A set of parameters called relative orbital elements were defined to describe the relative motion of the satellites in the formation flying. With the help of these parameters, the effect of the perturbations on the re...A set of parameters called relative orbital elements were defined to describe the relative motion of the satellites in the formation flying. With the help of these parameters, the effect of the perturbations on the relative orbit trajectory and geometric properties of satellite formation can be easily analyzed. First, the relative orbital elements are derived, and pointed out： if the eccentricity of the leading satellite is a small value, the relative orbit trajectory is determined by the intersection between an elliptic cylinder and a plane in the leading satellite orbit frame reference; and the parameters that describe the elliptic cylinder and the plane can be used to obtain the relative orbit trajectory and the relative orbital elements. Second, by analyzing the effects of gravitational perturbations on the relative orbit using the relative orbital elements,it is found that the propagation of a relative orbit consists of two parts ： one is the drift of the elliptic cylinder; and the other is the rotation of the plane resulted from the rotation of the normal of the plane. Meanwhile, the analytic formulae for the drift and rotation rates of a relative trajectory under gravitational perturbations are presented. Finally, the relative orbit trajectory and the corresponding changes were analyzed with respect to the J2 perturbation.展开更多
The transcendental equation of a true anomaly was written in a power series instead of a differential form. When the sufficient condition of the iterative convergence is satisfied, the relationship between the true an...The transcendental equation of a true anomaly was written in a power series instead of a differential form. When the sufficient condition of the iterative convergence is satisfied, the relationship between the true anomaly and the time was gotten by the iterative method. And for the others, the transcendental equation of an eccentric anomaly was solved by the iterative method. After the eccentric anomaly had been calculated, the relationship between the true anomaly and the time was gotten with the numerical integral method. The approximate equation, which included the first five terms in general expansion, was written for the spacecraft quasi-circular orbit. And the true anomaly as the function of the time was also gotten by the iterative method. The numerical simulation results show that these methods are efficient.展开更多
文摘A set of parameters called relative orbital elements were defined to describe the relative motion of the satellites in the formation flying. With the help of these parameters, the effect of the perturbations on the relative orbit trajectory and geometric properties of satellite formation can be easily analyzed. First, the relative orbital elements are derived, and pointed out： if the eccentricity of the leading satellite is a small value, the relative orbit trajectory is determined by the intersection between an elliptic cylinder and a plane in the leading satellite orbit frame reference; and the parameters that describe the elliptic cylinder and the plane can be used to obtain the relative orbit trajectory and the relative orbital elements. Second, by analyzing the effects of gravitational perturbations on the relative orbit using the relative orbital elements,it is found that the propagation of a relative orbit consists of two parts ： one is the drift of the elliptic cylinder; and the other is the rotation of the plane resulted from the rotation of the normal of the plane. Meanwhile, the analytic formulae for the drift and rotation rates of a relative trajectory under gravitational perturbations are presented. Finally, the relative orbit trajectory and the corresponding changes were analyzed with respect to the J2 perturbation.
文摘The transcendental equation of a true anomaly was written in a power series instead of a differential form. When the sufficient condition of the iterative convergence is satisfied, the relationship between the true anomaly and the time was gotten by the iterative method. And for the others, the transcendental equation of an eccentric anomaly was solved by the iterative method. After the eccentric anomaly had been calculated, the relationship between the true anomaly and the time was gotten with the numerical integral method. The approximate equation, which included the first five terms in general expansion, was written for the spacecraft quasi-circular orbit. And the true anomaly as the function of the time was also gotten by the iterative method. The numerical simulation results show that these methods are efficient.
