A method and system for order expansion of spherical crown harmonic model of earth disturbance gravitational field

Abstract

The invention discloses a method and system for extending orders of spherical cap harmonic models of earth disturbance gravity fields. The method comprises the following steps of: in an aircraft launching process, determining a spherical cap radius by taking a launching first area as a to-be-approached spherical cap area; determining a spherical cap boundary condition according to the spherical cap radius; and according to the spherical cap boundary condition, circularly calculating a zero root value of an associated Legendre function, and when a distance between zero root values obtained viatwo adjacent calculations is smaller than a preset limiting value, ending the calculation, namely, realizing the extension of an order of a spherical cap harmonic model of an earth disturbance gravityfield. According to the method and system, orders of spherical cap harmonic models are extended to a certain extent, assignment precision of along-track disturbance gravity of spacecraft is improved,and benefit is brought to accurate navigation.

Description

technical field [0001] The invention provides a method and system for expanding the order of the spherical crown harmonic model of the earth's disturbance gravitational field, which can improve the assignment accuracy of the orbital disturbance gravitational force of the spacecraft, and is mainly used in the fast maneuvering launch and high-precision orbiting of the aircraft. Background technique [0002] The aircraft flies in the outer space of the earth and is affected by the gravitational force of the earth. If the gravitational force of any point in the outer space of the earth is known, including the magnitude and direction, the force model of the entire operation stage of the aircraft can be refined to improve its guidance accuracy. In order to simply describe the gravitational force outside the earth, a rotating plastid with a regular shape is artificially selected as an approximation of the actual earth, and the gravitational force outside the plastid is as close as ...

AI Technical Summary

Problems solved by technology

This method is widely used in the calculation of aircraft orbital motion, but this method also has the following problems: (1) The spherical harmonic function reflects more of the low-frequency part of the earth's gravitational field, which is suitable for global gravitational field assignment, but not suitable for local Low-altitude gravitational field assignment

For long-range aircraft, the calculation of the active segment is not applicable

(2) Due to the need for recursive calculations, the amount of calculation is large when the order is high, which cannot meet the requirements of fast assignment

[0006] The theory of spherical crown harmonics needs to reverse the order of the non-integral Legendre function according to the boundary conditions, and the amount of calculation is very heavy. At the same time, due to the characteristics of the association Legendre function, when the order reaches a certain value, the function has divergence properties, using conventional methods, the zero root value that can be calculated is limited

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