A rapid compensation method for launch data of long-range rockets under influence of the Earth's disturbing gravity field

Abstract

Regarding the rapid compensation of the influence of the Earth’ s disturbing gravity field upon trajectory calculation, the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data. In view of this, this paper mainly expounds on two issues: one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket, deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the final-stage pitch program; the other is based on the initial positioning and orientation error propagation mechanism, proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth. The calculation results of correction data are simulated and verified under different circumstances. The simulation results are as follows: (1) the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%, and the ratio of calculation time between them is lower than 0.2%, thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed; (2) after the analytical solutions are compensated, the longitudinal landing deviation of the rocket is less than 20m and the lateral landing deviation of the rocket is less than 10m, demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.