Is it possible to measure the Lense-Thirring effect on the orbits of the planets in the gravitational field of the Sun?

In this paper we explore a novel approach to try to measure the post-Newtonian 1/c(2) Lense-Thirring secular effect induced by the gravitomagnetic field of the Sun on planetary orbital motion. Due to the relative smallness of the solar angular momentum J and the large values of the planetary semimajor axes a, the gravitomagnetic precessions, which affect the nodes. and the perihelia. and are proportional to J/a(3), are of the order of 10(-3) arcsec per century only for, e.g., Mercury. This value lies just at the edge of the present-day observational sensitivity in reconstructing the planetary orbits, although the future mission BepiColombo should allow it to be increased. The major problems come from the main sources of systematic errors. They are the aliasing classical precessions induced by the multipolar expansion of the Sun's gravitational potential and the classical secular N-body precessions which are of the same order of magnitude or much larger than the Lense-Thirring precessions of interest. This definitely rules out the possibility of analyzing only one orbital element of, e.g., Mercury. In order to circumvent these problems, we propose a suitable linear combination of the orbital residuals of the nodes of Mercury, Venus and Mars which is, by construction, independent of such classical secular precessions. A 1-sigma reasonable estimate of the obtainable accuracy yields a 36% error. Since the major role in the proposed combination is played by Mercury's node, it could happen that new, more accurate ephemerides available in the future thanks to the BepiColombo mission will offer an opportunity to improve the present unfavorable situation.