弹道计算中正常重力的计算方法分析
|
摘要
针对弹道计算中正常重力的计算问题,分析了两种正常重力计算方法的特点,认为拉普拉斯方法的缺点是大地水准面形状确定困难而斯托克斯方法缺少地球表面外空间的正常重力算法.根据斯托克斯方法所定义的正常重力模型,将索米里安公式推广到地球表面的外空间,从而得到了一种正常重力的精确算法.通过计算对比这两种重力计算方法的差异,得出在使用拉普拉斯方法计算正常重力并取合适的球谐级数项时,可直接采用正常地球椭球面作为大地水准面,不会对弹道计算造成大的计算误差.
Aiming at the problem of normal gravity calculation,the character of two normal gravity calculation methods is analyzed.It is concluded that the disadvantage of Laplace method lies in how to determinate the shape of geoid surface and the disadvantage of Stokes method lies in how to calculate the normal gravity in the space outside the geoid surface.Base on the normal gravity model defined by Stokes method,the Somigliano normal gravity equation is extended to the space outside geoid surface and an accurate normal gravity calculation method is achieved.By comparison of these two method,the conclusion is drawn that the normal earth ellipsoidal surface may be adopted as geoid surface when the Laplace method is adopted and proper terms of spherical harmonics is adopted.The calculation result shows that the error on trajectory caused by this approximation is negligible.
Aiming at the problem of normal gravity calculation,the character of two normal gravity calculation methods is analyzed.It is concluded that the disadvantage of Laplace method lies in how to determinate the shape of geoid surface and the disadvantage of Stokes method lies in how to calculate the normal gravity in the space outside the geoid surface.Base on the normal gravity model defined by Stokes method,the Somigliano normal gravity equation is extended to the space outside geoid surface and an accurate normal gravity calculation method is achieved.By comparison of these two method,the conclusion is drawn that the normal earth ellipsoidal surface may be adopted as geoid surface when the Laplace method is adopted and proper terms of spherical harmonics is adopted.The calculation result shows that the error on trajectory caused by this approximation is negligible.
引文
[1]方俊.重力测量与地球形状学(下册)[M].北京:科学出版社,1975:145-153.
[2]管泽霖,宁津生.地球形状及外部重力场[M].北京:测绘出版社,1981:207-219.
[3]徐明友.高等外弹道学[M].北京:高等教育出版社,2003.10:41-43.
[4]张毅,杨辉耀,李俊莉.弹道导弹弹道学[M].北京:国防科技大学出版社,1999.3:8-12,58-61,304-310.
[5]王谦身.重力学[M].北京:地震出版社,2003:371-373.
[6]韩子鹏,薛晓中,张莺,译.外弹道学(俄)[M].北京:国防工业出版社,2000:26-27.
[2]管泽霖,宁津生.地球形状及外部重力场[M].北京:测绘出版社,1981:207-219.
[3]徐明友.高等外弹道学[M].北京:高等教育出版社,2003.10:41-43.
[4]张毅,杨辉耀,李俊莉.弹道导弹弹道学[M].北京:国防科技大学出版社,1999.3:8-12,58-61,304-310.
[5]王谦身.重力学[M].北京:地震出版社,2003:371-373.
[6]韩子鹏,薛晓中,张莺,译.外弹道学(俄)[M].北京:国防工业出版社,2000:26-27.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心