research is focussed on different methods of detecting the position and movements of these small masses. In Atom gravimeters, the mass is a collection of atoms. For a given restoring force, the central frequency of the instrument is often given by (in radians per second) The term for the "force constant" changes if the restoring force is electrostatic, magnetostatic, electromagnetic, optical, microwave, acoustic, or any of dozens of different ways to keep the mass stationary. The "force constant" is just the coefficient of the displacement term in the equation of motion: m mass, a acceleration, b viscosity, v velocity, k force constant, x displacement F external force as a function of location/position and time. F is the force being measured, and is the acceleration. + higher derivatives of the restoring force Precise GPS stations can be operated as gravimeters since they are increasingly measuring three axis positions over time, which, when differentiated twice, give an acceleration signal. The satellite borne gravimeters GOCE, GRACE, are mostly operating in gravity gradiometer mode. They yield detailed information about the earth's time varying gravity field The spherical harmonic gravitational potential models are slowly improving in both spatial and temporal resolution. Taking the gradient of the potentials gives estimate of local acceleration which are what is measured by the gravimeter arrays. The superconducting gravimeter network has been used to ground truth the satellite potentials. This should eventually improve both the satellite and earth-based methods and intercomparisons. Transportable relative gravimeters also exist; they employ an extremely stable inertial platform to compensate for the masking effects of motion and vibration, a difficult engineering feat. The first transportable relative gravimeters were, reportedly, a secret military technology developed in the 1950–1960s as a navigational aid for nuclear submarines. Subsequently in the 1980s, transportable relative gravimeters were reverse engineered by the civilian sector for use on ship, then in air and finally satellite borne gravity surveys. Microgravimetry Microgravimetry is an important branch developed on the foundation of classical gravimetry. Microgravity investigations are carried out in order to solve various problems of engineering geology, mainly location of voids and their monitoring. Very detailed measurements of high accuracy can indicate voids of any origin, provided the size and depth are large enough to produce gravity effect stronger than is the level of confidence of relevant gravity signal. History The modern gravimeter was developed by Lucien LaCoste and Arnold Romberg in 1936. They