$MICROSCOPE$ Mission: final results of the test of the equivalence principle

Pierre Touboul (1) , Gilles Métris (2) , Manuel Rodrigues (3) , Joel Bergé (3) , Alain Robert (4) , Quentin Baghi (2) , Yves André (4) , Judicaël Bedouet (5) , Damien Boulanger (3) , Stefanie Bremer (6) , Patrice Carle (1) , Ratana Chhun (3) , Bruno Christophe (3) , Valerio Cipolla (4) , Thibault Damour (7) , Pascale Danto (4) , Louis Demange (2) , Hansjoerg Dittus (8) , Océane Dhuicque (3) , Pierre Fayet (9, 10) , Bernard Foulon (3) , Pierre-Yves Guidotti (4) , Daniel Hagedorn (11) , Emilie Hardy (3) , Phuong-Anh Huynh (3) , Patrick Kayser (3) , Stéphanie Lala (1) , Claus Lämmerzahl (6) , Vincent Lebat (3) , Françoise Liorzou (3) , Meike List (6) , Frank Löffler (12) , Isabelle Panet (13, 14) , Martin Pernot-Borràs (3) , Laurent Perraud (4) , Sandrine Pires (15) , Benjamin Pouilloux (4) , Pascal Prieur (4) , Alexandre Rebray (3) , Serge Reynaud (16) , Benny Rievers (6) , Hanns Selig (6) , Laura Serron (2) , Timothy Sumner (17) , Nicolas Tanguy (3) , Patrizia Torresi (4) , Pieter Visser (18)

1 ONERA, Université Paris Saclay [Palaiseau]
2 GEOAZUR 7329 - Géoazur
3 DPHY, ONERA, Université Paris Saclay [Châtillon]
4 CNES - Centre National d'Études Spatiales [Toulouse]
5 DTIS, ONERA, Université de Toulouse [Toulouse]
6 ZARM - Center of Applied Space Technology and Microgravity
7 IHES - Institut des Hautes Études Scientifiques
8 DLR - Deutsches Zentrum für Luft- und Raumfahrt [Köln]
9 Champs, Gravitation et Cordes
10 CPHT - Centre de Physique Théorique [Palaiseau]
11 LPENS - Laboratoire de physique de l'ENS - ENS Paris
12 PTB - Physikalisch-Technische Bundesanstalt [Braunschweig]
13 IPGP - Institut de Physique du Globe de Paris
14 ENSG - École nationale des sciences géographiques
15 AIM (UMR7158 / UMR_E_9005 / UM_112) - Astrophysique Interprétation Modélisation
16 LKB [Collège de France] - Laboratoire Kastler Brossel
17 Blackett Laboratory
18 Faculty of Aerospace Engineering [Delft]

The $MICROSCOPE$ mission was designed to test the weak equivalence principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of ${10}^{-15}$ in terms of the Eötvös ratio $\eta$. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultrasensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five months worth of science free-fall data, two-thirds with a pair of test masses of different compositions—titanium and platinum alloys—and the last third with a reference pair of test masses of the same composition—platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the titanium and platinum pair constrained to $\eta (\mathrm{Ti},\mathrm{Pt})=[-1.5\pm 2.3(\mathrm{stat})\pm 1.5(\mathrm{syst})]\times {10}^{-15}$ at $1\sigma$ in statistical errors.

Mots clés: equivalence principle: violation; force: electrostatic; error: statistical; stability: thermal; mass: gravitation; platinum; titanium; satellite; acceleration; general relativity: validity test; orbit

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique [physics]; Sciences de l'ingénieur [physics]

Pierre Touboul, Gilles Métris, Manuel Rodrigues, Joel Bergé, Alain Robert, et al.. $MICROSCOPE$ Mission: final results of the test of the equivalence principle. Physical Review Letters, 2022, 129 (12), pp.121102. ⟨10.1103/PhysRevLett.129.121102⟩. ⟨hal-03781337⟩