Abstract
We describe a space-borne experiment to detect the Lense-Thirring field produced by the proper rotation (mass-current) of the Earth. This gravitomagnetic field will generate an increasing signal in a gravity gradiometer orbiting the Earth in local inertial (gyroscope) orientation. For a polar orbit of 600 km altitude, the signal will grow with a (constant) rate of about 2 x 10−4 E per month (1E = 1 Eötvös = 10−9 sec −2). In view of instrumental accuracies achieved in the last years, this effect could, in principle, be detected at present by Paik's high-sensitive superconducting gravity gradiometer in combination with precise gyroscopes placed in a drag-free Earth's satellite. A preliminary error analysis for the experiment indicates that the effect could already be measured after ≈ 1 month with sufficient accuracy (relative error of ≈ 1%). To achieve this, precise gyroscopes would be necessary, which, however, were allowed to be less precise than the present Stanford gyroscopes by a factor of - 20. In addition, we present a method for isolating the gravitomagnetic signal from the dominant Newtonian background.
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References and Notes
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The exterior gravitational field of a slowly rotating spherical body can be described by the Kerr metric linearized in the angular momentum parameter α = JIM; see References 6–9, 14, and 19.
In the post-Schwarzschild approximation, deviations of the gravitational field from spherical symmetry — caused, e.g., by the proper rotation (cf. Ref. 16)) or the oblateness of the body — are considered to first order, whereas the mass of the central body is taken into account to all orders. To the appropriate order in 1/c (c velocity of light) this scheme reduces to the standard post-Newtonian approximation.
This (sidereal) frame refers to distant stars.
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Schiff precession is a gravitomagnetic effect, caused by' the proper rotation of a central mass and describes the dragging of local inertial frames (relative to the sidereal frame) in the post-Newtonian (weak-field) approximation; cf. Ref. 2.
Greek indices run from 0 to 3; Latin indices run from 1 to 3. Summation convention is used throughout.
In the post-Schwarzschild approximation, ΓLT is of the same form as Eq. (10), where A(T) is given by the expression (7); cf. References 7 and 8.
M.V. Moody, H.A. Chan, and H.J. Paik, J. Appl. Phys. 60, 4308 (1986); H.A. Chan and H.J. Paik, Phys. Rev. D 35, 3551 (1987); H.A. Chan, M.V. Moody, and H.J. Paik, Phys. Rev. D 35, 3572 (1987).
See, e.g., M.V. Moody and H.J. Paik, in Relativistic Gravitational Experiments in Space, proceedings of a workshop sponsored by the National Aeronautics and Space Administration, edited by R.W. Hellings (Scientific and Technical Information Division, NASA Conference Publication 3046, Washington, D.C., 1989), p. 211.
This signal subtraction method is similar to that described in Ref. 10; see also Ref. 13.
This Newtonian contribution is given by K N11 =ω2(1-3cos2ωτ), K N22 =ω2, K N33 =-(K N11 +K N22 ), K N13 =-3/2ω2sin2ωτ, K N12 =K N23 =0.
The components22 δΩi of the frequency vector describing the gyroscopes′ drift are given by the equations \(- [({{dDH^T } \mathord{\left/{\vphantom {{dDH^T } d}} \right.\kern-\nulldelimiterspace} d}\tau )D]_{ij} \equiv {{dI_{ij} } \mathord{\left/{\vphantom {{dI_{ij} } d}} \right.\kern-\nulldelimiterspace} d}\tau = \varepsilon _{ijk} \delta \Omega ^k ;\delta \Omega \equiv \sqrt {\delta \Omega _i \delta \Omega ^i }\).
See, e.g., C.W.F. Everitt, B.W. Parkinson, and J.P Turneau, in Relativistic Gravitational Experiments in Space, proceedings of a workshop sponsored by the National Aeronautics and Space Administration, edited by R.W. Hellings (Scientific and Technical Information Division, NASA Conference Publication 3046, Washington, D.C., 1989), p. 118.
There are, however, several errors that can be treated similarly as in Ref. 10 (sidereal orientation of gradiometer axes).
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Theiss, D.S. (1992). A gradiometer experiment to detect the gravitomagnetic field of the earth. In: Ehlers, J., Schäfer, G. (eds) Relativistic Gravity Research With Emphasis on Experiments and Observations. Lecture Notes in Physics, vol 410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56180-3_6
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