The Experts below are selected from a list of 57708 Experts worldwide ranked by ideXlab platform
Ta-kang Yeh - One of the best experts on this subject based on the ideXlab platform.
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analytical solution of a Satellite Orbit disturbed by lunar and solar gravitation
Monthly Notices of the Royal Astronomical Society, 2011Co-Authors: Ta-kang Yeh, Wu ChenAbstract:In this paper, we derive to the second order (5 x 10- 6 ) the analytical solution of a Satellite Orbit disturbed by the lunar gravitational force. The force vector is first expanded to omit terms smaller than the third order (10 -9 ). Then, four terms of potential functions are derived from the expanded force vector and set into the Lagrangian equations of Satellite motion to obtain the theoretical solutions. For the first term of the potential functions, the solutions are derived directly. For the second term, mathematical expansions and transformations are used to separate disturbances into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i, Ω) and secular terms with non-periodic functions of (a, e). The integrations are then carried out with respect to M, (ω, i, Ω) and t, to obtain the analytical solutions of Satellite Orbits with a program using mathematical symbolic operation software. The third potential function differs from the second by a factor and the fourth is simpler than the second. Therefore, the solutions are derived similarly using slightly modified programs, respectively. The results show that only two Keplerian elements (ω, M) are linearly perturbed by lunar gravitation; that is, the lunar attracting force will cause a linear regression (delay) of the perigee (orientation of the ellipse) and a linear delay of the position (mean anomaly) on an Earth Satellite. The Keplerian element a (semimajor axis of the ellipse) is not perturbed long periodically as the others. The derived solutions are also valid for solar and planetary gravitational disturbances. Because of the distance differences between the Moon, the Sun and the planets to the Earth or an Earth Satellite, the solutions are of third and fourth orders for solar and planetary gravitational disturbances on an Earth Satellite, respectively.
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Analytical solution of a Satellite Orbit disturbed by atmospheric drag
Monthly Notices of the Royal Astronomical Society, 2010Co-Authors: Xu Tianhe, Wu Chen, Ta-kang YehAbstract:In this paper, we derive the analytical solution of a Satellite Orbit disturbed by atmospheric drag. The disturbance force vector is first transformed and rotated to the Orbital frame so that it can be used in the simplified Gaussian equations of Satellite motion. Then, the force vector is expanded to triangular functions of the Keplerian angular elements and the disturbances are separated into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i) and secular terms [non-periodic functions of (a, e)] with a program using mathematical symbolic operation software. The integrations are then carried out with respect to M, (ω, i) and t, respectively, to obtain the analytical solutions of Satellite Orbits disturbed by atmospheric drag. Some interesting conclusions are obtained theoretically. The atmospheric disturbance force is not a function of Ω. The semimajor axis a of the Orbital ellipse is reduced in a constant and strong manner by the air disturbance; the shape of the ellipse (eccentricity e) changes towards a more circular Orbit in a linear and weak manner. The right ascension of the ascending node Ω and the mean anomaly M are influenced by the disturbance only short periodically.
P Schwintzer - One of the best experts on this subject based on the ideXlab platform.
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a high quality global gravity field model from champ gps tracking data and accelerometry eigen 1s
Geophysical Research Letters, 2002Co-Authors: Christoph Reigber, R Biancale, G Balmino, Jeanmichel Lemoine, P Schwintzer, A Bode, Rolf Konig, Sylvain Loyer, Hans Neumayer, Jeancharles MartyAbstract:[1] Using three months of GPS Satellite-to-Satellite tracking and accelerometer data of the CHAMP Satellite mission, a new long-wavelength global gravity field model, called EIGEN-1S, has been prepared in a joint German-French effort. The solution is derived solely from analysis of Satellite Orbit perturbations, i.e. independent of oceanic and continental surface gravity data. EIGEN-1S results in a geoid with an approximation error of about 20 cm in terms of 5 × 5 degree block mean values, which is an improvement of more than a factor of 2 compared to pre-CHAMP Satellite-only gravity field models. This impressive progress is a result of CHAMP's tailored Orbit characteristics and dedicated instrumentation, providing continuous tracking and direct on-Orbit measurements of non-gravitational Satellite accelerations.
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a new global earth s gravity field model from Satellite Orbit perturbations grim5 s1
Geophysical Research Letters, 2000Co-Authors: R Biancale, G Balmino, Jeanmichel Lemoine, J C Marty, Bernard Moynot, F Barlier, Pierre Exertier, Olivier Laurain, Pascal Gegout, P SchwintzerAbstract:A new model of the Earth's gravity field, called GRIM5-S1, was prepared in a joint German-French effort. The solution is based on Satellite Orbit perturbation analysis and exploits tracking data from 21 Satellites to solve simultaneously for the gravitational and ocean tide potential and tracking station positions. The Satellite-only solution results in a homogeneous representation of the geoid with an approximation error of about 45 cm in terms of 5×5 degree block mean values, and performs globally better in Satellite Orbit restitution than any previous gravity field model. The GRIM5 normals, which were generated taking into account the latest computational standards, shall be the reference for use during the coming geopotential Satellite mission CHAMP and should provide new standards in computing Orbits of next altimetric missions like Jason and ENVISAT. The GRIM5-S1 normals also give the basis for the tracking/surface data combined solution GRIM5-C1.
Wu Chen - One of the best experts on this subject based on the ideXlab platform.
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analytical solution of a Satellite Orbit disturbed by lunar and solar gravitation
Monthly Notices of the Royal Astronomical Society, 2011Co-Authors: Ta-kang Yeh, Wu ChenAbstract:In this paper, we derive to the second order (5 x 10- 6 ) the analytical solution of a Satellite Orbit disturbed by the lunar gravitational force. The force vector is first expanded to omit terms smaller than the third order (10 -9 ). Then, four terms of potential functions are derived from the expanded force vector and set into the Lagrangian equations of Satellite motion to obtain the theoretical solutions. For the first term of the potential functions, the solutions are derived directly. For the second term, mathematical expansions and transformations are used to separate disturbances into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i, Ω) and secular terms with non-periodic functions of (a, e). The integrations are then carried out with respect to M, (ω, i, Ω) and t, to obtain the analytical solutions of Satellite Orbits with a program using mathematical symbolic operation software. The third potential function differs from the second by a factor and the fourth is simpler than the second. Therefore, the solutions are derived similarly using slightly modified programs, respectively. The results show that only two Keplerian elements (ω, M) are linearly perturbed by lunar gravitation; that is, the lunar attracting force will cause a linear regression (delay) of the perigee (orientation of the ellipse) and a linear delay of the position (mean anomaly) on an Earth Satellite. The Keplerian element a (semimajor axis of the ellipse) is not perturbed long periodically as the others. The derived solutions are also valid for solar and planetary gravitational disturbances. Because of the distance differences between the Moon, the Sun and the planets to the Earth or an Earth Satellite, the solutions are of third and fourth orders for solar and planetary gravitational disturbances on an Earth Satellite, respectively.
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Analytical solution of a Satellite Orbit disturbed by atmospheric drag
Monthly Notices of the Royal Astronomical Society, 2010Co-Authors: Xu Tianhe, Wu Chen, Ta-kang YehAbstract:In this paper, we derive the analytical solution of a Satellite Orbit disturbed by atmospheric drag. The disturbance force vector is first transformed and rotated to the Orbital frame so that it can be used in the simplified Gaussian equations of Satellite motion. Then, the force vector is expanded to triangular functions of the Keplerian angular elements and the disturbances are separated into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i) and secular terms [non-periodic functions of (a, e)] with a program using mathematical symbolic operation software. The integrations are then carried out with respect to M, (ω, i) and t, respectively, to obtain the analytical solutions of Satellite Orbits disturbed by atmospheric drag. Some interesting conclusions are obtained theoretically. The atmospheric disturbance force is not a function of Ω. The semimajor axis a of the Orbital ellipse is reduced in a constant and strong manner by the air disturbance; the shape of the ellipse (eccentricity e) changes towards a more circular Orbit in a linear and weak manner. The right ascension of the ascending node Ω and the mean anomaly M are influenced by the disturbance only short periodically.
R Biancale - One of the best experts on this subject based on the ideXlab platform.
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a high quality global gravity field model from champ gps tracking data and accelerometry eigen 1s
Geophysical Research Letters, 2002Co-Authors: Christoph Reigber, R Biancale, G Balmino, Jeanmichel Lemoine, P Schwintzer, A Bode, Rolf Konig, Sylvain Loyer, Hans Neumayer, Jeancharles MartyAbstract:[1] Using three months of GPS Satellite-to-Satellite tracking and accelerometer data of the CHAMP Satellite mission, a new long-wavelength global gravity field model, called EIGEN-1S, has been prepared in a joint German-French effort. The solution is derived solely from analysis of Satellite Orbit perturbations, i.e. independent of oceanic and continental surface gravity data. EIGEN-1S results in a geoid with an approximation error of about 20 cm in terms of 5 × 5 degree block mean values, which is an improvement of more than a factor of 2 compared to pre-CHAMP Satellite-only gravity field models. This impressive progress is a result of CHAMP's tailored Orbit characteristics and dedicated instrumentation, providing continuous tracking and direct on-Orbit measurements of non-gravitational Satellite accelerations.
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a new global earth s gravity field model from Satellite Orbit perturbations grim5 s1
Geophysical Research Letters, 2000Co-Authors: R Biancale, G Balmino, Jeanmichel Lemoine, J C Marty, Bernard Moynot, F Barlier, Pierre Exertier, Olivier Laurain, Pascal Gegout, P SchwintzerAbstract:A new model of the Earth's gravity field, called GRIM5-S1, was prepared in a joint German-French effort. The solution is based on Satellite Orbit perturbation analysis and exploits tracking data from 21 Satellites to solve simultaneously for the gravitational and ocean tide potential and tracking station positions. The Satellite-only solution results in a homogeneous representation of the geoid with an approximation error of about 45 cm in terms of 5×5 degree block mean values, and performs globally better in Satellite Orbit restitution than any previous gravity field model. The GRIM5 normals, which were generated taking into account the latest computational standards, shall be the reference for use during the coming geopotential Satellite mission CHAMP and should provide new standards in computing Orbits of next altimetric missions like Jason and ENVISAT. The GRIM5-S1 normals also give the basis for the tracking/surface data combined solution GRIM5-C1.
Michael L Bender - One of the best experts on this subject based on the ideXlab platform.
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real time gps sensing of atmospheric water vapor precise point positioning with Orbit clock and phase delay corrections
Geophysical Research Letters, 2014Co-Authors: Xingxing Li, Galina Dick, Maorong Ge, S Heise, Jens Wickert, Michael L BenderAbstract:The recent development of the International Global Navigation Satellite Systems Service Real-Time Pilot Project and the enormous progress in precise point positioning (PPP) techniques provide a promising opportunity for real-time determination of Integrated Water Vapor (IWV) using GPS ground networks for various geodetic and meteorological applications. In this study, we develop a new real-time GPS water vapor processing system based on the PPP ambiguity fixing technique with real-time Satellite Orbit, clock, and phase delay corrections. We demonstrate the performance of the new real-time water vapor estimates using the currently operationally used near-real-time GPS atmospheric data and collocated microwave radiometer measurements as an independent reference. The results show that an accuracy of 1.0 ~ 2.0 mm is achievable for the new real-time GPS based IWV value. Data of such accuracy might be highly valuable for time-critical geodetic (positioning) and meteorological applications.
