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The spherical harmonic, even zonal, of degree 4 and order 0. 

The spherical harmonic, even zonal, of degree 4 and order 0. 

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Not Available I. Ciufolini, A. Paolozzi, E. Pavlis, R. Koenig, J. Ries, R. Matzner, R. Neubert, D. Rubincam, D. Arnold, V. Slabinski, G. Sindoni, C. Paris, M. Ramiconi, D. Spano, C. Vendittozzi, H. Neumayer.

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... 2004 and 2010, using the LAGEOS satellites and a number of 2004-2008 GRACE models, we obtained a test of the frame-dragging with an accuracy of about 10% ( Ciufolini et al. 2004, Ries et al 2008, Ciufolini et al. 2009, 2010, 2011). However, for a measurement of frame-dragging with an accuracy of the order of 1%, it is necessary to eliminate the uncertainty in the Earth's spherical harmonic of degree 4 and order 0 ( Figure 3) and, thus, it is necessary to use one additional observable that will be provided by the node of the LARES satellite (described in the next section). Our 2004-2008tests (Ciufolini et al. 2004, 2006) were obtained by analys- ing the laser-ranging data and the orbits of the LAGEOS satellites using the orbital analysis and data reduction software suites GEODYN II (NASA) and EPOS-OC (GFZ-DLR). ...

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... -Another example is the equivalence principle. Indeed, in several works [15][16][17][18][19] it has been recently claimed that LARES/WEBER-SAT would be able to greatly improve the accuracy level in testing such a cornerstone of general relativity and of all other competing metric theories of gravity. E.g., in [17] we find: "An additional physics goal of LARES is the improvement of the limits on the violation of the Einstein Equivalence Principle." ...
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It has often been claimed that the proposed Earth artificial satellite LARES/WEBER-SAT —whose primary goal is, in fact, the measurement of the general relativistic Lense-Thirring effect at a some percent level— would allow greatly improving, among (many) other things, the present-day (10−13) level of accuracy in testing the equivalence principle as well. Recent claims point towards even two orders of magnitude better, i.e. 10−15. In this letter we show that such a goal is, in fact, unattainable by many orders of magnitude being, instead, the achievable level ≈10−9.
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The satellites LAGEOS-I and LAGEOS-II are essential for the scientific study of various (geo)physical phenomena, such as geocenter motion and absolute scale. The high quality of such science products strongly depends on the absolute quality of the SLR observations and that of the orbit description. Therefore all accelerations experienced by the spacecraft need to be modeled as accurately as possible, the thermal radiation forces being one of them. Traditionally, this is done by estimating so-called empirical accelerations. However, the rotational dynamics of LAGEOS-I in particular no longer allows such a simple approach: a full modeling of the spin behavior, the temperature distribution over the spacecraft surface and the resulting net force prove necessary to achieve the best results. As a first step, a new model, Lageos Spin Axis Model (LOSSAM) has been developed. It is unique in its combination of analytical theory and empirical observations. Its mathematics is taken after previous investigators, although flaws have been corrected. LOSSAM describes the full spin behavior of LOSSAM based on the following phenomena: (1) the geomagnetic field, (2) the Earth's gravity field, (3) the satellite center of pressure offset, and (4) the effective difference in reflectivity between the satellite hemispheres. Its accuracy has been demonstrated by an improvement of about a 50% in the RMS residual of the Yarkovsky-Schach effect signal (as shown by Lucchesi et al. [2004]). Such a high-quality model for rotational behavior is indispensable for a proper force modeling, and hence also for the quality of typical LAGEOS science products.