Collision risk investigation for an operational spacecraft caused by space debris

The collision probability between an operational spacecraft and a population of space debris is investigated. By dividing the 3-dimensional operational space of the spacecraft into several space volume cells (SVC) and proposing a boundary selection method to calculate the collision probability in each SVC, the distribution of the collision risk, as functions of the time, the orbital height, the declination, the impact elevation, the collision velocity, etc., can be obtained. Thus, the collision risk could be carefully evaluated over a time span for the general orbital configurations of the spacecraft and the space debris. As an application, the collision risk for the Tiangong-2 space laboratory caused by the cataloged space debris is discussed and evaluated. Results show that most of the collision threat comes from the front left and front right in Tiangong-2’s local, quasi-horizontal plane. And the collision probability will also accumulate when Tiangong-2 moves to the largest declinations (about ±42∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\pm} 42^{\circ}$\end{document}). As a result, the manned space activities should be avoided at those declinations.