Geometric method for determining a safe orbit to prevent collisions with space debris

The method of searching for the orbit of a spacecraft to prevent a collision with space debris is considered. The work consists of two parts. The first part of the work addresses the problem of finding a safe orbit, geometrically closest to the original orbit, in order to avoid collisions with space debris objects. The initial orbit, orbits of space debris objects, and the minimum allowable distance from them are considered as given. The applied method of external penalty functions for solving the resulting optimization problem is described. The second part of the work consists in determining the relationship between the navigational uncertainty of the space debris object's orbit and its maximum deviation from the predicted position. The corresponding semi-analytical dependence is found for objects moving in sun-synchronous orbits and “Molniya” type orbits.