LARES/WEBER-SAT and the equivalence principle

The LAGEOS III/LARES/WEBER-SAT mission. -In 1976 Van Patten and Everitt [1,2] suggested measuring the general relativistic Lense-Thirring node precession [3] with a pair of counter-orbiting spacecraft to be placed in terrestrial polar orbits and endowed with active, drag-free apparatus to counter-act the non-gravitational perturbations. In 1977-1978 Cugusi and Proverbio [4,5] proposed using the existing passive geodetic satellite LAGEOS and, more generally, the Satellite Laser Ranging (SLR) technique to measure the Lense-Thirring effect in the terrestrial gravitational field with the existing artificial satellites. In 1986 Ciufolini [6] put forth a strategy somewhat equivalent to the ones by Van Patten and Everitt and Cugusi and Proverbio involving the launch of a passive, LAGEOSlike satellite-named LAGEOS III after the launch of LAGEOS II-in an orbit identical to that of LAGEOS (semimajor axis a = 12, 270 km, inclination of the orbital plane to the Earth's equator i = 110 deg, eccentricity e = 0.0045), apart from the inclination which should have been equal to i = 70 deg. The observable originally proposed was the sum of the nodes of LAGEOS and LAGEOS III: the particular orbital configuration of the new spacecraft was chosen to cancel out the aliasing impact of the even zonal harmonic coefficients J ℓ , ℓ = 2, 4, ... of the multipolar expansion of the Newtonian part of the Earth's gravitational potential which induce node precessions qualitatively identical to the relativistic ones but much larger. Although extensively studied by various groups [7,8], such an idea has not yet been implemented. In 1998, after its originally proposed eccentricity was augmented by almost one order of magnitude in order to use the perigee as well [9], renamed LAser RElativity Satellite (LARES), it was rejected by the Agenzia Spaziale Italiana (ASI, Italian Space Agency). With the name of WEBER-SAT1 , it is currently under examination by the Istituto Nazionale di Fisica Nucleare2 (INFN, National Institute of Nuclear Physics).

In addition to the original, by far principal, purpose of measuring the Lense-Thirring effect at some percent level, many other goals of fundamental physics have been recently added to the LARES mission in order to enhance its chances of being finally approved. In doing so it has gone too far by often making unrealistic claims. A typical example of such a policy is represented by the alleged possibility [10] of measuring the perigee precession [11] induced by the multi-dimensional braneworld model by Dvali, Gabadadze and Porrati (DGP) [12]. Amounting to 4 × 10 -3 milliarcseconds per year (mas yr -1 ), it has been proven to be undetectable in [13]. In such a work motivations mainly concerning the gravitational systematic errors were considered: here we will yield further, simple arguments related to the non-gravitational perturbations which the perigees of LAGEOS-like satellites are particularly sensitive to. In [14] it has been reported that the INFN team should be able to reduce the impact of the non-gravitational perturbations of thermal origin down to ≈ 10 -3 of the Lense-Thirring effect on LARES. Although not explicitly stated in [14], let us assume that this will be true for the perigee as well, which is certainly not an easy task to be implemented: the Lense-Thirring perigee precession for the originally proposed LARES orbital configuration amounts to about 30 mas yr -1 , so that a mismodelled precession of ≈ 10 -2 mas yr -1 of non-gravitational origin would be left, i.e. a bias just one order of magnitude larger than the DGP effect itself.

The equivalence principle. -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.” More precisely, in [15] it is explicitly written: “LARES would improve, by about two orders of magnitude, the accuracy in testing the equivalence principle […]”. Now, since the present-day level of accuracy in testing it is 10 -13 [20], it must be argued that Ciufolini is claiming in [15] that a level of 10 -15 is to be expected from the successful implementation of the LARES mission. Unfortunately, the authors of such claims nowhere explicitly explain how they would achieve such notable goals.

By contrast, the situation is quite different, and by many orders of magnitude. The possibility of testing the equivalence principle with artificial Earth satellites of different compositions was tackled in [21][22][23]. In [22] just the originally proposed configuration of LARES (a = 12, 270 km, i = 70 deg) was examined: the existing LAGEOS satellite would be used in conjunction with LARES/WEBER-SA

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