A Method to Determine Vertical Gravity Gradient by High-precision 3D Tracking Parabolic Motion

Objectives:  The vertical gravity gradient plays an important role in the exploration of the Earth's gravity field. It is more and more widely used in the fields of geodesy, geophysics and geodynamics. Therefore, it is urgent to obtain the vertical gravity gradient with high accuracy quickly and accurately.   Method:  A new method to determine vertical gravity gradients by 3D tracking parabolic motion is proposed. In a vacuum environment, firstly, the 3D tracking technology is used to dynamically track the parabolic falling target to obtain the 3D coordinate time series of the target movement, establish the trajectory observation equation, and extract the gravity vertical gradient using the least square method.   Result:  When the measurement accuracy of falling target reaches micron level, the main error sources of this measurement method are 3D tracking measurement error and time measurement error, of which the time measurement error has a small impact on the measurement accuracy of vertical gravity gradient. After adding the 3D tracking measurement random error with the STD is 10μm and the time measurement random error with the STD is 10ns to the parabolic motion coordinate time series, the RMS of the measurement error of vertical gravity gradient is about 1.31E.   Conclusion:  The proposed method of vertical gravity gradient measurement is effective and has good stability.