Ballistic gravimeter

In order to outline the main features of measuring the gravitational field with the help of ballistic gravimeter imagine that a small body falls inside a vacuum cylinder under the action of the gravitational field only. In accordance with Newton s second law in the inertial frame we have... 

For instance, if we would like to measure a field with an accuracy of 1 mgal, that is, dg/g = 10 , it is necessary to know the period 1 s with an accuracy dT — 0.5 x 10 s. In this light, it is useful to obtain similar relation for the ballistic gravimeter. In accordance with the solution of the equation of motion we have... 

As was pointed out earlier, when we have considered the physical principles of the ballistic gravimeter and the pendulum an influence of the Coriolis force was ignored. Now we will try to take into account this factor and consider the motion of a particle near the earth s surface. With this purpose in mind let us choose a non-inertial frame of reference, shown in Fig. 3.5a its origin 0 is located near the earth s surface and it rotates together with the earth with angular velocity a>. The unit vectors i, j, and k of this system are fixed relative to the earth and directed as follows i is horizontal, that is, tangential to the earth s surface and points south, j is also horizontal and points east, k is vertical and points upward. As is shown in Fig. 3.5a SN is the earth s axis, drawn from south to north, I is the unit vector along OiO, and K is a unit vector parallel to SN. 

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