地球重力场、重力、重力梯度在三维直角坐标系中的表达式

Expressions of Earth Gravity Field, Gravity and Gravity Gradient in 3D Cartesian Coordinates System

现代卫星重力测量主要利用星载GPS接收机、加速度计、星载测距仪等来确定重力卫星的轨道 ,削弱非保守力的干扰 ,由此根据卫星的位置、速度及其变率来确定地球重力场。而上述GPS等星载仪器所提供的数据 ,包括卫星轨道坐标及其速率、扰动加速度、星间距离及其变率 ,都是以三维直角坐标 (x ,y ,z)的形式表示的 ,因此 ,地球重力场。

In modern gravity satellite campaigns satellite-based GPS receiver, accelerator, K-band rangefinder etc. are used to measure the orbit of the gravity satellite. From these data earth gravity field can be derived. However, all the information provided by GPS and mentioned satellite-based instruments are in the format of 3D cartesian coordinates. So it is meaningful to derive the expressions of earth gravity field, gravity and gravity gradient in 3D cartesian coordinates system in the determination of earth gravity from the information given by gravity satellites.