Muhammad Abubakar Siddique, A. Kashif, M. Shoaib, S. Hussain
<jats:p>We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mn>2</mn> <mi>a</mi> </math> </jats:inline-formula> and <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mn>2</mn> <mi>b</mi> </math> </jats:inline-formula>. The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> </math> </jats:inline-formula> and <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mover accent="true"> <mi>m</mi> <mo>˜</mo> </mover> </math> </jats:i
{"title":"Stability Analysis of the Rhomboidal Restricted Six-Body Problem","authors":"Muhammad Abubakar Siddique, A. Kashif, M. Shoaib, S. Hussain","doi":"10.1155/2021/5575826","DOIUrl":"https://doi.org/10.1155/2021/5575826","url":null,"abstract":"<jats:p>We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mn>2</mn>\u0000 <mi>a</mi>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mn>2</mn>\u0000 <mi>b</mi>\u0000 </math>\u0000 </jats:inline-formula>. The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mi>m</mi>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mover accent=\"true\">\u0000 <mi>m</mi>\u0000 <mo>˜</mo>\u0000 </mover>\u0000 </math>\u0000 </jats:i","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46788899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To model the interaction with the atmosphere of fragments of a disrupted asteroid, which move independently of each other, it is necessary to know their mass distribution. In this regard, an analogy is drawn with fragmentation in high-speed impact experiments performed to simulate the disruption of asteroids at their collisions in outer space. Based on the results of impact experiments and assuming a power law for the mass distribution in a differential form, we obtained the cumulative number of fragments as a function of the fragment mass m normalized to the total mass of fragments, the mass fraction of the largest fragment(s), the number of the largest fragments, and the power index. The formula for the cumulative number of fragments of a disrupted body is used to describe the results of impact experiments for different fragmentation types. The proposed fragment mass distribution is also tested by comparison with the mass distributions of recovered meteorites in the cases of Mbale, Bassikounou, Almahata Sitta, Košice, and Chelyabinsk meteorite falls.
{"title":"On the Mass Distribution of Fragments of an Asteroid Disrupted in the Earth’s Atmosphere","authors":"I. Brykina, L. Egorova","doi":"10.1155/2021/9914717","DOIUrl":"https://doi.org/10.1155/2021/9914717","url":null,"abstract":"To model the interaction with the atmosphere of fragments of a disrupted asteroid, which move independently of each other, it is necessary to know their mass distribution. In this regard, an analogy is drawn with fragmentation in high-speed impact experiments performed to simulate the disruption of asteroids at their collisions in outer space. Based on the results of impact experiments and assuming a power law for the mass distribution in a differential form, we obtained the cumulative number of fragments as a function of the fragment mass m normalized to the total mass of fragments, the mass fraction of the largest fragment(s), the number of the largest fragments, and the power index. The formula for the cumulative number of fragments of a disrupted body is used to describe the results of impact experiments for different fragmentation types. The proposed fragment mass distribution is also tested by comparison with the mass distributions of recovered meteorites in the cases of Mbale, Bassikounou, Almahata Sitta, Košice, and Chelyabinsk meteorite falls.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43174700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this research, an approximation symbolic algorithm is suggested to obtain an approximate solution of multipantograph system of type delay differential equations (DDEs) using a combination of Laplace transform and variational iteration algorithm (VIA). The corresponding convergence results are acquired, and an efficient algorithm for choosing a feasible Lagrange multiplier is designed in the solving process. The application of the Laplace variational iteration algorithm (LVIA) for the problems is clarified. With graphics and tables, LVIA approximates to a high degree of accuracy with a few numbers of iterates. Also, computational results of the considered examples imply that LVIA is accurate, simple, and appropriate for solving a system of multipantograph delay differential equations (SMPDDEs).
{"title":"An Analytical Computational Algorithm for Solving a System of Multipantograph DDEs Using Laplace Variational Iteration Algorithm","authors":"M. Bahgat, A. Sebaq","doi":"10.1155/2021/7741166","DOIUrl":"https://doi.org/10.1155/2021/7741166","url":null,"abstract":"In this research, an approximation symbolic algorithm is suggested to obtain an approximate solution of multipantograph system of type delay differential equations (DDEs) using a combination of Laplace transform and variational iteration algorithm (VIA). The corresponding convergence results are acquired, and an efficient algorithm for choosing a feasible Lagrange multiplier is designed in the solving process. The application of the Laplace variational iteration algorithm (LVIA) for the problems is clarified. With graphics and tables, LVIA approximates to a high degree of accuracy with a few numbers of iterates. Also, computational results of the considered examples imply that LVIA is accurate, simple, and appropriate for solving a system of multipantograph delay differential equations (SMPDDEs).","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":"2021 1","pages":"1-16"},"PeriodicalIF":1.4,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44722623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Parfitt, A. McSweeney, L. De Backer, C. Orgel, A. Ball, Michael Khan, S. Vijendran
While the vast majority of ESA’s funding for Mars exploration in the 2020s is planned to be invested in ExoMars and Mars Sample Return, there is an interest to assess the possibility of implementing a small mission to Mars in parallel with, or soon after, the completion of the MSR programme. A study was undertaken in the Concurrent Design Facility at ESA ESTEC to assess low-cost mission architectures for small satellite missions to Mars. Given strict programmatic constraints, the focus of the study was on a low-cost (<250MEuro Cost at Completion), short mission development schedule with a cost-driven spacecraft design and mission architecture. The study concluded that small, low-cost Mars missions are technically feasible for launch within the decade.
{"title":"Small Mars Mission Architecture Study","authors":"C. Parfitt, A. McSweeney, L. De Backer, C. Orgel, A. Ball, Michael Khan, S. Vijendran","doi":"10.1155/2021/5516892","DOIUrl":"https://doi.org/10.1155/2021/5516892","url":null,"abstract":"While the vast majority of ESA’s funding for Mars exploration in the 2020s is planned to be invested in ExoMars and Mars Sample Return, there is an interest to assess the possibility of implementing a small mission to Mars in parallel with, or soon after, the completion of the MSR programme. A study was undertaken in the Concurrent Design Facility at ESA ESTEC to assess low-cost mission architectures for small satellite missions to Mars. Given strict programmatic constraints, the focus of the study was on a low-cost (<250MEuro Cost at Completion), short mission development schedule with a cost-driven spacecraft design and mission architecture. The study concluded that small, low-cost Mars missions are technically feasible for launch within the decade.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":"1-12"},"PeriodicalIF":1.4,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48700487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bin Jiang, Xi Fang, Yang Liu, Xingzhu Wang, Jie Liu
With the rapid growth in astronomical spectra produced by large sky survey telescopes, traditional manual classification processes can no longer fulfill the requirements of precision and efficiency of spectral classification. There is an urgent need to employ machine learning approaches to conduct automated spectral classification tasks. Feature extraction is a critical step which has a great impact on any classification result. In this paper, a novel gradient-based method together with principal component analysis is proposed for the extraction of partial features of stellar spectra, that is, a feature vector indicating obvious local changes in data, which corresponds to the element line positions in the spectra. Furthermore, a general feature vector is utilized as an additional characteristic centering on the overall tendency of spectra, which can indicate stellar effective temperature. The two feature vectors and raw data are input into three neural networks, respectively, for training and each network votes for a predicted category of spectra. By selecting the class having the maximum votes, different types of spectra can be classified with high accuracy. The experimental results prove that a better performance can be achieved using the partial and general methods in this paper. The method could also be applied to other similar one-dimensional spectra, and the concepts proposed could ultimately expand the scope of machine learning application in astronomical spectral processing.
{"title":"Spectral Feature Extraction Using Partial and General Method","authors":"Bin Jiang, Xi Fang, Yang Liu, Xingzhu Wang, Jie Liu","doi":"10.1155/2021/6748261","DOIUrl":"https://doi.org/10.1155/2021/6748261","url":null,"abstract":"With the rapid growth in astronomical spectra produced by large sky survey telescopes, traditional manual classification processes can no longer fulfill the requirements of precision and efficiency of spectral classification. There is an urgent need to employ machine learning approaches to conduct automated spectral classification tasks. Feature extraction is a critical step which has a great impact on any classification result. In this paper, a novel gradient-based method together with principal component analysis is proposed for the extraction of partial features of stellar spectra, that is, a feature vector indicating obvious local changes in data, which corresponds to the element line positions in the spectra. Furthermore, a general feature vector is utilized as an additional characteristic centering on the overall tendency of spectra, which can indicate stellar effective temperature. The two feature vectors and raw data are input into three neural networks, respectively, for training and each network votes for a predicted category of spectra. By selecting the class having the maximum votes, different types of spectra can be classified with high accuracy. The experimental results prove that a better performance can be achieved using the partial and general methods in this paper. The method could also be applied to other similar one-dimensional spectra, and the concepts proposed could ultimately expand the scope of machine learning application in astronomical spectral processing.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43682015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present a modified version of Hill’s dynamical system that is called the quantized Hill’s three-body problem in the sense that the equations of motion for the classical Hill’s problem are now derived under the effects of quantum corrections. To do so, the position variables and the parameters that correspond to the quantum corrections of the respective quantized three-body problem are scaled appropriately, and then by taking the limit when the parameter of mass ratio tends to zero, we obtain the relevant equations of motion for the spatial quantized Hill’s problem. Furthermore, the Hamiltonian formula and related equations of motion are also derived.
{"title":"A Quantized Hill’s Dynamical System","authors":"Elbaz I. Abouelmagd, V. Kalantonis, A. Perdiou","doi":"10.1155/2021/9963761","DOIUrl":"https://doi.org/10.1155/2021/9963761","url":null,"abstract":"In this paper, we present a modified version of Hill’s dynamical system that is called the quantized Hill’s three-body problem in the sense that the equations of motion for the classical Hill’s problem are now derived under the effects of quantum corrections. To do so, the position variables and the parameters that correspond to the quantum corrections of the respective quantized three-body problem are scaled appropriately, and then by taking the limit when the parameter of mass ratio tends to zero, we obtain the relevant equations of motion for the spatial quantized Hill’s problem. Furthermore, the Hamiltonian formula and related equations of motion are also derived.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":"2021 1","pages":"1-7"},"PeriodicalIF":1.4,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49439789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuan He, Yunfei Yang, X. Bai, Song Feng, Bo Liang, W. Dai
The Mount Wilson magnetic classification of sunspot groups is thought to be meaningful to forecast flares’ eruptions. In this paper, we adopt a deep learning method, CornerNet-Saccade, to perform the Mount Wilson magnetic classification of sunspot groups. It includes three stages, generating object locations, detecting objects, and merging detections. The key technologies consist of the backbone as Hourglass-54, the attention mechanism, and the key points’ mechanism including the top-left corners and the bottom-right corners of the object by corner pooling layers. These technologies improve the efficiency of detecting the objects without sacrificing accuracy. A dataset is built by a total of 2486 composited images which are composited with the continuum images and the corresponding magnetograms from HMI and MDI. After training the network, the sunspot groups in a composited solar full image are detected and classified in 3 seconds on average. The test results show that this method has a good performance, with the accuracy, precision, recall, and mAP as 0.94, 0.93, 0.94, and 0.90, respectively. Moreover, the flare productivities of different types of sunspot groups from 2011 to 2020 are calculated. As I tot ≥ 1, the flare productivities of α , β , β γ , β δ , and β γ δ sunspot groups are 0.14, 0.28, 0.61, 0.71, and 0.87, respectively. As I tot ≥ 10, the flare productivities are 0.02, 0.07, 0.27, 0.45, and 0.65, respectively. It means that the β γ , β δ , and β γ δ types are indeed very closely related to the eruption of solar flares, especially the β γ δ type. Based on the reliability of this method, the sunspot groups of the HMI solar full images from 2011 to 2020 are detected and classified, and the detailed data are shared on the website (https://61.166.157.71/MWMCSG.html).
{"title":"Research on Mount Wilson Magnetic Classification Based on Deep Learning","authors":"Yuan He, Yunfei Yang, X. Bai, Song Feng, Bo Liang, W. Dai","doi":"10.1155/2021/5529383","DOIUrl":"https://doi.org/10.1155/2021/5529383","url":null,"abstract":"The Mount Wilson magnetic classification of sunspot groups is thought to be meaningful to forecast flares’ eruptions. In this paper, we adopt a deep learning method, CornerNet-Saccade, to perform the Mount Wilson magnetic classification of sunspot groups. It includes three stages, generating object locations, detecting objects, and merging detections. The key technologies consist of the backbone as Hourglass-54, the attention mechanism, and the key points’ mechanism including the top-left corners and the bottom-right corners of the object by corner pooling layers. These technologies improve the efficiency of detecting the objects without sacrificing accuracy. A dataset is built by a total of 2486 composited images which are composited with the continuum images and the corresponding magnetograms from HMI and MDI. After training the network, the sunspot groups in a composited solar full image are detected and classified in 3 seconds on average. The test results show that this method has a good performance, with the accuracy, precision, recall, and mAP as 0.94, 0.93, 0.94, and 0.90, respectively. Moreover, the flare productivities of different types of sunspot groups from 2011 to 2020 are calculated. As \u0000 \u0000 \u0000 \u0000 I\u0000 \u0000 \u0000 tot\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ≥\u0000 \u0000 1, the flare productivities of \u0000 \u0000 α\u0000 ,\u0000 β\u0000 ,\u0000 β\u0000 γ\u0000 ,\u0000 β\u0000 δ\u0000 \u0000 , and \u0000 \u0000 β\u0000 γ\u0000 δ\u0000 \u0000 sunspot groups are 0.14, 0.28, 0.61, 0.71, and 0.87, respectively. As \u0000 \u0000 \u0000 \u0000 I\u0000 \u0000 \u0000 tot\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ≥\u0000 \u0000 10, the flare productivities are 0.02, 0.07, 0.27, 0.45, and 0.65, respectively. It means that the \u0000 \u0000 β\u0000 γ\u0000 ,\u0000 β\u0000 δ\u0000 \u0000 , and \u0000 \u0000 β\u0000 γ\u0000 δ\u0000 \u0000 types are indeed very closely related to the eruption of solar flares, especially the \u0000 \u0000 β\u0000 γ\u0000 δ\u0000 \u0000 type. Based on the reliability of this method, the sunspot groups of the HMI solar full images from 2011 to 2020 are detected and classified, and the detailed data are shared on the website (https://61.166.157.71/MWMCSG.html).","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44273522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Trigo-Rodríguez, J. Dergham, M. Gritsevich, E. Lyytinen, E. Silber, I. Williams
In this study, we investigate the ablation properties of bolides capable of producing meteorites. The casual dashcam recordings from many locations of the Chelyabinsk superbolide associated with the atmospheric entry of an 18 m in diameter near-Earth object (NEO) have provided an excellent opportunity to reconstruct its atmospheric trajectory, deceleration, and heliocentric orbit. In this study, we focus on the study of the ablation properties of the Chelyabinsk bolide on the basis of its deceleration and fragmentation. We explore whether meteoroids exhibiting abrupt fragmentation can be studied by analyzing segments of the trajectory that do not include a disruption episode. We apply that approach to the lower part of the trajectory of the Chelyabinsk bolide to demonstrate that the obtained parameters are consistent. To do that, we implemented a numerical (Runge–Kutta) method appropriate for deriving the ablation properties of bolides based on observations. The method was successfully tested with the cases previously published in the literature. Our model yields fits that agree with observations reasonably well. It also produces a good fit to the main observed characteristics of Chelyabinsk superbolide and provides its averaged ablation coefficient σ = 0.034 s2 km−2. Our study also explores the main implications for impact hazard, concluding that tens of meters in diameter NEOs encountering the Earth in grazing trajectories and exhibiting low geocentric velocities are penetrating deeper into the atmosphere than previously thought and, as such, are capable of producing meteorites and even damage on the ground.
{"title":"A Numerical Approach to Study Ablation of Large Bolides: Application to Chelyabinsk","authors":"J. Trigo-Rodríguez, J. Dergham, M. Gritsevich, E. Lyytinen, E. Silber, I. Williams","doi":"10.1155/2021/8852772","DOIUrl":"https://doi.org/10.1155/2021/8852772","url":null,"abstract":"In this study, we investigate the ablation properties of bolides capable of producing meteorites. The casual dashcam recordings from many locations of the Chelyabinsk superbolide associated with the atmospheric entry of an 18 m in diameter near-Earth object (NEO) have provided an excellent opportunity to reconstruct its atmospheric trajectory, deceleration, and heliocentric orbit. In this study, we focus on the study of the ablation properties of the Chelyabinsk bolide on the basis of its deceleration and fragmentation. We explore whether meteoroids exhibiting abrupt fragmentation can be studied by analyzing segments of the trajectory that do not include a disruption episode. We apply that approach to the lower part of the trajectory of the Chelyabinsk bolide to demonstrate that the obtained parameters are consistent. To do that, we implemented a numerical (Runge–Kutta) method appropriate for deriving the ablation properties of bolides based on observations. The method was successfully tested with the cases previously published in the literature. Our model yields fits that agree with observations reasonably well. It also produces a good fit to the main observed characteristics of Chelyabinsk superbolide and provides its averaged ablation coefficient σ = 0.034 s2 km−2. Our study also explores the main implications for impact hazard, concluding that tens of meters in diameter NEOs encountering the Earth in grazing trajectories and exhibiting low geocentric velocities are penetrating deeper into the atmosphere than previously thought and, as such, are capable of producing meteorites and even damage on the ground.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43764819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We make a systematic examination of the basic theory of general relativity and reemphasize the meaning of coordinates. Firstly, we prove that Einsteinʼs gravitational field equation has the light speed invariant solution and black holes are not an inevitable prediction of general relativity. Second, we show that the coupling coefficient of the gravitational field equation is not unique and can be modified as 4 π G to replace the previous − 8 π G , distinguish gravitational mass from the inertial mass, and prove that dark matter and dark energy are not certain existence and the expansion and contraction of the universe are proven cyclic, and a new distance-redshift relation which is more practical is derived. After that, we show that galaxies and celestial bodies are formed by gradual growth rather than by the accumulation of existing matter and prove that new matter is generating gradually in the interior of celestial bodies. For example, the radius of the Earth increases by 0.5 mm every year, and its mass increases by 1.2 trillion tons. A more reasonable derivation of the precession of planetary orbits is given, and the evolution equation of planetary orbits in the expanding space-time is also given. In a word, an alive universe unfolds in front of readers and the current cosmological difficulties are given new interpretations.
{"title":"Modification of Gravitational Field Equation due to Invariance of Light Speed and New System of Universe Evolution","authors":"J. Yang","doi":"10.1155/2021/5579060","DOIUrl":"https://doi.org/10.1155/2021/5579060","url":null,"abstract":"We make a systematic examination of the basic theory of general relativity and reemphasize the meaning of coordinates. Firstly, we prove that Einsteinʼs gravitational field equation has the light speed invariant solution and black holes are not an inevitable prediction of general relativity. Second, we show that the coupling coefficient of the gravitational field equation is not unique and can be modified as \u0000 \u0000 4\u0000 π\u0000 G\u0000 \u0000 to replace the previous \u0000 \u0000 −\u0000 8\u0000 π\u0000 G\u0000 \u0000 , distinguish gravitational mass from the inertial mass, and prove that dark matter and dark energy are not certain existence and the expansion and contraction of the universe are proven cyclic, and a new distance-redshift relation which is more practical is derived. After that, we show that galaxies and celestial bodies are formed by gradual growth rather than by the accumulation of existing matter and prove that new matter is generating gradually in the interior of celestial bodies. For example, the radius of the Earth increases by 0.5 mm every year, and its mass increases by 1.2 trillion tons. A more reasonable derivation of the precession of planetary orbits is given, and the evolution equation of planetary orbits in the expanding space-time is also given. In a word, an alive universe unfolds in front of readers and the current cosmological difficulties are given new interpretations.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42163197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Emad A.-B. Abdel-Salam, Mohamed I. Nouh, Yosry A. Azzam, M. S. Jazmati
The helium burning phase represents the second stage that the star used to consume nuclear fuel in its interior. In this stage, the three elements, carbon, oxygen, and neon, are synthesized. The present paper is twofold: firstly, it develops an analytical solution to the system of the conformable fractional differential equations of the helium burning network, where we used, for this purpose, the series expansion method and obtained recurrence relations for the product abundances, that is, helium, carbon, oxygen, and neon. Using four different initial abundances, we calculated 44 gas models covering the range of the fractional parameter <span><svg height="8.69875pt" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 18.648 8.69875" width="18.648pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,11.017,0)"></path></g></svg><span></span><svg height="8.69875pt" style="vertical-align:-0.3499298pt" version="1.1" viewbox="22.230183800000002 -8.34882 35.39 8.69875" width="35.39pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,22.28,0)"></path></g><g transform="matrix(.013,0,0,-0.013,28.52,0)"></path></g><g transform="matrix(.013,0,0,-0.013,31.484,0)"></path></g><g transform="matrix(.013,0,0,-0.013,40.63,0)"></path></g><g transform="matrix(.013,0,0,-0.013,51.166,0)"></path></g></svg></span> with step <span><svg height="8.8423pt" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 26.975 8.8423" width="26.975pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><use xlink:href="#g113-223"></use></g><g transform="matrix(.013,0,0,-0.013,19.344,0)"><use xlink:href="#g117-34"></use></g></svg><span></span><span><svg height="8.8423pt" style="vertical-align:-0.2064009pt" version="1.1" viewbox="30.5571838 -8.6359 21.957 8.8423" width="21.957pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,30.607,0)"><use xlink:href="#g113-49"></use></g><g transform="matrix(.013,0,0,-0.013,36.847,0)"><use xlink:href="#g113-47"></use></g><g transform="matrix(.013,0,0,-0.013,39.811,0)"><use xlink:href="#g113-49"></use></g><g transform="matrix(.013,0,0,-0.013,46.051,0)"><use xlink:href="#g113-54"></use></g></svg>.</span></span> We found that the effects of the fractional parameter on the product abundances are small which coincides with the results obtained by a previous study. Secondly, we introduced the mathematical model of the neural network (NN) and developed a neural network algorithm to simulate the helium burning network using a feed-forward process. A comparison between the NN and the analytical models revealed very good agreement for all
{"title":"Conformable Fractional Models of the Stellar Helium Burning via Artificial Neural Networks","authors":"Emad A.-B. Abdel-Salam, Mohamed I. Nouh, Yosry A. Azzam, M. S. Jazmati","doi":"10.1155/2021/6662217","DOIUrl":"https://doi.org/10.1155/2021/6662217","url":null,"abstract":"The helium burning phase represents the second stage that the star used to consume nuclear fuel in its interior. In this stage, the three elements, carbon, oxygen, and neon, are synthesized. The present paper is twofold: firstly, it develops an analytical solution to the system of the conformable fractional differential equations of the helium burning network, where we used, for this purpose, the series expansion method and obtained recurrence relations for the product abundances, that is, helium, carbon, oxygen, and neon. Using four different initial abundances, we calculated 44 gas models covering the range of the fractional parameter <span><svg height=\"8.69875pt\" style=\"vertical-align:-0.3499298pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.34882 18.648 8.69875\" width=\"18.648pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.017,0)\"></path></g></svg><span></span><svg height=\"8.69875pt\" style=\"vertical-align:-0.3499298pt\" version=\"1.1\" viewbox=\"22.230183800000002 -8.34882 35.39 8.69875\" width=\"35.39pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,22.28,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,28.52,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,31.484,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,40.63,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,51.166,0)\"></path></g></svg></span> with step <span><svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 26.975 8.8423\" width=\"26.975pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,8.327,0)\"><use xlink:href=\"#g113-223\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.344,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><span><svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"30.5571838 -8.6359 21.957 8.8423\" width=\"21.957pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,30.607,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,36.847,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,39.811,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,46.051,0)\"><use xlink:href=\"#g113-54\"></use></g></svg>.</span></span> We found that the effects of the fractional parameter on the product abundances are small which coincides with the results obtained by a previous study. Secondly, we introduced the mathematical model of the neural network (NN) and developed a neural network algorithm to simulate the helium burning network using a feed-forward process. A comparison between the NN and the analytical models revealed very good agreement for all ","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":"84 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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