The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are \lesssim 10 ^ { -3 } arcseconds per century . Recent improvements in planetary orbit determination may yield the first observational evidence of such a tiny effect . Indeed , corrections to the known perihelion rates of -0.0036 \pm 0.0050 , -0.0002 \pm 0.0004 and 0.0001 \pm 0.0005 arcseconds per century were recently estimated by E.V . Pitjeva for Mercury , the Earth and Mars , respectively , on the basis of the EPM2004 ephemerides and a set of more than 317,000 observations of various kinds . The predicted relativistic Lense-Thirring precessions for these planets are -0.0020 , -0.0001 and -3 \times 10 ^ { -5 } arcseconds per century , respectively and are compatible with the determined perihelia corrections . The relativistic predictions fit better than the zero-effect hypothesis , especially if a suitable linear combination of the perihelia of Mercury and the Earth , which a priori cancels out any possible bias due to the solar quadrupole mass moment , is considered . However , the experimental errors are still large . Also the latest data for Mercury processed independently by Fienga et al . with the INPOP ephemerides yield preliminary insights about the existence of the solar Lense-Thirring effect . The data from the forthcoming planetary mission BepiColombo will improve our knowledge of the orbital motion of this planet and , consequently , the precision of the measurement of the Lense-Thirring effect . As a by-product of the present analysis , it is also possible to constrain the strength of a Yukawa-like fifth force to a 10 ^ { -12 } -10 ^ { -13 } level at scales of about one Astronomical Unit ( 10 ^ { 11 } m ) .