The project GP-C (Gravity Probe C) serves to investigate a possible new test of General Relativity which concerns the nature of space-time nearby rotating masses. For weak fields and small velocities, gravitational phenomena become similar to those known from, among them the precession of a gyroscope in the gravitomagnetic field of the rotating Earth as the analogue of the precession of a spinning dipole in a magnetic field. However, the gravitomagnetic field not only makes a test gyro to precess about the field lines but also affects the motion of a test body resulting in a difference in the proper period for co- and counter-revolving particles. According to General Relativity, two satellites moving along equatorial orbits about the Earth but in opposite directions show a difference in their periods of about 100 ns (so-called gravitomagnetic clock effect). A successful observation of this effect could therefore directly establish the existence of the terrestrial gravitomagnetic field and thus prove one of the fundamental predictions of General Relativity.
The main difficulties, which arise in connection with such an experiment are twofold:
(1) the exact measurement of the satellite trajectories,
(2) the consideration and modeling of all perturbations that affect the revolution time of the satellites.
The mere non-sphericity of the Earth involves a change in the period of about 15 s for a satellite of 7000 km altitude. Therefore, to determine gravitomagnetic control on the difference in the periods, the gravitational potential of the Earth must be accurately known, only then the relativistic effect may be separated from all other perturbations. Upon expansion of the terrestrial gravity field in terms of spherical harmonics (based on NASA's EGM-96 model), it is found that the uncertainty in the lower coefficients limits the calculation of the time of revolution of satellites orbiting in several thousand km altitude to an accuracy of 10-5-10-6 s. The figure shows the error δP in the modeled period as a function of the even zonal harmonics Cn0 for 3 different orbital radii.
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