正常椭球重力平均值处纬度与偏心率的表达式

加速度计的精度是影响惯性导航精度的最直接的和最重要的因素,对正常重力平均值的选取是否合理将直接影响到加速度计的精度的高低。传统上还是直接以纬度45°处的正常重力值作为平均值,这是不科学、不合理的。在计算机代数系统中,将正常重力计算公式利用级数展开、牛顿迭代法,推导出纬度关于椭球第一偏心率的函数式,并在考虑推广到太阳系中各天体的基础上,推导出纬度随椭球第一偏心率变化而变化的函数关系式,得到部分天体数据验证,具有一定科学意义。

Expression of Latitude at the Average of the Normal Ellipsoidal Gravity and Eccentricity

The accuracy of accelerometer is the most direct and important factor that affects the accuracy of inertial navigation,however,the selection of normal gravity mean value will directly affect the accuracy of the accelerometer.Traditionally,normal gravity at latitude 45° has been used as the average value,which is unscientific and unreasonable.In computer algebra system,by using series expansion and Newton iteration method,the normal gravity calculation formula is deduced as a function of latitude about the first eccentricity of ellipsoid.,and on the basis of considering the extension to the celestial bodies in the solar system,the functional relationship of latitude with the first eccentricity of ellipsoid is derived,then obtains the partial celestial body data verification,has certain scientific significance.