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不規(guī)則形狀小行星引力環(huán)境建模及 球諧系數(shù)求取方法

Modeling for the gravitation potential environment of an irregular-shaped asteroid and the spherical harmonic coefficient estimation

  • 摘要: 在實(shí)施小行星探測(cè)任務(wù)之前,需要對(duì)不規(guī)則形狀小行星的引力場(chǎng)有一個(gè)清楚的認(rèn)識(shí),以便于進(jìn)行環(huán)繞或著陸小行星的軌道設(shè)計(jì)。文章提出了一種小行星引力場(chǎng)建模及球諧系數(shù)的求取方法。首先,由多面體模型方法重構(gòu)出小行星外部的引力環(huán)境并以此作為虛擬觀測(cè)量。在此基礎(chǔ)上,根據(jù)球諧系數(shù)與引力勢(shì)能間的關(guān)系,通過(guò)求解超定線性方程組得到小行星引力場(chǎng)的各階次球諧系數(shù)。與傳統(tǒng)的將小行星近似成三軸橢球體進(jìn)而計(jì)算球諧系數(shù)的方法相比,該方法可大幅度提高引力場(chǎng)建模的精度。通過(guò)與由NEAR探測(cè)器軌道數(shù)據(jù)解算的Eros433小行星的球諧系數(shù)比較表明,其最大誤差不超過(guò)6%。計(jì)算表明,該方法可以為小行星探測(cè)任務(wù)發(fā)射前的軌道設(shè)計(jì)提供更為精確的數(shù)據(jù)。

     

    Abstract: The pre-mission certification of the irregular- shaped asteroid gravitation is essential for the orbit design (in orbiting phase or landing phase). This paper proposes a novel algorithm for the irregular-shaped asteroid spherical harmonic coefficient estimation, where the gravitation potential of the asteroid is reconstructed using the polyhedral model method and is taken as the virtual measurements. Then a formula for the relationship between the spherical harmonic coefficients and the gravitation is suggested. Finally the spherical harmonic coefficients of the asteroid gravity are computed by solving the over-determined equations based on the least squares method (LSM). Compared with the traditional method which approximates the asteroid as a tri-axial ellipsoid, the algorithm proposed in this paper could obviously improve the asteroid gravitation modeling resolution. When compared with the spherical harmonic coefficients of Eros 433 derived from NEAR probe orbit data, the relative error is less than 6%. The result indicates that it is more accurate and will offer more information for pre-mission orbit design.

     

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