Abstract
The inclination I of an Earth’s satellite in polar orbit undergoes a secular De Sitter precession of -,7.6 milliarcseconds per year for a suitable choice of the initial value of its non-circulating node Omega . The competing long-periodic harmonic rates of change of I due to the even and odd zonal harmonics of the geopotential vanish for either a circular or polar orbit, while no secular rates occur at all. This may open up, in principle, the possibility of measuring the geodesic precession in the weak-field limit with an accurately tracked satellite by improving the current bound of 9times 10^{-4} from Lunar Laser Ranging, which, on the other hand, may be even rather optimistic, by one order of magnitude, or, perhaps, even better. The most insidious competing effects are due to the solid and ocean components of the K_1 tide since their perturbations have nominal huge amplitudes and the same temporal pattern of the De Sitter signature. They vanish for polar orbits. Departures of simeq {10^{-5}}^circ mathrm{to} {10^{-3}}^circ from the ideal polar geometry allow to keep the K_1 tidal perturbations to a sufficiently small level. Most of the other gravitational and non-gravitational perturbations vanish for the proposed orbital configuration, while the non-vanishing ones either have different temporal signatures with respect to the De Sitter effect or can be modeled with sufficient accuracy. In order to meet the proposed goal, the measurement accuracy of I should be better than simeq 35~text {microarcseconds}=0.034~text {milliarcseconds} over, say, 5 year.
Highlights
According to general relativity1 [32], when a spinning gyroscope follows a geodesic trajectory in the spacetime describ-The geodetic precession plays a role in the binary systems hosting at least one emitting radiopulsar
The competing long-periodic harmonic rates of change of I due to the even and odd zonal harmonics of the geopotential vanish for either a circular or polar orbit, while no secular rates occur at all. This may open up, in principle, the possibility of measuring the geodesic precession in the weak-field limit with an accurately tracked satellite by improving the current bound of 9 × 10−4 from Lunar Laser Ranging, which, on the other hand, may be even rather optimistic, by one order of magnitude, or, perhaps, even better
While Gravity Probe B (GP-B) reached a relative accuracy of 3 × 10−3 [22,23], the lunar laser ranging (LLR) technique [18] recently allowed to obtain a measurement of such a relativistic effect accurate to about 9 × 10−4 [27]
Summary
According to general relativity1 [32], when a spinning gyroscope follows a geodesic trajectory in the spacetime describ-. The geodetic precession was revealed in other binary pulsars such as PSR B1534+12 [38], PSR J1141-6545 [28] and PSR J1906+0746 [45], with a modest accuracy; see Kramer [40] for a recent overview. The most recent and accurate measurement was performed by Breton et al [7] with the double pulsar PSR J0737-3039A/B [9,49]; the accuracy level reached is of the order of 13%. While GP-B reached a relative accuracy of 3 × 10−3 [22,23], the lunar laser ranging (LLR) technique [18] recently allowed to obtain a measurement of such a relativistic effect accurate to about 9 × 10−4 [27].
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