An onboard measurement system of gravity gradients using inertial accelerometers

A method of making possible the onboard measurement of gravity gradients is proposed in this paper. First, analytical solutions of gravity gradients are derived as the second order spatial gradients of the gravitational potential in the conservative field. Next, it is shown that the gravity gradients can be obtained from the outputs of inertial accelerometers placed some distance away from each other, and a concept of measurement system is clarified. Third, it is analytically shown that a gravity gradiometer system can be continued using twelve single-degree-of-freedom accelerometers or six two-degree-of-freedom accelerometers or four three-degree-of freedom accelerometers. Finally, it is concluded that a new type of inertial navigation system using gravity gradiometers will be configured when it becomes possible to precisely measure gravity gradients.