Prediction of the space debris spatial distribution on the basis of the evolution equations

•New evolution equations for predicting the statistical distribution of space debris over the perigee altitude are derived.•The algorithms for solution of evolution equations are developed.•The application of new equations makes it possible to decrease computer time expenses by several orders of magnitude.

The numerical–analytical technique for long-term prediction of the space debris (SD) spatial distribution, based on derivation and solution of new evolution equations, is developed. These equations are represented in two forms — difference and differential. In the latter case the problem is reduced to integration of the system of two ordinary differential equations. A high efficiency of the proposed technique, as compared to the traditional approach, is demonstrated.