Aorde
4.2 The concept
The idea can now be transformed into a concept as shown in figure 6. In a low
orbiting satellite at, approximately 250 km altitude, test masses are tied by springs
to their equilibrium position, the center of mass, on three perpendicular axes, but
each mass is otherwise free to move along its spring axis. At the positions of the test
masses, the compensation of gravitational force and centrifugal force is not
complete, resulting in small tidal accelerations that move the test masses away
from their equilibrium positions. These displacements are a measure of the
gravitational acceleration at the location of the proof mass; the acceleration
difference, divided by the distance between the proof masses is a first order
approximation of the gravity gradient in the direction of the axes. In practice, residual
non-inertial accelerations of the frame are unavoidable (e.g. due to atmospheric
drag); they are eliminated when forming the difference of the displacements of
pairs of masses on one axis. The sum of the displacements then measures these
non-inertial accelerations, and that information may be used to restitute the orbit
via thrusters, i.e., to compensate for non-inertial accelerations. Rotation of the
frame, i.e., angular velocities and angular accelerations, also affect the difference
of the displacements. We may, however, correct for frame rotation if acceleration
differences are taken in all possible spatial combinations (full tensor gradiometer).
The displacements are very small, typically about 10"7 m.
They have to be determined to circa 7 significant digits to meet the mission goals,
approximately once every second (in that time the satellite moves about 8 km), so
we are talking about length scales of the order of 1 0 14 m. That is truly remarkable
when one recalls that the radius of an atomic nucleus is only one order of magnitude
smaller.
Figure 6: GOCE concept
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