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- Title
How accurate is the cancelation of the first even zonal harmonic of the geopotential in the present and future LAGEOS-based Lense-Thirring tests?
- Authors
Iorio, Lorenzo
- Abstract
The strategy followed so far in the performed or proposed tests of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with laser-ranged satellites of LAGEOS type relies upon the cancelation of the disturbing huge precessions induced by the first even zonal harmonic coefficient J of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential by means of suitably designed linear combinations of the nodes Ω of more than one spacecraft. Actually, such a removal does depend on the accuracy with which the coefficients of the combinations adopted can be realistically known. Uncertainties of the order of 2 cm in the semimajor axes a and 0.5 milliarcseconds in the inclinations I of LAGEOS and LAGEOS II, entering the expression of the coefficient c of the combination of their nodes used so far, yield an uncertainty δc = 1.30 × 10. It gives an imperfectly canceled J signal of 10.8 milliarcseconds per year corresponding to 23% of the Lense-Thirring signature. Uncertainties of the order of 10-30 microarcseconds in the inclinations yield δc = 7.9 × 10 which corresponds to an uncanceled J signature of 6.5 milliarcseconds per year, i.e. 14% of the Lense-Thirring signal. Concerning a future LAGEOS-LAGEOS II-LARES combination with coefficients k and k, the same uncertainties in a and the less accurate uncertainties in I as before yield δk = 1.1 × 10, δk = 2 × 10; they imply a residual J combined precession of 14.7 milliarcseconds per year corresponding to 29% of the Lense-Thirring trend. Uncertainties in the inclinations at ≈ 10 microarcseconds level give δk = 5 × 10, δk = 2 × 10; the uncanceled J effect is 7.9 milliarcseconds per year, i.e. 16% of the relativistic effect.
- Subjects
GRAVITY; NATURAL satellite orbits; EARTH (Planet); NEWTONIAN cosmology; ELECTROMAGNETISM
- Publication
General Relativity & Gravitation, 2011, Vol 43, Issue 6, p1697
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-011-1151-4