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An effective way to solving this problem is the implementation of the prediction of dangerous convergences in several stages. Each stage is the check of the possibility of dangerous conver-

There are three stages of checking the possibilities of dangerous convergence implemented for a given pair of orbital objects. In the first stage, the overlapping region of heights above the Earth's surface, where their trajectories pass is checked. The second stage is based on the fact that the conflict between orbital objects is possible only when their trajectories intersect. It is assumed that the orbital object cannot deviate from the position on the calculated trajectory more than a certain distance. Hence, in each moment of time, the orbital object may be within a sphere, which has the center of the calculated trajectory, and radius is Rcr. A pair of sections of trajectories will be called a node of the mechanical conflicts, if that trajectories are located on the distance L<Lcr from each other. If for a pair of trajectories of orbital objects there is defined a node of conflict, then the condition of the second stage is fulfilled. The third stage is based on the fact that the conflict convergence is possible during simultaneous motion of orbital objects on segments of trajectories, which form a node of conflict. In the third stage, the time intervals of orbital objects' motion through the node of conflicts are defined. If these time intervals overlap each other, then

Assume [11] that the set of the cataloged orbital objects is considered as a multi-element mechanical system. There are some quasiregular components in the movement of the elements of this system. Meanwhile, the interactions of the elements of the system are not taken into account. Such restrictions allow the allocation of the node of conflict at the current time, which is formed by the dangerous parts of the trajectories of orbital objects k and l. This node of conflict restricts the dangerous part of the trajectory of each of these orbital objects. Considering the regularity of the motion parameters of the objects allows to simulate space debris as a

Probabilistic modeling is an important method of risk analysis and justification of preventive

Methods of calculating ballistic trajectories and assessment of collision risks with space debris are based on conversion of inaccurate source data, results of which are random variables.

Preventive measures for controlled spacecraft are reduced to change of trajectory, which could

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

gence based on some rule or the simplified method of prediction.

208 Probabilistic Modeling in System Engineering

dangerous convergence is possible, and its probability can be calculated.

Therefore, the risk of collision can be specified as a probability measure.

combination of deterministic and probabilistic models.

measures for space systems and technologies.

3. Summary

prevent or reduce this risk.

4. Conclusion

space debris.

Nikolay Paramonov

Address all correspondence to: paramonov\_n\_b@mail.ru

Moscow Technological University Mirea, Russia
