Quick solving algorithm for relative movement periodic orbit of low earth orbit satellite

Abstract

The invention discloses a quick solving algorithm for the relative movement periodic orbit of a low earth orbit satellite. The algorithm comprises the following steps that: establishing the relative movement model of the low earth orbit satellite; and through a time domain point collocation method, solving a nonlinear relative movement model. J2 perturbation, the nonlinear term of gravity potential and an eccentricity ratio influence are considered to obtain a derived kinetic model of satellite relative movement, the model is the accurate nonlinear relative movement model with a J2 term since no approximation is in the presence in the kinetic model, and therefore, on the basis, the relative movement periodic orbit of the low earth orbit satellite can be accurately searched; then, on the basis of the time domain point collocation method, the relative movement periodic orbit of the satellite is solved, so that the periodic orbit in the relative movement model can be searched by aiming at different orbit parameters, and the relative movement periodic orbit of the low earth orbit satellite can be quickly and accurately obtained.

Description

technical field [0001] The invention relates to the field of aerospace, in particular to a fast solution algorithm for the relative motion period orbit of near-earth satellites. Background technique [0002] In recent years, the relative motion of satellites in earth orbit has attracted more and more attention. For the relative motion of two satellites in orbit, scientists have established a variety of models and applied them to various space missions. The first developed and most famous mathematical model of relative motion is the Clohessy-Wiltshire (C-W) equation, which has high practical value in solving rendezvous problems. [0003] In many studies, people have devoted themselves to continuously expanding the C-W equation. However, when considering nonlinear differential gravity, J 2 The initial conditions used in these studies cannot be used when the effects of perturbations and large eccentricities are present. Moreover, some assumptions are used in the C-W equatio...

AI Technical Summary

Problems solved by technology

However, when considering nonlinear differential gravity, J 2 perturbation and large eccentricity, the initial conditions used in these studies cannot be used

Moreover, some assumptions are used in the C-W equation, which leads to errors in the model, and these errors cannot be ignored: the initial value conditions provided by the C-W equation are only satisfied when the circular reference orbit, the earth is spherical, and the linear gravitational acceleration is satisfied at the same time only valid if

Its scope of application is small, and if the scope is to be expanded, the calculation speed will be slow and the time will be long, which cannot meet the calculation of the periodic relative motion orbit that is very important for the maintenance of relative motion and the formation flight of spacecraft

[0004] At the same time, in the existing technology, most of the numerical integration problems of the equations in the C-W equation have adopted the fourth-order Runge-Kutta method (RK4). In order to avoid the inherent limitations of ordinary numerical integration, people have invented some New semi-analytical methods to solve nonlinear equations, such as the Harmonic Balance Method; but none of them can meet the requirements of accurate and fast solutions

Images