4. Conclusion

This section contains examples of the probabilistic risk analysis of collision of satellites with space debris.

It is shown how to predict the dangerous convergence between space objects and to justify preventive measures to reduce collision risk, solving tasks of modeling with random parameters.

The approach to constructing a probabilistic mathematical model of a complex system based on the principles of functional integration of the models of elements and subsystems in a single integrated software and implemented algorithms to perform the simulation processes for different input conditions and current state of the real system is given.

Modeling the motion of such satellites typically boils down to the obtainment of systems of ordinary differential equations of object motion and their integration by any method. The result is a dependence of the parameters of motion from time under given initial conditions. These equations are the form of representation of the laws of dynamics and kinematics, and can be supplemented with the equations of control.

Considering the catalogs of space objects (such catalogs exist in Russia and the United States), it is possible to estimate their relative position and to forecast their movement. In particular, it is possible to assess the threat of convergence and even the collision of spacecrafts.
