Precise definition of the effective measurement height of free-fall absolute gravimeters

For up-to-date absolute gravimeters, the trajectory of the test mass during a free-fall experiment (drop) is about 20 cm along the vertical, and the corresponding gravity change is about 60 × 10 −8 ms −2 . The reference height of the derived free-fall acceleration g has to be defined with an accuracy of 1 mm to 2 mm within the dropping distance to preserve the accuracy of the measurement system (e.g. FG5: 1 m s −2 to 2 × 10 −8 ms −2 ). The equation of motion comprises a vertical gravity gradient to take the height dependence of g into account. In general, a linear vertical gravity gradient γ is introduced that has been measured by relative gravimeters. In that case, the g-value refers to the origin of the coordinate system (z = 0), which is normally the starting position of the drop. In the case of an unknown or uncertain gradient we recommend an alternative approach. A simple parabolic equation (assumption γ = 0) can be used to evaluate the time/distance data pairs and later these g-determinations have to be corrected for the vertical gravity gradient using the effective measurement height. The solution presented is not restricted to low initial velocities alone. It considers time/distance measurements equally spaced in distance. Also, in extreme cases, unknown non-linearities within the vertical gravity gradient do not significantly affect the result of the absolute gravity determination.