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K V Kholshevnikov - One of the best experts on this subject based on the ideXlab platform.
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central field motion with Perturbing Acceleration varying according to the inverse square law in the reference frame associated with the radius vector
Astronomy Reports, 2020Co-Authors: T N Sannikova, K V KholshevnikovAbstract:The motion of a point with zero mass under the action of attraction to the central body $$\mathcal{S}$$ and Perturbing Acceleration $${\mathbf{P}}{\kern 1pt} ' = {\mathbf{P}}{\text{/}}{{r}^{2}}$$ , inversely proportional to the square of the distance to $$\mathcal{S}$$ , is considered. It is assumed that $${\mathbf{P}}{\kern 1pt} '$$ is small in absolute value compared to the main Acceleration, caused by the attraction of the central body. Further, the vector $${\mathbf{P}}$$ components are constant in the reference frame used in astronomy, with the origin in the central body and the axes directed along the radius vector, the transversal (perpendicular to the radius vector in the osculating plane in the direction of motion), and the binormal (directed along the area vector). Earlier, we performed an averaging transformation of Euler-type equations of motion in osculating elements and obtained mean element evolutionary differential equations of motion in the first approximation in a small parameter. This article is devoted to solving the averaged equations, which are integrated completely. Moreover, the quadratures were expressed via elementary functions. The solution found has singularities at zero eccentricity and in the absence of the transverse Acceleration. These and some other special cases are considered separately. There are at least two applications of the problem considered which are: an asteroid’s motion with allowance for the Yarkovsky–Radzievsky effect and a spacecraft’s motion with a solar sail. In both cases, the perturbation is inversely proportional to the squared distance from the Sun.
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The Averaged Equations of Motion in the Presence of an Inverse-Square Perturbing Acceleration
Astronomy Reports, 2019Co-Authors: T N Sannikova, K V KholshevnikovAbstract:The motion of a zero-mass point under the action of a gravitational force toward a central body \({\cal S}\) and a Perturbing Acceleration P′ whose magnitude is inversely proportional to the square of the distance to \({\cal S}\) is considered. The direction of P′ is constant in one of the three coordinate systems most widely used in astronomy: the main inertial system \({\cal O}\) and two orbiting systems \({{\cal O}_s}\) with their x axes along the radius vector for s = 1 and along the velocity vector for s = 2.The ratio of |P′|to the main Acceleration due to the gravitation of the central body is taken to be small. An averaging transformation in a first approximation in a small parameter of the problem is applied to the equations of motion in the osculating elements. Closed expressions are obtained for the right-hand sides of the equations of motion in the mean elements. These are expressed in terms of elementary functions in the systems \({\cal O}\) and \({{\cal O}_1}\); complete elliptical integrals arise in the system \({{\cal O}_2}\). Closed expressions are obtained for the change-of-variable functions. All the functions encountered in the systems \({\cal O}\) and \({{\cal O}_1}\) are elementary functions, apart from those determining the variations of the mean anomaly. The latter is given by an integral of an elementary function, as well as a series in powers of the eccentricity that converges absolutely and uniformly when 0 ⩽ e ⩽ 1. All functions in the system \({{\cal O}_2}\) apart from those determining the variations of the mean anomaly can be expressed in terms of incomplete elliptical integrals. The variations of the mean anomaly are calculated using a Fourier series in the mean anomaly. Integration of the averaged equations of motion will be considered in future papers. Possible applications of this model problem include the motion of an asteroid taking into account the Yarkovsky-Radziewski effect, and the motion of a spacecraft with a solar sail, when the Perturbing action is inversely proportional to the square of the distance from the Sun. It stands to reason that determining the components of the vector P′ requires knowledge of the thermal-physical characteristics of the body in question and the parameters of its rotational motion in the former case, and of the orientation of the solar sail in the latter case.
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motion in a central field in the presence of a constant Perturbing Acceleration in a coordinate system comoving with the velocity vector
Astronomy Reports, 2018Co-Authors: T N Sannikova, K V Kholshevnikov, N BatmunkhAbstract:The motion of a zero-mass point under the action of gravitation toward a central body and a Perturbing Acceleration P is considered. The magnitude of P is taken to be small compared to the main Acceleration due to the gravitation of the central body, and the components of the vector P are taken to be constant in a reference frame with its origin at the central body and its axes directed along the velocity vector, normal to the velocity vector in the plane of the osculating orbit, and along the binormal. The equations in the mean elements were obtained in an earlier study. The algorithm used to solve these equations is given in this study. This algorithm is analogous to one constructed earlier for the case when P is constant in a reference frame tied to the radius vector. The properties of the solutions are similar. The main difference is that, in the most important cases, the quadratures to which the solution reduces lead to non-elementary functions. However, they can be expressed as series in powers of the eccentricity e that converge for e < 1, and often also for e = 1.
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the norm of the position shift of a celestial body upon variation of its orbit
Astronomy Reports, 2016Co-Authors: N Batmunkh, T N Sannikova, K V Kholshevnikov, Sh V ShaidulinAbstract:A precise estimate of the variation of the position of a celestial body in the case of small variations of the elements of its orbit is obtained using an Euclidean (mean-square) norm for the deviation in the position. A relatively simple expression for the mean-square deviation of the radius vector d r in terms of the deviations of the elements is derived. These are taken to be first-order small quantitites, with second-order quantities neglected. This relation is applied to estimate the norm ||d r|| in two problems. In the first one, small and constant differences between six orbital elements (including the mean anomaly) are considered for two orbits. In the second one, a zero-mass point moves under the gravitation of a central body and a small Perturbing Acceleration F. The vector F is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the binormal vector. In this latter problem, d r is the difference between the position vectors in the osculating and mean orbit. The norm ||d r||2 is the weighted sum of the squares of the components of F, neglecting higher-order small quantities. The coefficients of the quadratic form depend only on the semi-major axis and the eccentricity of the mean orbit. The results are applied to the motion of a small asteroid under the action of a low-thrust engine imparting a small force.
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motion in a central field in the presence of a constant Perturbing Acceleration in a co moving coordinate system
Astronomy Reports, 2015Co-Authors: T N Sannikova, K V KholshevnikovAbstract:The motion of a point mass under the action of a gravitational force toward a central body and a Perturbing Acceleration P is considered. The magnitude of P is taken to be small compared to the main gravitational Acceleration due to the central body, and the direction of P to be constant in a standard astronomical coordinate system with its origin at the central body and axes directed along the radius vector, the transversal, and the binormal. Consideration of a constant vector Perturbing Acceleration simplifies averaging of the Euler equations for the motion in osculating elements, making it straightforward to obtain evolutionary differential equations of motion in the mean elements, as was done earlier in a first small-parameter approximation. This paper is devoted to integration of the mean equations. The system is integratable by quadratures if at least one component of the Perturbing Acceleration is zero, and also if the orbit is initially circular. Moreover, all the quadratures can be expressed in terms of elementary functions and elliptical integrals of the first kind in Jacobi form. If all three components of P are non-zero, this problem reduces to a system of two first-order differential equations, which are apparently not integrable. Possible applications include the motion of natural and artificial satellites taking into account light pressure, the motion of a spacecraft with low thrust, and the motion of an asteroid subject to a thrust from an engine mounted on it or to a gravitational tractor designed, for example, to avoid a collision with Earth.
Mathis Bloßfeld - One of the best experts on this subject based on the ideXlab platform.
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Observation-Based Attitude Realization for Accurate Jason Satellite Orbits and Its Impact on Geodetic and Altimetry Results
Remote Sensing, 2020Co-Authors: Mathis Bloßfeld, Sergei Rudenko, J Zeitlhöfler, Denise DettmeringAbstract:For low Earth orbiting satellites, non-gravitational forces cause one of the largest Perturbing Accelerations. During a precise orbit determination (POD), the accurate modeling of the satellite-body attitude and solar panel orientation is important since the satellite’s effective cross-sectional area is directly related to the Perturbing Acceleration. Moreover, the position of tracking instruments that are mounted on the satellite body are affected by the satellite attitude. For satellites like Jason-1/-2/-3, attitude information is available in two forms—as a so-called nominal yaw steering model and as observation-based (measured by star tracking cameras) quaternions of the spacecraft body orientation and rotation angles of the solar arrays. In this study, we have developed a preprocessing procedure for publicly available satellite attitude information. We computed orbits based on Satellite Laser Ranging (SLR) observations to the Jason satellites at an overall time interval of approximately 25 years, using each of the two satellite attitude representations. Based on the analysis of the orbits, we investigate the influence of using preprocessed observation-based attitude in contrast to using a nominal yaw steering model for the POD. About 75% of all orbital arcs calculated with the observation-based satellite attitude data result in a smaller root mean square (RMS) of residuals. More precisely, the resulting orbits show an improvement in the overall mission RMS of SLR observation residuals of 5.93% (Jason-1), 8.27% (Jason-2) and 4.51% (Jason-3) compared to the nominal attitude realization. Besides the satellite orbits, also the estimated station coordinates benefit from the refined attitude handling, that is, the station repeatability is clearly improved at the draconitic period. Moreover, altimetry analysis indicates a clear improvement of the single-satellite crossover differences (6%, 15%, and 16% reduction of the mean of absolute differences and 1.2%, 2.7%, and 1.3% of their standard deviations for Jason-1/-2/-3, respectively). On request, the preprocessed attitude data are available.
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Towards thermospheric density estimation from SLR observations of LEO satellites: a case study with ANDE-Pollux satellite
Journal of Geodesy, 2019Co-Authors: Francesca Panzetta, Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Eren Erdogan, Horst MüllerAbstract:The present contribution investigates the possibility to obtain thermospheric neutral density estimates using satellite laser ranging (SLR) observations of low Earth orbiters (LEOs). This approach is based on the analysis of the satellite atmospheric drag, driven by the fact that the drag force is the largest non-gravitational perturbation acting on LEOs. Due to the uncertainty of current thermospheric models, it is the main error source in the LEO orbit determination process. Moreover, the drag is physically related to the thermospheric density distribution, the interaction of the satellite surface with the surrounding thermosphere and thermospheric winds. For this investigation, a spherical satellite called “Atmospheric Neutral Density Experiment-Pollux” (ANDE-P) developed by the Naval Research Laboratory (USA) is adopted as a case study. The satellite flew at the very low altitude of about 350 km. The most important Perturbing Acceleration at this altitude, the atmospheric drag, is easier to model for a spherical satellite like ANDE-P than for a satellite of complex geometry. A precise orbit determination of ANDE-P was performed with the DGFI Orbit and Geodetic parameter estimation Software (DOGS) over a period of 49 days (16 August 2009 until 3 October 2009) using SLR observations to this satellite and different thermospheric models. In total, we tested four thermospheric models, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. Correspondingly, scale factors of these reference models are estimated with a 6-h resolution. The results confirm that the estimation of force model parameters from SLR measurements of the ANDE-P satellite is sensitive to differences in the density distributions provided by different models. As a consequence, information on the discrepancies between the various models and the true density can be derived from SLR measurements. Moreover, it is found that SLR observations to LEO satellites at very low altitudes are capable to estimate corrections to (scale factors of) the integrated thermospheric density if all other Perturbing Accelerations are modelled with sufficient accuracy. We derived time series of estimated scale factors of the thermospheric densities provided by the models and obtained the following mean values during the processed period of time at the ANDE-P altitude: $$0.65\pm 0.26$$ 0.65 ± 0.26 for CIRA86, $$0.65\pm 0.25$$ 0.65 ± 0.25 for NRLMSISE00, $$0.79\pm 0.24$$ 0.79 ± 0.24 for DTM2013, and $$0.89\pm 0.27$$ 0.89 ± 0.27 for JB2008. This suggests that all models overestimate the true thermospheric density along the ANDE-P trajectory during the processed period to a certain extent. The thermospheric densities need to be scaled downwards to fit ANDE-P SLR observations with JB2008 requiring the least amount of scaling.
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Calibration of Empirical Models of Thermospheric Density Using Satellite Laser Ranging Observations to Near-Earth Orbiting Spherical Satellites
International Symposium on Advancing Geodesy in a Changing World, 2018Co-Authors: Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Chao Xiong, Hermann LührAbstract:The thermosphere causes by far the largest non-gravitational Perturbing Acceleration of near-Earth orbiting satellites. Especially between 80 km and 1,000 km, the thermospheric density distribution and variations are required to model accurately this Acceleration for precise orbit determination (POD), ephemeris computation and re-entry prediction of the Low-Earth Orbiting (LEO) satellites. So far, mostly on-board accelerometers are used to measure the thermospheric density. However, such type of satellite is usually of complex shape and any error or mismodelling in the satellite drag coefficient and satellite effective cross-sectional area will directly propagate into the derived thermospheric density values. At GFZ, an empirical model of the thermospheric mass density denoted as “CH-Therm-2018” has been developed by using 9 years (2001–2009) of CHAMP observations.
Sergei Rudenko - One of the best experts on this subject based on the ideXlab platform.
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Observation-Based Attitude Realization for Accurate Jason Satellite Orbits and Its Impact on Geodetic and Altimetry Results
Remote Sensing, 2020Co-Authors: Mathis Bloßfeld, Sergei Rudenko, J Zeitlhöfler, Denise DettmeringAbstract:For low Earth orbiting satellites, non-gravitational forces cause one of the largest Perturbing Accelerations. During a precise orbit determination (POD), the accurate modeling of the satellite-body attitude and solar panel orientation is important since the satellite’s effective cross-sectional area is directly related to the Perturbing Acceleration. Moreover, the position of tracking instruments that are mounted on the satellite body are affected by the satellite attitude. For satellites like Jason-1/-2/-3, attitude information is available in two forms—as a so-called nominal yaw steering model and as observation-based (measured by star tracking cameras) quaternions of the spacecraft body orientation and rotation angles of the solar arrays. In this study, we have developed a preprocessing procedure for publicly available satellite attitude information. We computed orbits based on Satellite Laser Ranging (SLR) observations to the Jason satellites at an overall time interval of approximately 25 years, using each of the two satellite attitude representations. Based on the analysis of the orbits, we investigate the influence of using preprocessed observation-based attitude in contrast to using a nominal yaw steering model for the POD. About 75% of all orbital arcs calculated with the observation-based satellite attitude data result in a smaller root mean square (RMS) of residuals. More precisely, the resulting orbits show an improvement in the overall mission RMS of SLR observation residuals of 5.93% (Jason-1), 8.27% (Jason-2) and 4.51% (Jason-3) compared to the nominal attitude realization. Besides the satellite orbits, also the estimated station coordinates benefit from the refined attitude handling, that is, the station repeatability is clearly improved at the draconitic period. Moreover, altimetry analysis indicates a clear improvement of the single-satellite crossover differences (6%, 15%, and 16% reduction of the mean of absolute differences and 1.2%, 2.7%, and 1.3% of their standard deviations for Jason-1/-2/-3, respectively). On request, the preprocessed attitude data are available.
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Towards thermospheric density estimation from SLR observations of LEO satellites: a case study with ANDE-Pollux satellite
Journal of Geodesy, 2019Co-Authors: Francesca Panzetta, Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Eren Erdogan, Horst MüllerAbstract:The present contribution investigates the possibility to obtain thermospheric neutral density estimates using satellite laser ranging (SLR) observations of low Earth orbiters (LEOs). This approach is based on the analysis of the satellite atmospheric drag, driven by the fact that the drag force is the largest non-gravitational perturbation acting on LEOs. Due to the uncertainty of current thermospheric models, it is the main error source in the LEO orbit determination process. Moreover, the drag is physically related to the thermospheric density distribution, the interaction of the satellite surface with the surrounding thermosphere and thermospheric winds. For this investigation, a spherical satellite called “Atmospheric Neutral Density Experiment-Pollux” (ANDE-P) developed by the Naval Research Laboratory (USA) is adopted as a case study. The satellite flew at the very low altitude of about 350 km. The most important Perturbing Acceleration at this altitude, the atmospheric drag, is easier to model for a spherical satellite like ANDE-P than for a satellite of complex geometry. A precise orbit determination of ANDE-P was performed with the DGFI Orbit and Geodetic parameter estimation Software (DOGS) over a period of 49 days (16 August 2009 until 3 October 2009) using SLR observations to this satellite and different thermospheric models. In total, we tested four thermospheric models, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. Correspondingly, scale factors of these reference models are estimated with a 6-h resolution. The results confirm that the estimation of force model parameters from SLR measurements of the ANDE-P satellite is sensitive to differences in the density distributions provided by different models. As a consequence, information on the discrepancies between the various models and the true density can be derived from SLR measurements. Moreover, it is found that SLR observations to LEO satellites at very low altitudes are capable to estimate corrections to (scale factors of) the integrated thermospheric density if all other Perturbing Accelerations are modelled with sufficient accuracy. We derived time series of estimated scale factors of the thermospheric densities provided by the models and obtained the following mean values during the processed period of time at the ANDE-P altitude: $$0.65\pm 0.26$$ 0.65 ± 0.26 for CIRA86, $$0.65\pm 0.25$$ 0.65 ± 0.25 for NRLMSISE00, $$0.79\pm 0.24$$ 0.79 ± 0.24 for DTM2013, and $$0.89\pm 0.27$$ 0.89 ± 0.27 for JB2008. This suggests that all models overestimate the true thermospheric density along the ANDE-P trajectory during the processed period to a certain extent. The thermospheric densities need to be scaled downwards to fit ANDE-P SLR observations with JB2008 requiring the least amount of scaling.
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Calibration of Empirical Models of Thermospheric Density Using Satellite Laser Ranging Observations to Near-Earth Orbiting Spherical Satellites
International Symposium on Advancing Geodesy in a Changing World, 2018Co-Authors: Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Chao Xiong, Hermann LührAbstract:The thermosphere causes by far the largest non-gravitational Perturbing Acceleration of near-Earth orbiting satellites. Especially between 80 km and 1,000 km, the thermospheric density distribution and variations are required to model accurately this Acceleration for precise orbit determination (POD), ephemeris computation and re-entry prediction of the Low-Earth Orbiting (LEO) satellites. So far, mostly on-board accelerometers are used to measure the thermospheric density. However, such type of satellite is usually of complex shape and any error or mismodelling in the satellite drag coefficient and satellite effective cross-sectional area will directly propagate into the derived thermospheric density values. At GFZ, an empirical model of the thermospheric mass density denoted as “CH-Therm-2018” has been developed by using 9 years (2001–2009) of CHAMP observations.
Horst Müller - One of the best experts on this subject based on the ideXlab platform.
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Towards thermospheric density estimation from SLR observations of LEO satellites: a case study with ANDE-Pollux satellite
Journal of Geodesy, 2019Co-Authors: Francesca Panzetta, Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Eren Erdogan, Horst MüllerAbstract:The present contribution investigates the possibility to obtain thermospheric neutral density estimates using satellite laser ranging (SLR) observations of low Earth orbiters (LEOs). This approach is based on the analysis of the satellite atmospheric drag, driven by the fact that the drag force is the largest non-gravitational perturbation acting on LEOs. Due to the uncertainty of current thermospheric models, it is the main error source in the LEO orbit determination process. Moreover, the drag is physically related to the thermospheric density distribution, the interaction of the satellite surface with the surrounding thermosphere and thermospheric winds. For this investigation, a spherical satellite called “Atmospheric Neutral Density Experiment-Pollux” (ANDE-P) developed by the Naval Research Laboratory (USA) is adopted as a case study. The satellite flew at the very low altitude of about 350 km. The most important Perturbing Acceleration at this altitude, the atmospheric drag, is easier to model for a spherical satellite like ANDE-P than for a satellite of complex geometry. A precise orbit determination of ANDE-P was performed with the DGFI Orbit and Geodetic parameter estimation Software (DOGS) over a period of 49 days (16 August 2009 until 3 October 2009) using SLR observations to this satellite and different thermospheric models. In total, we tested four thermospheric models, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. Correspondingly, scale factors of these reference models are estimated with a 6-h resolution. The results confirm that the estimation of force model parameters from SLR measurements of the ANDE-P satellite is sensitive to differences in the density distributions provided by different models. As a consequence, information on the discrepancies between the various models and the true density can be derived from SLR measurements. Moreover, it is found that SLR observations to LEO satellites at very low altitudes are capable to estimate corrections to (scale factors of) the integrated thermospheric density if all other Perturbing Accelerations are modelled with sufficient accuracy. We derived time series of estimated scale factors of the thermospheric densities provided by the models and obtained the following mean values during the processed period of time at the ANDE-P altitude: $$0.65\pm 0.26$$ 0.65 ± 0.26 for CIRA86, $$0.65\pm 0.25$$ 0.65 ± 0.25 for NRLMSISE00, $$0.79\pm 0.24$$ 0.79 ± 0.24 for DTM2013, and $$0.89\pm 0.27$$ 0.89 ± 0.27 for JB2008. This suggests that all models overestimate the true thermospheric density along the ANDE-P trajectory during the processed period to a certain extent. The thermospheric densities need to be scaled downwards to fit ANDE-P SLR observations with JB2008 requiring the least amount of scaling.
Michael Schmidt - One of the best experts on this subject based on the ideXlab platform.
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Towards thermospheric density estimation from SLR observations of LEO satellites: a case study with ANDE-Pollux satellite
Journal of Geodesy, 2019Co-Authors: Francesca Panzetta, Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Eren Erdogan, Horst MüllerAbstract:The present contribution investigates the possibility to obtain thermospheric neutral density estimates using satellite laser ranging (SLR) observations of low Earth orbiters (LEOs). This approach is based on the analysis of the satellite atmospheric drag, driven by the fact that the drag force is the largest non-gravitational perturbation acting on LEOs. Due to the uncertainty of current thermospheric models, it is the main error source in the LEO orbit determination process. Moreover, the drag is physically related to the thermospheric density distribution, the interaction of the satellite surface with the surrounding thermosphere and thermospheric winds. For this investigation, a spherical satellite called “Atmospheric Neutral Density Experiment-Pollux” (ANDE-P) developed by the Naval Research Laboratory (USA) is adopted as a case study. The satellite flew at the very low altitude of about 350 km. The most important Perturbing Acceleration at this altitude, the atmospheric drag, is easier to model for a spherical satellite like ANDE-P than for a satellite of complex geometry. A precise orbit determination of ANDE-P was performed with the DGFI Orbit and Geodetic parameter estimation Software (DOGS) over a period of 49 days (16 August 2009 until 3 October 2009) using SLR observations to this satellite and different thermospheric models. In total, we tested four thermospheric models, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. Correspondingly, scale factors of these reference models are estimated with a 6-h resolution. The results confirm that the estimation of force model parameters from SLR measurements of the ANDE-P satellite is sensitive to differences in the density distributions provided by different models. As a consequence, information on the discrepancies between the various models and the true density can be derived from SLR measurements. Moreover, it is found that SLR observations to LEO satellites at very low altitudes are capable to estimate corrections to (scale factors of) the integrated thermospheric density if all other Perturbing Accelerations are modelled with sufficient accuracy. We derived time series of estimated scale factors of the thermospheric densities provided by the models and obtained the following mean values during the processed period of time at the ANDE-P altitude: $$0.65\pm 0.26$$ 0.65 ± 0.26 for CIRA86, $$0.65\pm 0.25$$ 0.65 ± 0.25 for NRLMSISE00, $$0.79\pm 0.24$$ 0.79 ± 0.24 for DTM2013, and $$0.89\pm 0.27$$ 0.89 ± 0.27 for JB2008. This suggests that all models overestimate the true thermospheric density along the ANDE-P trajectory during the processed period to a certain extent. The thermospheric densities need to be scaled downwards to fit ANDE-P SLR observations with JB2008 requiring the least amount of scaling.
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Calibration of Empirical Models of Thermospheric Density Using Satellite Laser Ranging Observations to Near-Earth Orbiting Spherical Satellites
International Symposium on Advancing Geodesy in a Changing World, 2018Co-Authors: Sergei Rudenko, Michael Schmidt, Mathis Bloßfeld, Chao Xiong, Hermann LührAbstract:The thermosphere causes by far the largest non-gravitational Perturbing Acceleration of near-Earth orbiting satellites. Especially between 80 km and 1,000 km, the thermospheric density distribution and variations are required to model accurately this Acceleration for precise orbit determination (POD), ephemeris computation and re-entry prediction of the Low-Earth Orbiting (LEO) satellites. So far, mostly on-board accelerometers are used to measure the thermospheric density. However, such type of satellite is usually of complex shape and any error or mismodelling in the satellite drag coefficient and satellite effective cross-sectional area will directly propagate into the derived thermospheric density values. At GFZ, an empirical model of the thermospheric mass density denoted as “CH-Therm-2018” has been developed by using 9 years (2001–2009) of CHAMP observations.