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The determination of the orbit of a target satellite by means of observed angle measurement data has a very important applicative value. In order to solve this problem, an optimization mathematic model labelled STSM is first constructed. Next is given the necessary numerical procedure of finding the initial values by polynomial fitting of the angle measurement data. Thirdly, the properties of STSM are analyzed in detail, from which the basic method for solving the optimization problem is found. Finally, the above-mentioned method is applied to a large number of simulation calculations and a preliminary analysis of the results is made. The calculated results show that for a given accuracy and density of data, it is feasible to determine the orbital elements of the target satellite by using space-based angle measurement data according to the procedure given.

The unit vector method (PUVM1) by which the observed data of artificial satellites are used to determine the perturbed initial orbits has been widely applied. In order to further perfect and improve this method, first, a mathematical model (MMUVM) corresponding to this method is constructed on the basis of measuring errors. In essence, the MMUVM is a nonlinear optimization problem. In the light of the MMUVM, simulated and observed data of multiple circuits are taken to form specific objective functions, which are then processed by means of a direct search method and with of a tri-diagonal quadratic interpolation model for solving optimization problems. The calculated results show that the optimization model MMUVM is right and reasonable and the adopted direct method is practical and effective. Secondly, the relation between PUVM1 and MMUVM is further clarified: PUVM1 is essentially a simplified form of the MMUVM, and the primary reason is found from mathematical principles, why it is that PUVM1 can only be applied to short-arc data within one circuit and not to long-arc or multi-circuit data. Finally, a preliminary theoretical analysis of the convergence of the iteration algorithm of PUVM1 is carried out and instancesof numerical verification given. It is pointed out that the iterative scheme of PUVM1 is conditionally convergent. This means that sometimes, even though the quasi-normalization equation is reasonable, the iteration diverges.

We present a method of unit vectors of calculating preliminary orbit with single-station and single-arc ranging data, assuming known orbital plane parameters i and Ω. Practical calculations show that this method is effective. This method is particularly valuable in cases where the angle data are either unavailable or obviously less accurate than the ranging data.

Sufficient and necessary conditions for the stability of the libration points in the perturbed circular restricted three-body problem are given. The conditions are in terms of the coefficients of the characteristic equations of the variational equations of the libration points, and can be used very conveniently. The effect of the perturbation of an arbitrary external force on the stability of the triangular libration points in the classical circular restricted three-body problem and the effect of the perturbation of the inertial drag on the stability of the principal libration points in the Robe circular restricted three-body problem are discussed by taking advantage of the obtained conditions.