  Here we explore a novel approach in order to try to measure the
post-Newtonian 1/c^2 Lense-Thirring secular effect induced by the
gravitomagnetic field of the Sun on the 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 Omega and the perihelia omega and are proportional to J/a^3, are of the
order of 10^-3 arcseconds 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 future missions to Mercury like Messenger and
BepiColombo could allow to increase it. 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 the
Mercury's node, it could happen that the new, more accurate ephemerides
available in future thanks to the Messenger and BepiColombo missions will offer
an opportunity to improve the present unfavorable situation.
