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The features of upper atmospheric midnight density maximum (MDM) around low geographic latitudes are studied based on neutral mass densities data at altitudes 360–480 km, derived from the accelerometer measurements aboard on the three polar orbiting satellites CHAMP (CHAllenging Minisatellite Payload), GRACE-A (Gravity Recovery and Climate Experiment-A), and SWARM-C (The Earth's Magnetic Field and Environment Explorers-C). The MDM appears during the local times from 23:00 to 02:00 LT (Local Time), whose peak locates at the low latitudes within 15 ∘ and two valleys locate at the middle latitudes between 35 ∘ and 45 ∘ on both hemispheres separately. The structure of MDM drifts toward the southern hemisphere overall. The MDM's amplitude decreases with increases in altitude and solar radiation level. The seasonal effect weakens the MDM's amplitudes around the summer and winter solstices, while the amplitudes around the spring and autumn equinoxes are extremely significant due to the slight seasonal difference between both hemispheres. Three atmospheric density models DTM2000 (Drag Temperature Model 2000), NRLMSISE00 (US Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Extended atmosphere model), and JB2008 (Jacchia-Bowman 2008 model) are used to simulate the MDM along these three satellites' orbits, and compared with the observations. It is found that the JB2008 model is failed to describe the MDM, and the other two models underestimate the MDM's amplitudes at altitudes 360 km and 480 km: the simulated amplitudes by the DTM2000 model are 46% and 53% of the observed amplitudes, respectively, and only 33% and 26% for the NRLMSISE00 model. These three models are also failed to depict the MDM's variation with altitude, solar radiation level, and seasonal effects. In order to correct the model prediction, a 6th-order Legendre polynomial of geographic latitude, coupled with arguments of local time and altitude, is designed to fit the MDM signals from the three satellites' observations. In terms of amplitude and phase of the MDM, the fitting results agree with the observations very well, and the correlation coefficient is 0.923. It indicates that this empirical polynomial could be helpful to the density model correction and high accuracy prediction of spacecrafts in low Earth orbits. [ABSTRACT FROM AUTHOR]

Adopting the precise radiation pressure model, we compute the real perturbation force caused by the solar radiation on the GRACE satellites and estimate the scale factors of accelerometer's y axis and z axis. Setting these scale factors constant and using the dynamical orbit determination (OD), we estimate the rest four calibration parameters, i.e. the scale factor of the x axis and the biases of three axes. On this basis, we obtain the daily calibration parameters from 2002 to 2014. The average values and standard deviations of scale factors of the x , y and z axes are 0.9435 ± 0.0187, 0.9393 ± 0.0444, 1.0371 ± 0.0391 for GRACE-A, and 0.9313 ± 0.0170, 0.9488 ± 0.0452, 1.0274 ± 0.0446 for GRACE-B, respectively. Compared with our previous work, this new method constrains the scale factors of the y and z axes with the precise radiation pressure model, which can reduce the influence of data errors on the weak-signal axes ( y , z ), as well as reduce the correlation between scale factors and biases, and eventually improve the stability of calibration parameters. Taking the y and z axes of GRACE-A as an example, the standard deviations of scale factors with this new method are about 0.0391–0.0444, while the previous results obtained by the unconstrained dynamical orbit determination were about 0.21–0.31. It is shown that the standard deviations of scale factors in this paper have been reduced by more than 78%, and those of biases have been reduced by more than 85%. Therefore, the calibration parameters estimated with the new method are more stable and will be of particular interest for the study on the rotation speed and wind field of the Earth's thermosphere. [ABSTRACT FROM AUTHOR]

The Earth gravitational field model is one of the most important dynamic models in satellite orbit computation. Several space gravity missions made great successes in recent years, prompting the publishing of several gravitational filed models. In this paper, two classical (JGM3, EGM96) and four latest (EIGEN-CHAMP05S, GGM03S, GOCE02S, EGM2008) models are evaluated by employing them in the precision orbit determination (POD) and prediction. These calculations are performed based on the laser ranging observation of four Low Earth Orbit (LEO) satellites, including CHAMP, GFZ-1, GRACE-A, and SWARM-A. The residual error of observation in POD is adopted to describe the accuracy of six gravitational field models. The main results we obtained are as follows. (1) For the POD of LEOs, the accuracies of 4 latest models are at the same level, and better than those of 2 classical models; (2) Taking JGM3 as reference, EGM96 model's accuracy is better in most situations, and the accuracies of the 4 latest models are improved by 12%-47% in POD and 63% in prediction, respectively. We also confirm that the model's accuracy in POD is enhanced with the increasing degree and order if they are smaller than 70, and when they exceed 70, the accuracy keeps constant, implying that the model's degree and order truncated to 70 are sufficient to meet the requirement of LEO computation of centimeter precision. [ABSTRACT FROM AUTHOR]

In the orbital determination of low earth orbit satellites, the solar radiation index F 10 . 7 is an important input parameter, which is commonly used to describe the effects on the density of upper atmosphere and orbit perturbation, directly or indirectly caused by solar activities, respectively. So the accuracy of the index F 10 . 7 will affect the precision of orbit prediction. Based on the characteristic of the 27-day short-term oscillation in the solar activity, a method is studied in this paper for the 54-day mid-term forecast of F 10 . 7 by using its historical data of the past 135 days. Thus the method can predict the variation of solar radiation for the future two rotational periods. In comparison with the other widely-used forecast methods, it is shown that: (1) the method is obviously better than the traditional triangle function method; (2) in the short-term forecast (7 days), the method is a little better than that developed by the Space Weather Prediction Center in USA, and the root mean square could be reduced by about 19%; and (3) in the mid-term forecast (27 days), the accuracy of the method is almost equivalent to the 54-order autoregression method which is used widely in our country, but this method requires to input fewer parameters and historical data, and with a stable precision, it is more convenient in the application of orbit determination. Moreover, up to the 54th day the correlation coeffcient between the prediction and the actual index is still greater than 0.92, implying that the method can keep stable in the mid-term forecast. Overall, the advantage of this method is that with fewer historical data of radiation indices, it can make the mid-term prediction of solar radiation as long as 54 days without the need of extra solar observation data, to provide the reasonable and reliable solar radiation indices for the short- and mid-term orbit predictions in space flight missions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the expression of V k lm (I) in the Gooding method is rewritten to be the form convenient for calculation, and a standard recursive lm procedure is used to calculate Ak lm (I). We have rewritten the Gooding's program under the assumption that l and k have the same odd-even parity, this makes the program be shorten for one half, the computational effciency and readability of the program be raised, the computing time be shortened for 41%, and the computational accuracy and stability are also slightly improved. [Copyright &y& Elsevier]

Abstract: In this paper, a method to calculate the inclination function with Jacobi polynomials is studied, the formulation of this method is very simple, it needs not to concern about whether k and l have the same parity, and to calcu- late the non-integral factorials, nor to concern about the conversion between the case of k < 0 and the case of k ≥ 0, and the recurrent formula can be the stan- dard recurrent formula for Jacobi polynomials. In addition, its computational accuracy and applicable order-numbers are equivalent to those of the Gooding method, but its calculating time is shorter than that of the Gooding method for 9%. [Copyright &y& Elsevier]

Abstract: Two kinds of recursion relations of hypergeometric series were derived, and hereby the Gooding''s recursion formula of inclination function. In addition, it was demonstrated that this recursion formula can be derived also on the basis of the recursion relation of Jacobi polynomials. Comparing with the hypergeometric series, the recursion process based on the Jacobi polynomials is much simpler, indicating that the Gooding''s method is the recursion of Jacobi polynomials in essence. [Copyright &y& Elsevier]

Abstract: This paper gives a definite integration method for calculating the inclination function and its derivative, which has a very simple expression, and the accuracies as high as 10-15 for the inclination function, and 10-13 for its derivative, comparable with the accuracy of Gooding''s method. By through a lot of numerical simulations, it is proved that this method has a good stability and an wide applicable range of inclinations, hence it can be used to calculate the inclination function to the maximum order of L max ≤ 50. [Copyright &y& Elsevier]