Download or read book Mathematical Formulation of the Variational Equations for the Determination of the Earth s Gravity Field written by James C. Perry and published by . This book was released on 1974 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expressions for the coefficients and forcing term are derived for the variational equations to be used in a new computer program being developed to determine the earth's gravity field (Program TERRA). Also a brief idea of the role of variational equations is sketched. (Author).
Download or read book The Gravity Field of the Earth written by Michele Caputo and published by Elsevier. This book was released on 2016-06-03 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Geophysics Series, Volume 10: The Gravity Field of the Earth: From Classical and Modern Methods explores the theory of the gravity field of the earth based on both classical and modern methods. Classical method involves observations of gravity taken over the earth's surface, while the modern method uses observations of variation of orbital elements of artificial satellites caused by the gravity field of the earth. This book is organized into two parts encompassing 12 chapters. Part I describes the solution of physical problems that are treated as Dirichlet problems or solved by means of integral equations. This part also deals with the determination of the geoid form from ground gravity measurements using the Stokes formula. The method of obtaining the Stokes formula by means of an integral equation is also outlined. Part II contains modern mathematical techniques developed to utilize the observations of artificial satellites for geodetic purposes. This book could be used as a textbook for students in the fields of geodesy, geophysics, or astronomy.
Download or read book An Analysis of Variational Equations for the Direct Evaluation of the Earth s Gravity Field written by Ohio State University. Department of Geodetic Science and published by . This book was released on 1971 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Analysis of Variational Equations for the Direct Evaluation of the Earth s Gravity Field written by Willard D. Haverland and published by . This book was released on 1971 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The variational equations, proposed by Obenson and proposed by Rapp, which are used to generate observation equation coefficients in the direct combination of satellite and gravimetric data are critically reviewed. Each procedure is tested with respect to accuracy as a function of step size, integration procedure, and orbit time. The two procedures are combined into a single program that combines the best features of the original proposals. The study concludes that if an orbit arc of less than 15 hours is being considered, Rapp's method with a fixed fourth-order predictor and a fifth order corrector gives the best results. If orbit arcs greater than 15 hours are being used, the combine solution composed of a fixed fourth order predictor and fifth order corrector for anomaly integration and Obenson's method for element integration gives the best results. (Author).
Download or read book Gravity Field and Dynamics of the Earth written by Milan Bursa and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the Czech edition was published four years ago, the authors have revised the original text tobring it up to date. During these four years, thanks to satellite altimetry the accuracy of the global descrip tion of the gravity field (model GEM-T2), of the fundamental astro geodetic constants, of the principal moments of inertia of the Earth and, in particular, of their differences, of the precession constant, and of a number of other dynamical parameters of the Earth have been improved. The authors have included most of these improvements in the revised English edition. They have, of course, also made factual, formal and other corrections and have modified some of the figures. Additions to the index and references have also been made. Praha, Czech Republic M. BuRSA and K. PF:c August 1993 Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals of Determining the Parameters 1 Defining the Earth's Gravitational Field by Satellite Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 1 Satellite Equations of Motion . . . . . . . . . . . . . . . . . 6 1. 2 Perturbing Function and Perturbing Potential . . . . 23 1. 3 General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 3. 1 Perturbing Gravitational Potential of the Earth in 1. 3. 2 Outer Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Perturbations due to the Moon and the Sun . . . . . . 27 1. 3. 3 Solution of the Perturbed Motion . . . . . . . . . . . . . . 28 1. 4 1. 5 Transformation of the Perturbing Gravitational Potential into the Function of the Satellite's Orbital Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1. 5. 1 Transformation of Potential Rs$ . . . . . . . . . . . . . . . 32 1. 5. 2 Transformation of Potentials L1 Vs»' L1 Vso . . . . . . . .
Download or read book Analysis of the Gravity Field written by Fernando Sansò and published by Springer Nature. This book was released on 2022-06-09 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a comprehensive treatment of the theory and implementation of inverse methods in the analysis and interpretation of Earth’s gravity field. By restricting their consideration to a local rather than global level, the authors focus on the use of observations and data that are more sensitive to local mass anomalies. All necessary theoretical aspects are reformulated in terms of a Euclidean framework so that less complex tools from mathematical analysis can be utilized. Divided into three parts, the text begins with a review of basic mathematical properties of gravitation, computing gravity from mass distributions, and relevant methods from Fourier analysis. In the second part of the text, the Earth’s gravity field and its properties are introduced, and the preprocessing and processing of gravity data are explored. Finally, elementary inverse theory is discussed, after which the general inversion problem is considered via application of both the Tikhonov deterministic approach and a stochastic MCMC model. Throughout, examples and exercises are provided to both clarify material and to illustrate real-word applications for readers. Analysis of the Gravity Field: Direct and Inverse Problems is carefully written to be accessible to both mathematicians and geophysicists without sacrificing mathematical rigor. Readers should have a familiarity with the basics of mathematical analysis, as well as some knowledge of statistics and probability theory. Detailed proofs of more advanced results are relegated to appendices so that readers can concentrate on solution algorithms.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods and Technologies for Measuring the Earth s Gravity Field Parameters written by V. G. Peshekhonov and published by Springer Nature. This book was released on 2022-11-30 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers extensive information on the operation of gravimeters, including airborne, marine and terrestrial ones, and on the associated data processing methods such as optimal and adaptive filtering, smoothing, structural and parametric identification. Further, it describes specific features relating to the study of the gravitational field in remote areas of the Earth, with the necessary modifications of equipment and software for all-latitude applications. Findings from gravity studies in such remote areas are also presented. Advanced methods for studying the gravitational field, including those for simultaneous determination of gravity anomalies and deflection of the vertical are described and analyzed in detail. Gravity gradiometers and cold atom gravimeters are also covered. Last but not least, the book deals with the development of Earth’s gravity field models and their various applications, including map-aided navigation, with a special attention to model accuracy estimation. Gathering research findings and best practice recommendations relating to Earth’s gravity field measurements, collected by a team of researchers and professionals, the book offers a unique guide for engineers, scientists and graduate students dealing with terrestrial, marine and airborne gravimetry. It will also help other specialists involved in developing and using navigation systems in practice, including designers of gravimetric equipment and navigators.
Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1975 with total page 2834 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Determination of the Earth s Gravity Field in Spheroidal Coordinates written by M. Spencer Hamilton (Jr.) and published by . This book was released on 1961 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monthly Catalog of United States Government Publications Cumulative Index written by United States. Superintendent of Documents and published by . This book was released on 1976 with total page 1408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Gravimetric Determination of the Parameters of the Earth and Its Gravity Field written by Helmut Moritz and published by . This book was released on 1965 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements written by and published by . This book was released on 1974 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book IV Hotine Marussi Symposium on Mathematical Geodesy written by Battista Benciolini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the IV Hotine-Marussi Symposium held in Trento, the volume covers three important topics: boundary value problems, satellite geodesy and stochastic methods in geodesy. The first part deals with boundary value problems which are tackled from both the theoretical and the numerical point of view. The part on satellite geodesy deals with the simulation of the GOCE mission, the integration of satellite gradiometry and airborne gravity for gravity-filed recovery, satellite-to-satellite tracking and orbit sensitivity analysis. Various applied and theoretical contributions are devoted to the stochastic methods applied to geodesy. The book presents the state-of-the-art of the main topics in the theoretical and methodological aspects of geodesy.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Annual Index written by and published by . This book was released on 1983 with total page 1378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Index written by and published by . This book was released on 1975 with total page 1262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
