in the data from the Kepler mission; by contrast, thousands of confirmed circumstellar planets orbiting around single stars have been detected using automated algorithms. Automated detection of CBPs is challenging because their transits are strongly aperiodic with irregular profiles. Here, we describe an efficient and automated technique for detecting circumbinary planets that transit their binary hosts in Kepler light curves. Our method accounts for large transit timing variations (TTV

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Murphy, Simon J., Nicholas H. Barbara, Daniel Hey, Timothy R. Bedding, and Ben D. Fulcher. "Finding binaries from phase modulation of pulsating stars with Kepler – VI. Orbits for 10 new binaries with mischaracterized primaries." Monthly Notices of the Royal Astronomical Society 493, no. 4 (2020): 5382–88. http://dx.doi.org/10.1093/mnras/staa562.

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ABSTRACT Measuring phase modulation in pulsating stars has proven to be a highly successful way of finding binary systems. The class of pulsating main-sequence A and F variables, known as δ Scuti stars consists of particularly good targets for this, and the Kepler sample of these has been almost fully exploited. However, some Keplerδ Scuti stars have incorrect temperatures in stellar properties catalogues, and were missed in previous analyses. We used an automated pulsation classification algorithm to find 93 new δ Scuti pulsators among tens of thousands of F-type stars, which we then searched

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Vavrukh, M., D. Dzikovskyi, and O. Stelmakh. "Analytical images of Kepler's equation solutions and their applications." Mathematical Modeling and Computing 10, no. 2 (2023): 351–58. http://dx.doi.org/10.23939/mmc2023.02.351.

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The simple fast-converging analytical calculations algorithms for eccentric anomaly are proposed for an arbitrary eccentricity 0<e≤1. The kinematic characteristics of Halley's comet are calculated as the function of time. Mass of Galaxy + NGC 224 system using the model of elliptical relative motion is also estimated.

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Journal, Baghdad Science. "On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms." Baghdad Science Journal 11, no. 1 (2014): 186–92. http://dx.doi.org/10.21123/bsj.11.1.186-192.

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In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

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Rasheed, Mohammed S. "On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms." Baghdad Science Journal 11, no. 1 (2014): 186–92. http://dx.doi.org/10.21123/bsj.2014.11.1.186-192.

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In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

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Tommasini, Daniele, and David N. Olivieri. "Fast Switch and Spline Function Inversion Algorithm with Multistep Optimization and k-Vector Search for Solving Kepler’s Equation in Celestial Mechanics." Mathematics 8, no. 11 (2020): 2017. http://dx.doi.org/10.3390/math8112017.

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Obtaining the inverse of a nonlinear monotonic function f(x) over a given interval is a common problem in pure and applied mathematics, the most famous example being Kepler’s description of orbital motion in the two-body approximation. In traditional numerical approaches, this problem is reduced to solving the nonlinear equation f(x)−y=0 in each point y of the co-domain. However, modern applications of orbital mechanics for Kepler’s equation, especially in many-body problems, require highly optimized numerical performance. Ongoing efforts continually attempt to improve such performance. Recent

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Huang, Weidong, and Bowen Liu. "Solar Position Algorithm Based on the Kepler Equation." Applied Sciences 12, no. 11 (2022): 5449. http://dx.doi.org/10.3390/app12115449.

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When calculating the position of the sun, earth’s motion can be assumed to be an ellipse if the accuracy of calculation is required to be 0.01 degrees. Then, Kepler’s equation can be applied from the mean anomaly of the sun at a specific time to calculate the true anatomy of the sun at the time, and the sun’s position can be calculated. The average absolute error of calculating the sun’s altitude and azimuth is only 0.04 and 0.06 mrad, respectively, which can meet the requirements of a concentrated solar tracking system. This method only needs to correct the length of the regression year and t

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Sarafrazi, Soroor, Hossein Nezamabadi-pour, and Saeid R. Seydnejad. "A novel hybrid algorithm of GSA with Kepler algorithm for numerical optimization." Journal of King Saud University - Computer and Information Sciences 27, no. 3 (2015): 288–96. http://dx.doi.org/10.1016/j.jksuci.2014.10.003.

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23

Fellahi, Anwar, Souhil Mouassa, and Hacene Mellah. "Optimal power flow solution incorporating hybrid conventional and renewable resources using electric eel foraging optimization algorithm." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e11612. https://doi.org/10.54021/seesv5n2-632.

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In recent years, metaheuristic algorithms have become the main tool in solving the Optimal Power Flow (OPF) problem due to their effectiveness in addressing complicated modern power systems. This complexity is fueled by the rise of Renewable Energy Resources (RERs) and the need to decrease greenhouse emissions. This research presents a comprehensive approach that aims to optimize the performance of power networks in the presence of thermal, wind, and Solar Photovoltaic (SPV) units. The algorithm implemented is named Electrical Eel Foraging Optimization (EEFO). It is carried out using the modif

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Liu, Yuchang, Shuai Wang, Geqiang Li, Bo Mao, Zhenle Dong, and Donglin Li. "Optimal parameter identification of hydro-pneumatic suspension for mine cars." International Journal for Simulation and Multidisciplinary Design Optimization 15 (2024): 26. https://doi.org/10.1051/smdo/2024022.

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This article proposes a method for matching parameters of hydro-pneumatic suspension with the goal of improving the vehicle ride comfort of mine cars. Considering the nonlinear characteristics of the hydro-pneumatic suspension, a 7-DOF dynamic model is established for the entire vehicle, The Kepler optimization algorithm is applied for parameter matching and simulation analysis of the hydro-pneumatic suspension based on vehicle ride comfort. Comparative verification shows that compared with the fitness functions of other algorithms, the KOA algorithm converges the fastest and has the highest p

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Raposo-Pulido, V., and J. Peláez. "An efficient code to solve the Kepler equation." Astronomy & Astrophysics 619 (November 2018): A129. http://dx.doi.org/10.1051/0004-6361/201833563.

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Context. This paper introduces a new approach for solving the Kepler equation for hyperbolic orbits. We provide here the Hyperbolic Kepler Equation–Space Dynamics Group (HKE–SDG), a code to solve the equation. Methods. Instead of looking for new algorithms, in this paper we have tried to substantially improve well-known classic schemes based on the excellent properties of the Newton–Raphson iterative methods. The key point is the seed from which the iteration of the Newton–Raphson methods begin. If this initial seed is close to the solution sought, the Newton–Raphson methods exhibit an excelle

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Kgoadi, R., I. Whittingham, and C. Engelbrecht. "Searching for Pulsating Stars Using Clustering Algorithms." Proceedings of the International Astronomical Union 14, S339 (2017): 310–13. http://dx.doi.org/10.1017/s1743921318002855.

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AbstractClustering algorithms constitute a multi-disciplinary analytical tool commonly used to summarise large data sets. Astronomical classifications are based on similarity, where celestial objects are assigned to a specific class according to specific physical features. The aim of this project is to obtain relevant information from high-dimensional data (at least three input variables in a data-frame) derived from stellar light-curves using a number of clustering algorithms such as K-means and Expectation Maximisation. In addition to identifying the best performing algorithm, we also identi

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Bugnet, L., R. A. García, S. Mathur, et al. "FliPerClass: In search of solar-like pulsators among TESS targets." Astronomy & Astrophysics 624 (April 2019): A79. http://dx.doi.org/10.1051/0004-6361/201834780.

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The NASA Transiting Exoplanet Survey Satellite (TESS) is about to provide full-frame images of almost the entire sky. The amount of stellar data to be analysed represents hundreds of millions stars, which is several orders of magnitude more than the number of stars observed by the Convection, Rotation and planetary Transits satellite (CoRoT), and NASA Kepler and K2 missions. We aim at automatically classifying the newly observed stars with near real-time algorithms to better guide the subsequent detailed studies. In this paper, we present a classification algorithm built to recognise solar-lik

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S. Rasheed, Mohammed. "An Improved Algorithm For The Solution of Kepler‘s Equation For An Elliptical Orbit." Engineering and Technology Journal 28, no. 7 (2010): 1316–20. http://dx.doi.org/10.30684/etj.28.7.4.

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Taaki, Jamila S., Athol J. Kemball, and Farzad Kamalabadi. "Robust Detrending of Spatially Correlated Systematics in Kepler Light Curves Using Low-rank Methods." Astronomical Journal 167, no. 2 (2024): 60. http://dx.doi.org/10.3847/1538-3881/ad1110.

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Abstract Light curves produced by wide-field exoplanet transit surveys such as CoRoT, Kepler, and the Transiting Exoplanet Survey Satellite are affected by sensor-wide systematic noise, which is correlated both spatiotemporally and with other instrumental parameters such as the photometric magnitude. Robust and effective systematics mitigation is necessary to achieve the level of photometric accuracy required to detect exoplanet transits and to faithfully recover other forms of intrinsic astrophysical variability. We demonstrate the feasibility of a new exploratory algorithm to remove spatiall

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Ms., Rasika P. Arbat. "COMPARATIVE STUDY ON SINGLE SOURCE SHORTEST PATH ALGORITHM." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 1 (2017): 81–84. https://doi.org/10.5281/zenodo.230948.

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We propose architecture for graph analysis to find out the single source shortest path to all other vertices is a common problem. The solution to this problem is Bellman- Ford’s algorithm that solves such a single source shortest path (SSSP) problem and better applies to be parallelized for many core architectures. In this we get, the high degree of parallelism is guaranteed at the cost of low work efficiency which is compared to similar algorithms in literature (e.g. Dijkstra’s) involves much more redundant work and a consequent waste of power consumption. This architecture is a parallel impl

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Heller, René, Michael Hippke, and Kai Rodenbeck. "Transit least-squares survey." Astronomy & Astrophysics 627 (July 2019): A66. http://dx.doi.org/10.1051/0004-6361/201935600.

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The extended Kepler mission (K2) has revealed more than 500 transiting planets in roughly 500 000 stellar light curves. All of these were found either with the box least-squares algorithm or by visual inspection. Here we use our new transit least-squares (TLS) algorithm to search for additional planets around all K2 stars that are currently known to host at least one planet. We discover and statistically validate 17 new planets with radii ranging from about 0.7 Earth radii (R⊕) to roughly 2.2 R⊕ and a median radius of 1.18 R⊕. EPIC 201497682.03, with a radius of 0.692+0.059−0.048, is the secon

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Ding, Xu, KaiFan Ji, XuZhi Li, et al. "Fast Derivation of Contact Binary Parameters for Large Photometric Surveys." Astronomical Journal 164, no. 5 (2022): 200. http://dx.doi.org/10.3847/1538-3881/ac8e66.

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Abstract Thanks to an enormous release of light curves of contact binaries, it is a challenge to derive the parameters of contact binaries using the Phoebe program and the Wilson–Devinney program with the Markov chain Monte Carlo (MCMC) algorithm. In this paper, we use neural network (NN) and MCMC algorithm to derive the parameters of contact binaries. The fitting of models is still done with the MCMC algorithm, but that the neural network is used to establish the mapping relationship between the parameters and the light curves generated beforehand by Phoebe. The NN model is trained with a set

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Heller, René, Michael Hippke, Jantje Freudenthal, Kai Rodenbeck, Natalie M. Batalha, and Steve Bryson. "Transit least-squares survey." Astronomy & Astrophysics 638 (June 2020): A10. http://dx.doi.org/10.1051/0004-6361/201936929.

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The Sun-like star Kepler-160 (KOI-456) has been known to host two transiting planets, Kepler-160 b and c, of which planet c shows substantial transit-timing variations (TTVs). We studied the transit photometry and the TTVs of this system in our search for a suspected third planet. We used the archival Kepler photometry of Kepler-160 to search for additional transiting planets using a combination of our Wōtan detrending algorithm and our transit least-squares detection algorithm. We also used the Mercury N-body gravity code to study the orbital dynamics of the system in trying to explain the ob

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Alqahtani, Mohammed H., Sulaiman Z. Almutairi, Abdullah M. Shaheen, and Ahmed R. Ginidi. "Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow." Axioms 13, no. 7 (2024): 419. http://dx.doi.org/10.3390/axioms13070419.

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Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. The mathematical model of MDOPF involves formulating it as a non-linear, non-convex optimization problem aimed at minimizing specific objective functions while adhering to equality and inequality constraints. The objective function typically includes terms representing the Fuel Cost (FC), Entire Network Losses (ENL), and Entire Emissions (EE), while

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Leleu, A., G. Chatel, S. Udry, Y. Alibert, J. B. Delisle, and R. Mardling. "Alleviating the transit timing variation bias in transit surveys." Astronomy & Astrophysics 655 (November 2021): A66. http://dx.doi.org/10.1051/0004-6361/202141471.

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Transit timing variations (TTVs) can provide useful information for systems observed by transit, as they allow us to put constraints on the masses and eccentricities of the observed planets, or even to constrain the existence of non-transiting companions. However, TTVs can also act as a detection bias that can prevent the detection of small planets in transit surveys that would otherwise be detected by standard algorithms such as the Boxed Least Square algorithm if their orbit was not perturbed. This bias is especially present for surveys with a long baseline, such as Kepler, some of the TESS

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van Veen, Hendrik, Nathaniel Saul, David Eargle, and Sam Mangham. "Kepler Mapper: A flexible Python implementation of the Mapper algorithm." Journal of Open Source Software 4, no. 42 (2019): 1315. http://dx.doi.org/10.21105/joss.01315.

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H.U., Dike, and Isaac A.E. "Determination of Eccentric Anomaly for Kepler’s Satellite Orbit Using Perturbation-Based Seeded Secant Iteration Scheme." British Journal of Computer, Networking and Information Technology 4, no. 1 (2021): 21–27. http://dx.doi.org/10.52589/bjcnit-m7xkp8rv.

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In this paper, the determination of eccentric anomaly (E) for Kepler’s satellite orbit using Perturbation-Based Seeded Secant (PBSS) iteration algorithm is presented. The solution is meant for Kepler’s orbit with the value of eccentricity (e) in the range 0 ≤ e ≤ 1. Such orbits are either circular or elliptical. The demonstration of the applicability of the PBSS iteration is presented using sample numerical examples with different values of mean anomaly (M) and eccentricity (e). The summary of the results of E for M = 30° and e in the range 0.001 ≤ e ≤1 showed that the convergence cycle (n) in

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Stumpe, Martin C., Jeffrey C. Smith, Jeffrey E. Van Cleve, et al. "Kepler Presearch Data Conditioning I—Architecture and Algorithms for Error Correction in Kepler Light Curves." Publications of the Astronomical Society of the Pacific 124, no. 919 (2012): 985–99. http://dx.doi.org/10.1086/667698.

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Freudenthal, J., C. von Essen, A. Ofir, et al. "Kepler Object of Interest Network." Astronomy & Astrophysics 628 (August 2019): A108. http://dx.doi.org/10.1051/0004-6361/201935879.

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Context. The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised for follow-up observations of transiting planet candidate Kepler objects of interest with large transit timing variations (TTVs). The main goal of KOINet is the completion of their TTV curves as the Kepler telescope stopped observing the original Kepler field in 2013. Aims. We ensure a comprehensive characterisation of the investigated systems by analysing Kepler data combined with new ground-based transit data using a photodynamical model. This method is applied to the Kepl

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Deng, Chen, Xin Wu, and Enwei Liang. "The use of Kepler solver in numerical integrations of quasi-Keplerian orbits." Monthly Notices of the Royal Astronomical Society 496, no. 3 (2020): 2946–61. http://dx.doi.org/10.1093/mnras/staa1753.

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ABSTRACT A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the eccentric anomaly relies on the true anomaly that is associated with a unit radial vector calculated by an integrator. This scheme rigorously conserves all integrals and orbital elements except the mean longitude. However, the Kepler energy, angular momentum vector, and Laplace–Runge–Lenz vector for perturbed Kepler problems are slowly varying quanti

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Freudenthal, J., C. von Essen, S. Dreizler, et al. "Kepler Object of Interest Network." Astronomy & Astrophysics 618 (October 2018): A41. http://dx.doi.org/10.1051/0004-6361/201833436.

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Context. The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised to follow up transiting planet-candidate Kepler objects of interest (KOIs) with large transit timing variations (TTVs). Its main goal is to complete their TTV curves, as the Kepler telescope no longer observes the original Kepler field. Aims. Combining Kepler and new ground-based transit data we improve the modelling of these systems. To this end, we have developed a photodynamical model, and we demonstrate its performance using the Kepler-9 system as an example. Methods. Ou

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Hu, Gang, Changsheng Gong, Xiuxiu Li, and Zhiqi Xu. "CGKOA: An enhanced Kepler optimization algorithm for multi-domain optimization problems." Computer Methods in Applied Mechanics and Engineering 425 (May 2024): 116964. http://dx.doi.org/10.1016/j.cma.2024.116964.

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Dhanpal, Siddharth, Othman Benomar, Shravan Hanasoge, et al. "Measuring Frequency and Period Separations in Red-giant Stars Using Machine Learning." Astrophysical Journal 928, no. 2 (2022): 188. http://dx.doi.org/10.3847/1538-4357/ac5247.

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Abstract Asteroseismology is used to infer the interior physics of stars. The Kepler and TESS space missions have provided a vast data set of red-giant lightcurves, which may be used for asteroseismic analysis. These data sets are expected to significantly grow with future missions such as PLATO, and efficient methods are therefore required to analyze these data rapidly. Here, we describe a machine-learning algorithm that identifies red giants from the raw oscillation spectra and captures p- and mixed-mode parameters from the red-giant power spectra. We report algorithmic inferences for large

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Wang, Dongming. "A Method for Proving Theorems in Differential Geometry and Mechanics." JUCS - Journal of Universal Computer Science 1, no. (9) (1995): 658–73. https://doi.org/10.3217/jucs-001-09-0658.

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A zero decomposition algorithm is presented and used to devise a method for proving theorems automatically in differential geometry and mechanics. The method has been implemented and its practical efficiency is demonstrated by several non-trivial examples including Bertrand s theorem, Schell s theorem and Kepler-Newton s laws.

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Hippke, Michael, and René Heller. "Optimized transit detection algorithm to search for periodic transits of small planets." Astronomy & Astrophysics 623 (February 28, 2019): A39. http://dx.doi.org/10.1051/0004-6361/201834672.

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We present a new method to detect planetary transits from time-series photometry, the transit least squares (TLS) algorithm. TLS searches for transit-like features while taking the stellar limb darkening and planetary ingress and egress into account. We have optimized TLS for both signal detection efficiency (SDE) of small planets and computational speed. TLS analyses the entire, unbinned phase-folded light curve. We compensated for the higher computational load by (i.) using algorithms such as “Mergesort” (for the trial orbital phases) and by (ii.) restricting the trial transit durations to a

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Su, Kanhua, Zhiyou Zeng, Zhen Guan, et al. "Research on a Detailed Drilling Condition Identification Method Based on the KOA-RF Model." Processes 13, no. 6 (2025): 1736. https://doi.org/10.3390/pr13061736.

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The accurate identification of drilling conditions is pivotal for optimizing drilling operations. Detailed condition identification enables refined management of the drilling process, facilitates the detection of non-productive time (NPT), and offers actionable insights to improve drilling performance. In this study, a novel predictive model is presented that integrates the Kepler optimization algorithm (KOA) with random forest (RF) for detailed drilling condition identification. This method enhances the granularity of the operation differentiation and improves the classification accuracy. A s

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Bulut, B., M. Gunay, K. Ozgun, and J. W. Ledet. "OPTIMIZING BUS LINES USING GENETIC ALGORITHM FOR PUBLIC TRANSPORTATION." International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLVI-4/W5-2021 (December 23, 2021): 131–36. http://dx.doi.org/10.5194/isprs-archives-xlvi-4-w5-2021-131-2021.

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Abstract. Due to increasing human population, the need for quality public transportation has also increased. This study takes stop density, stop layout, and passenger population of those stops into consideration to offer a better regulated public transportation network design that can satisfy the increased demand. In this study, the boarding data is provided by the public transportation department of the city of Antalya, Turkey. Remaining required data was automatically generated using web services and stored in a PostgreSQL database hosted on a cloud server. After visualizing inputs such as b

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Ulaş, Burak. "A Deep Learning Neural Network Algorithm for Classification of Eclipsing Binary Light Curves." Turkish Journal of Astronomy and Astrophysics 6, no. 1 (2025): 18–27. https://doi.org/10.55064/tjaa.1708479.

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We present an image classification algorithm utilising a deep learning convolutional neural network architecture, which categorises the morphologies of eclipsing binary systems based on their light curves. The algorithm trains the machine with light curve images generated from the observational data of eclipsing binary stars in contact, detached and semi-detached morphologies, whose light curves are provided by Kepler, ASAS and CALEB catalogues. The structure of the architecture is explained, the parameters of the network layers and the resulting metrics are discussed. Our results show that th

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Ford, Eric B. "Parallel algorithm for solving Kepler’s equation on Graphics Processing Units: Application to analysis of Doppler exoplanet searches." New Astronomy 14, no. 4 (2009): 406–12. http://dx.doi.org/10.1016/j.newast.2008.12.001.

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Markmann, Andreas, Frank Graziani, and Victor S. Batista. "Kepler Predictor–Corrector Algorithm: Scattering Dynamics with One-Over-R Singular Potentials." Journal of Chemical Theory and Computation 8, no. 1 (2011): 24–35. http://dx.doi.org/10.1021/ct200452h.

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