Abstract: It is important to analyze the orbital evolution behavior of space debris cluster quickly and accurately for collision avoidance of spacecraft in orbit.Under the action of each perturbation force，the evolutionary movement of space debris cluster presents complex nonlinear characteristics.The space debris population has a large number of individuals.If the orbital integration of each space debris in the space debris population is used to analyze the population prediction，the amount of calculation will be too large.To solve this problem，a fast orbit prediction method based on polynomial approximation was proposed.This method divided space debris cluster into a small number of nominal fragments and a large number of other associated fragments.For orbit prediction of nominal debris，numerical integration was used to ensure the accuracy of prediction.For a large number of other associated debris orbit prediction problems，polynomial Taylor expansion semi-analytical method was used，so as to effectively reduce the calculation of space debris cluster orbit prediction on the precondition of ensuring the prediction accuracy.Orbit prediction simulations for different space debris cluster were carried out.The simulation results show that when the orbit prediction accuracy is set within 1 meter，the calculation efficiency of polynomial approximation algorithm is 2.2 to 17.2 times higher than that of Monte Carlo method，which verifies the effectiveness of the proposed method.

Key words: space debris cluster, orbital perturbation, orbit prediction, taylor expansion, polynomial approximation, nominal debris, associated debris