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We study the machine learning method for classifying the basic shape of space debris in both simulated and observed data experiments, where light curves are used as the input features. In the dataset for training and testing, simulated light curves are derived from four types of debris within different shapes and materials. Observed light curves are extracted from Mini-Mega TORTORA (MMT) database which is a publicly accessible source of space object photometric records. The experiments employ the deep convolutional neural network, make comparisons with other machine learning algorithms, and the results show CNN (Convolutional Neural Network) is better. In simulational experiments, both types of cylinder can be distinguished perfectly, and two other types of satellite have around 90% probability to be classified. Rockets and defunct satellites can achieve 99% success rate in binary classification, but in further sub-classes classifications, the rate becomes relatively lower.

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.

The method of controlling highly eccentric accompanying flight orbit using the solar wing is proposed in this paper. The formation is maintained by controlling the orbit of the accompanying satellite (follower). The accompanying satellite rotates around its inertial principal axis with a constant angular velocity. The control on the accompanying satellite is divided into the in-plane control and out-of-plane control. The in-plane control is superior to the out-of-plane control. The out-of-plane control force is applied when the in-plane error is eliminated or the in-plane control force can not be supplied due to some geometrical factors. By the sliding mode control method, the magnitude and direction of the control force required by the in-plane orbit control are calculated. Then accordingly, the expression of the solar wing orientation with respect to the satellite body in the control process is derived, so that by adjusting the orientation of the solar wing, the required control force can be obtained. Finally, the verification on this method is performed by numerical simulations, including the orbit adjustment, error elimination, and the orbit maintenance. It is shown that this method can keep the error less than 5 m, and it is feasible for the space formation flight.

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.

With the rising number of space debris, people pay more and more attention to the space debris collision avoidance system (SDCAS). In the early 1990s, the BOX method is commonly used as a collision criterion to decide whether the avoiding maneuver is necessary for a spacecraft. But this method has low practicability, so the method of collision probability is developed. This method takes the relative distance and other geometrical parameters at the en time of two space objects into consideration. However, the mathematical model of this collision criterion depends highly on the orbit errors, so it may lead to some inaccurate results. In this paper, the rendezvous of two orbits are sim, and the errors are considered, then the relative distance at the moment of their closest approach and the collision probability are calculated. The re indicate that the covariance of position errors plays an indispensable role in measuring the risk of collision. When the precision of orbit prediction is not very good, it is better to combine the BOX method and the collision probability method in the SDCAS.

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.

Due to the various factors of image degradation in the optical observation of space objects, the imaging process is affected, it reduces the detection accuracy and brings difficulty to the high-precision positioning calculation. In order to improve the positioning accuracy of space objects, the maximum entropy method is adopted for image restoration, with an a priori PSF (Point Spread Function) model. The measuring errors of object positions before and after restoration are compared to investigate the effectiveness of the image restoration. The experimental results indicate that the influences of image degradation are reduced, and the positioning accuracy of degraded images is obviously improved by using the maximum entropy method.

From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J (2) and J (22) of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.

Due to the relative movement between space debris and background stars, the blending of objects and stars is ineluctable through observation. It brings down position accuracy of objects and even makes the tracking break down in worse conditions. In view of the difference of geometry between stars and objects in space debris observation, a technique for separating blended objects based on mathematical morphology is presented. It's sufficiently flexible to be applied in image processing, and the blending images can be separated effectively with a high degree of centroid precision.

In the observation of space objects with a full-frame transfer CCD camera, the camera shutter is often removed, and therefore the smeared images are produced, which affect seriously the object detection and location. Based on the difference of geometrical morphology between star images and smears, a mathematical morphology method is proposed to process the smeared images. By comparing the position accuracies of stars and space objects before and after processing, it is verified that the morphological method can effectively remove the smears from astronomical images, and can significantly improve the detection rates and position accuracies of stars and moving objects. The result indicates that this is an effective method to eliminate the smearing effect.

Based on the latest release of the SGP4/SDP4 (Simplified General Perturbation Version 4/ Simplified Deep-space Perturbation Version 4) model, in this paper we have designed an orbit determination program. Through calculations for the 1120 objects with various types and orbital elements selected from the space objects database, we have obtained the accuracies of the orbit determination prediction dealt with various types of space objects by the SGP4/SDP4 model. The results show that the accuracies of the near-earth objects are in the order of magnitude of 100 meters; the averages of the orbit determination accuracies of the semi-synchronous and geosynchronous orbits are, respectively, 0.7 and 1.9 km. The orbit determination accuracies of the elliptical orbit objects are related to their eccentricities. Except for few elliptical orbit objects with e > 0.8, the orbit determination errors of the vast majority of the elliptical orbit objects are all less than 10 km. By using the SGP4/SDP4 model to make 3 days predictions for near-earth objects, 30 days for semi-synchronous orbit objects, 15 days for geosynchronous orbit objects and 1 day for elliptical orbit objects, the errors of prediction generally don’t exceed 40 km.

This paper discusses the problem of variable air drag perturbation of man-made space vehicles. An analytical solution of the perturbation is given and a comparison made with usual drag perturbation. Two main conclusions are found: 1. The variable drag perturbation retains the basic characteristics of usual drag perturbation. 2. The variable drag solution depends on the orientation of the solar panel.

The two previous papers of this series[1,2] qualitatively clarified the main function of symplectic algorithm[3–6] of maintaining the global structure of hamiltonian systems. In this paper we exploit one of its quantitative advantages—the control of rapid growth of along-track error. With a small improvement in the explicit symplectic difference scheme for separable systems, the algorithm can be extended to more general systems containing small dissipative and non-separable terms. Very good results were obtained showing that the symplectic algorithm has great advantages over usual, non-symplectic ones.

The aim of this study was to explore the molecular pathological characteristics of cervical cancer in women aged below 35, disclose the factors that indicate the unfavorable prognosis, and provide some useful targets for improving therapeutic outcome.64 cases of pathological data originating from cervical cancer patients aged below 35 served as the study group to perform a retrospective research, and pathological data from 90 cases of cervical cancer patients beyond age 35, who underwent treatment during the same time, were selected at random as the reference group. Immunohistochemistry and quantified image analysis were utilized to detect synchronously the protein expression difference of survivin and p27 between the 2 groups.The total 5-year survival rate of the study group was 65.6% compared to 84.4% in the reference group, while the lymph node metastasis rate was 25% compared to 12.2% in the reference group. Both differences were statistically significant (p0.05). Survivin expression is much greater in the study group than in the reference group (p0.05); there is no statistical difference of the p27 expression between the 2 groups (p0.05), but p27 expression is related to lymph node metastasis.Younger female patients have a worse prognosis than older ones, and survivin expression is associated with poor prognosis. Targeting these molecular factors may lead to a hopeful biomedical therapy to improve the prognosis of young female cervical cancer patients.