Testing the gravitational redshift by time transfer with Moonlight constellation

The recent boost toward lunar exploration and the ensuing increase in the number of missions to the Moon makes the development of a Lunar Radio Navigation System (LRNS) highly desirable. To this aim, ESA conceived the Moonlight project: a constellation of small satellites in highly eccentric orbits around the Moon, composed of four satellites in Elliptic Lunar Frozen Orbits (ELFOs) with a good coverage of the southern hemisphere. Eccentricities are about 0.63, periselenium altitudes about 1800 km, while the orbital periods are 24 hours. Thanks to radio tracking at X or K band from Earth stations, the Moonlight constellation will provide a communication and navigation service for users on the lunar surface and cis-lunar space 1. These orbits and radio configuration may be favorable for improved tests of the foundations of general relativity. The Local Lorentz and Local Position invariances (LLI, LPI), together with the Universality of Free Fall (UFF), constitute the Einstein Equivalence Principle (EEP). The validity of the EEP is one of the cornerstones of the General Relativity (GR). LLI and LPI are usually tested by comparing the GR predictions with the measured gravitational redshift of clocks onboard Earth satellites or interplanetary spacecraft (Galileo mission, 2). To date, the LPI has been verified up to a 10-5 level by the analysis of Doppler data provided by GSAT0201 and GSAT0202 satellites of the GALILEO constellation 3. Our aim is to investigate, by means of detailed simulations, if the one-way Doppler link between the clocks onboard the Moonlight satellites and the Earth stations can be used to improve the current knowledge about the Local Lorentz and Local Position invariances. We simulate the experiment by assuming different scenarios, such as 1) type of onboard clocks (e.g. miniRAFS or DSAC-2), 2) orbital geometry and 3) mission duration. 1 L. Iess et al. (2023)Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado,September 2023, pp. 4029-4050. https://doi.org/10.33012/2023.19428 2 Krisher, T. (1993) The Galileo Solar Redshift Experiment. PRL 70, 15.https://doi.org/10.1103/PhysRevLett.70.2213. 3 Delva, P. et al. (2018) Gravitational Redshift Test Using Eccentric Galileo Satellites, Phys. Rev. Lett., 121, 231. https://doi.org/10.1103/PhysRevLett.121.231101