New physics beyond the standard model of particles might cause a deviation from the inverse-square law of gravity. In some theories, it is parameterized by a power-law correction to the Newtonian gravitational force, which might originate from the simultaneous exchange of particles or modified and extended theories of gravity. Using the supplementary advances of the perihelia provided by INPOP 10a （IMCCE, France） and EPM2011 （IAA RAS, Russia） ephemerides, we obtain preliminary limits on this correction. In our estimation, we take the Lense-Thirring effect due to the Sun＇s angular momentum into account. The parameters of the power-law correction and the uncertainty of the Sun＇s quadrupole moment are simultaneously estimated with the method of minimizing X2. From INPOP10a, we find N - 0.605 for the exponent of the power-law correction. However, from EPM2011, we find that, although it yields N = 3.001, the estimated uncertainty in the Sun＇s quadrupole moment is much larger than the value given by current observations. This might be caused by the intrinsic nonlinearity in the power-law correction, which makes the estimation very sensitive to the supplementary advances of the perihelia.
We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express （MEX） spacecraft to test possible violations of local Lorentz invariance （LLI） and local position invariance （LPI）. These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China. These downlink signals were sent by MEX for telemetry at X-band. Because we are not able to decode the data in the form of teleme- try and separate them from the carrier frequency, this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s^-1. Even so, the residuals can still impose upper bounds on LLI and LPI at 10^-1, which is consistent with the prediction based on our analysis of the detectability. Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work, one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.
Ground-based and space-borne observatories used for studying exoplanet transits now and in the future will considerably increase the number of exoplanets known from transit data and the precision of the measured times of transit minima.Variations in the transit times can not only be used to infer the presence of additional planets,but might also provide opportunities to test the general theory of relativity in these systems.To build a framework for these possible tests,we extend previous studies on the observability of the general relativistic precessions of periastron in transiting exoplanets to variations in secular transit timing under parametrized post-Newtonian formalism.We find that if one can measure the difference between observed and predicted variations of general relativistic secular transit timing to 1 s yr-1in a transiting exoplanet system with a Sun-like mass,a period of;day and a relatively small eccentricity of;.1,general relativity will be tested to the level of;%.
