In this paper 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 the future hermean mission BepiColombo should 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 BepiColombo mission will offer an opportunity to improve the present unfavorable situation .