First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data

The general relativistic Lense–Thirring (LT) precessions of the perihelia of the inner planets of the Solar System amount to ≲ 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 ± 0.0050 , - 0.0002 ± 0.0004 and 0.0001 ± 0.0005 arcseconds per century ( ″ cy - 1 ) were recently estimated by E.V. Pitjeva for Mercury, the Earth and Mars, respectively, on the basis of on the EPM2004 ephemerides and a set of more than 317,000 observations of various kinds. The predicted relativistic LT precessions for these planets are - 0.0020 , - 0.0001 and - 3 × 10 - 5 ″ cy - 1 , respectively, and are compatible with the determined perihelia corrections. The relativistic prediction fits 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 overall 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 LT 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 LT 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 ).