在电子计算机上自动推导Flora群小行星的普遍摄动Ⅰ.Hansen方法应用  

COMPUTERIZED COMPUTATION OF GENERAL PERTURBATIONS FOR THE ASTEROIDS OF FLORA GROUP I. APPLICATION OF HANSEN METHOD

作　　者：何妙福[1] 张捷[1] 

机构地区：[1]中国科学院上海天文台

出　　处：《天文学报》1990年第1期27-38,共12页Acta Astronomica Sinica

摘　　要：在IBKM 4341电子计算机上应用Hansen方法和运行Broucke R.开发的Poisson级数展开程序系统，自动推导了木星对Flora群小行星的普遍摄动，将将计算得到的摄动系数表与前人应用Bohlin群法所得相应表作了比对。由此得到结论：1．取代Bohlin群法，用在电子计算机上建立的Hansen方法程序能够既快又精确地计算小行星的普遍摄动；2．对于1000″＜n＜1100″（n为小行星的周日平均运动，单位以弧秒／日表示）情形，如果小行星轨道的偏心率e和交角i不太大，Stroemberg表是适用的，最大误差不到20″；3．对于n-1047″情形，因此时n′/n－2／7，接近通约状态（n′为木星的周日平均运动），必须计及（2－7）长周期项，而de la Villemarque所给出的公式不够精确；4．对于975″＜n＜1000″情形，Stromberg表因其精度低而不适用，当e,i较大时尤甚；5．对于n-997″情形，因此时n′／n-3/10，即接近另一种通约状态，必须计及（3－10）长周期项。The general perturbations of the asteroids of Flora group (975″<n<1150″, n～the mean daily motion) due to Jupiter have been automatically computed on IBM 4341 Computer with Hansen method by manipulating Broucke's Symbolic Poisson Series Processor. The results have been compared to that computed with Bohlin group method before. The obtained conclusions are as follows: 1. Instead of Bohlin group method, the program for Hansen method coded on IBM4341 Computer is available to compute the general perturbations of the asteroids with much accuracy and efficiency. 2. In 1000″<n<1100″ case, when both eccentricity (e) and inclinat tion (i) of the asteroidal orbit are moderate, Strmberg table is suitable to be applied to compute the perturbative coefficients. Its maximum error would be less than 20′. 3. In n～1047″ case, n′/n～2/7 (n′-the mean daily motion of Jupiter), that is close to the commensurability, the long periodic term (2—7) should be taken into account. But the formula of de la Villemarque used to compute the coefficients of this term is less precise. 4. In 975′<n<1000′ case, Strmberg table is unsuitable to use, especially, when both e,i are larger. Therefore, de la Villemarque's view is incorrect. 5. In n～997′ case, n′/n～3/10, that is close to another commensurability, the long periodic term (3—10) should be taken into account.

关 键 词：小行星 轨道 普遍摄动 电子计算机 木星 摄动系数 

分 类 号：P133[天文地球—天体力学]