Prepared by: MORE Team MORE Relativity Meeting February 16-17, 2009 Rome Simulation of the solar conjunction experiment with BepiColombo

MORE Relativity Meeting, February , Rome Introduction being r 1 and r 2, respectively, the Sun-S/C and Sun-Earth distances, and b the impact parameter. A solar conjunction experiment in cruise is foreseen for April In principle, the accuracy of the measurement of the post-Newtonian parameter γ should be higher in cruise rather than in orbit, due to the absence of gravity gradient An electromagnetic wave passing near the Sun is affected by a relativistic delay, expressed as:

MORE Relativity Meeting, February , Rome Goals of the simulation Goals:  Simulating the solar conjunction experiment occurring in 2016; a best case will be presented (upper limit to the accuracy in the estimation of γ);  Comparing the results to what we can achieve doing the experiment in 2017;  Determining the effect of uncalibrated non-gravitational acceleration noise on the measurement. S/C SEP Geometry: b Sun Earth

MORE Relativity Meeting, February , Rome Relativistic delay variation Sun–Earth–Probe angle variation Relativistic delay variation

MORE Relativity Meeting, February , Rome Simulation setup Dynamic model:  Model for solar pressure: flat plate of 55 m 2 area, average thermo-optical coefficients, always pointing toward the Sun (in order to maintain a constant sun-aspect-angle)  Absence of orbital and attitude maneuvers Observables:  Observables: range, one measurement every 20 sec (the range rate does not give a significant contribution), for 20 days  Two DSN stations, providing a coverage of 15 hours per day  Observables under 8 solar radii have not been considered  Gaussian noise added (we have supposed to cancel the plasma noise, by using the multi-frequency link), with a standard deviation of 20 cm

MORE Relativity Meeting, February , Rome Estimation Estimation:  Estimation of the state vector of BepiColombo and γ  The starting value of γ has been set to that obtained with the Cassini mission γ = 1 + (2.1 ± 2.3)x10 -5 γ = 1 – (8.5 ± 8.7)x10 -6 Above the goal of the experiment!

MORE Relativity Meeting, February , Rome Estimation γ = 1 + (1.5 ± 2.6)x10 -6 Compatible with the goal of the experiment

MORE Relativity Meeting, February , Rome Conclusions In conclusion:  The geometry of the solar conjunction in 2016 seems not to meet the scientific objective of MORE. In particular, the accuracy is more than 3 times worse wrt what we would like to achieve;  On the contrary, the solar conjunction in 2017 could allow a very precise measurement.