Prospects on measuring intrinsic gravitomagnetism with Lunar Laser Ranging.pdf

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2017-04-06 发布于江苏
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Prospects on measuring intrinsic gravitomagnetism with Lunar Laser Ranging.pdf

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Prospects on measuring intrinsic gravitomagnetism with Lunar Laser Ranging

a r X i v : 0 8 0 9 .4 0 1 4 v 3 [ g r - q c ] 2 8 S e p 2 0 0 8 Prospects on measuring intrinsic gravitomagnetism with Lunar Laser Ranging Lorenzo Iorio INFN-Sezione di Pisa. Permanent address for correspondence: Viale Unita? di Italia 68, 70125, Bari (BA), Italy. E-mail: lorenzo.iorio@libero.it Received ; accepted – 2 – ABSTRACT In this note we explore the possibility of measuring the action of the intrinsic gravitomagnetic field of the rotating Earth on the orbital motion of the Moon with the Lunar Laser Ranging (LLR) technique. Expected improvements in it should push the precision in measuring the Earth-Moon range to the mm level; the present-day Root-Mean-Square (RMS) accuracy in reconstructing the radial component of the lunar orbit is about 2 cm; its harmonic terms can be determined at the mm level. The current uncertainty in measuring the lunar precession rates is about 10?1 milliarcseconds per year. The Lense-Thirring secular, i.e. averaged over one orbital period, precessions of the node and the perigee of the Moon induced by the Earth’s spin angular momentum amount to 10?3 milliarcseconds per year yielding transverse and normal shifts of 10?1 ? 10?2 cm yr?1. In the radial direction there is only a short-period, i.e. non-averaged over one orbital revolution, oscillation with an amplitude of 10?5 m. Major limitations come also from some systematic errors induced by orbital perturbations of classical origin like, e.g., the secular precessions induced by the Sun and the oblateness of the Moon whose mismodelled parts are several times larger than the Lense-Thirring signal. Subject headings: Experimental studies of gravity, Moon – 3 – 1. Introduction In the framework of the linearized weak-field and slow-motion approximation of general relativity, the gravitomagnetic effects (Ruggiero and Tartaglia 2002; Scha?fer 2004) are induced by the off-diagonal components g0i, i = 1, 2, 3 of the space-time metric tensor (Mashhoon 2001, 2007) which are proportional