A method for calculating probability of collision between space objects

A method is developed to calculate probability of collision. Based on geometric features of space objects during the encounter, it is reasonable to separate the radial orbital motions from those in the cross section for most encounter events that occur in a near-circular orbit. Therefore, the probability of collision caused by differences in both altitude of the orbit in the radial direction and the probability of collision caused by differences in arrival time in the cross section are calculated. The net probability of collision is expressed as an explicit expression by multiplying the above two components. Numerical cases are applied to test this method by comparing the results with the general method. The results indicate that this method is valid for most encounter events that occur in near-circular orbits.

Improved astrometry of space debris with image restoration

In order to implement an observing strategy, image degradation that occurs during optical observation of space debris is ineluctable and has distinct characteris- tics. Image restoration is presented as a way to remove the influence of degradation in CCD images of space debris, based on assumed PSF models with the same F-WHM as images of the object. In the process of image restoration, the maximum entropy method is adopted. The results of reduction using observed raw CCD images indi- cate that the precision in estimating positions of objects is improved and the effects of degradation are reduced. Improving the astrometry of space debris using image restoration is effective and feasible.

An improved astrometric calibration technique for space debris observation

An optical survey is the main technique for detecting space debris. Due to the specific character- istics of observation, the pointing errors and tracking errors of the telescope as well as image degradation may be significant, which make it difficult for astrometric calibration. Here we present an improved method that corrects the pointing and tracking errors, and measures the image position precisely. The pipeline is tested on a number of CCD images obtained from a 1-m telescope administered by Xinjiang Astronomical Observatory while observing a GPS satellite. The results show that the position measurement error of the background stars is around 0.1 pixel, while the time cost for a single frame is about 7.5 s; hence the relia- bility and accuracy of our method are demonstrated. In addition, our method shows a versatile and feasible way to perform space debris observation utilizing non-dedicated telescopes, which means more sensors could be involved and the ability to perform surveys could be improved.

Experiment on diffuse reflection laser ranging to space debris and data analysis

Space debris poses a serious threat to human space activities and needs to be measured and cataloged. As a new technology for space target surveillance, the measurement accuracy of diffuse reflection laser ranging （DRLR） is much higher than that of microwave radar and optoelectronic measurement. Based on the laser ranging data of space debris from the DRLR system at Shanghai Astronomical Observatory acquired in March-April, 2013, the characteristics and precision of the laser ranging data are analyzed and their applications in orbit determination of space debris are discussed, which is implemented for the first time in China. The experiment indicates that the precision of laser ranging data can reach 39 cm-228 cm. When the data are sufficient enough （four arcs measured over three days）, the orbital accuracy of space debris can be up to 50 m.

Electromagnetic effects on the orbital motion of a charged spacecraft

This paper deals with the effects of electromagnetic forces on the orbital motion of a spacecraft. The electrostatic charge which a spacecraft generates on its surface in the Earth＇s magnetic field will be subject to a perturbative Lorentz force. A model incorporating all Lorentz forces as a function of orbital elements has been developed on the basis of magnetic and electric fields. This Lorentz force can be used to modify or perturb the spacecraft＇s orbits. Lagrange＇s planetary equations in the Gauss variational form are derived using the Lorentz force as a perturbation to a Keplerian orbit. Our approach incorporates orbital inclination and the true anomaly. The numer- ical results of Lagrange＇s planetary equations for some operational satellites show that the perturbation in the orbital elements of the spacecraft is a second order perturba- tion for a certain value of charge. The effect of the Lorentz force due to its magnetic component is three times that of the Lorentz force due to its electric component. In addition, the numerical results confirm that the strong effects are due to the Lorentz force in a polar orbit, which is consistent with realistic physical phenomena that occur in polar orbits. The results confirm that the magnitude of the Lorentz force depends on the amount of charge. This means that we can use artificial charging to create a force to control the attitude and orbital motion of a spacecraft.

Application of two special orbits in the orbit determination of lunar satellites

Using inter-satellite range data, the combined autonomous orbit determina- tion problem of a lunar satellite and a probe on some special orbits is studied in this paper. The problem is firstly studied in the circular restricted three-body problem, and then generalized to the real force model of the Earth-Moon system. Two kinds of spe- cial orbits are discussed： collinear libration point orbits and distant retrograde orbits. Studies show that the orbit determination accuracy in both cases can reach that of the observations. Some important properties of the system are carefully studied. These findings should be useful in the future engineering implementation of this conceptual study.

Feasible region and stability analysis for hovering around elongated asteroids with low thrust

This paper investigates properties of low-thrust hovering, including the feasible region and stability, in terms of the dynamical parameters for elongated asteroids. An approximate rotating mass dipole model, by which the description of the rotational gravitational field is reduced to two independent parameters, is employed to construct normalized dynamical equations. The boundaries of the feasible region are determined by contours representing the magnitude of the active control. The effects of a rotating gravitational field and maximal magnitude of the low thrust on the feasible hovering regions are analyzed with numerical results. The stability conditions are derived according to the forms of the eigenvalues of the linearized equation near the hovering position. The stable regions are then determined by a grid search and the effects of the relevant parameters are analyzed in a parametric way. The results show that a close hovering can be easier to realize near the middle of the asteroid than near the two ends in the sense of both required control magnitude and stability.

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

The attitude dynamics of a rigid artificial satellite subject to a gravity gradient and Lorentz torques in a circular orbit are considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the charged satellite＇s surface. We assume that the satellite is moving in a Low Earth Orbit in the geomagnetic field, which is considered to be a dipole. Our model of torque due to the Lorentz force is developed for an artificial satellite with a general shape, and the nonlinear differential equations of Euler are used to describe its attitude orientation. All equilibrium positions are determined and conditions for their existence are obtained.The numerical results show that the charge q and radius ρ0of the center of charge for the satellite provide a certain type of semi-passive control for the attitude of the satellite. The technique for this kind of control would be to increase or decrease the electrostatic screening on the satellite. The results obtained confirm that the change in charge can affect the magnitude of the Lorentz torque, which can also affect control of the satellite. Moreover, the relationship between magnitude of the Lorentz torque and inclination of the orbit is investigated.

Asteroid body-fixed hovering using nonideal solar sails

The problem of body-fixed hovering over an asteroid using a compact form of nonideal solar sails with a controllable area is investigated. Nonlinear dynamic equations describing the hovering problem are constructed for a spherically symmet- ric asteroid. Numerical solutions of the feasible region for body-fixed hovering are obtained. Different sail models, including the cases of ideal, optical, parametric and solar photon thrust, on the feasible region is studied through numerical simulations. The influence of the asteroid spinning rate and the sail area-to-mass ratio on the feasi- ble region is discussed. The required orientations for the sail and their corresponding variable lightness numbers are given for different hovering radii to identify the feasible region of the body-fixed hovering. An attractive scenario for a mission is introduced to take advantage of solar sail hovering.