15 May 2023
Testing the fundamentals of modern physics
Einstein’s theory of gravitation predicts that time moves faster the further away from the Earth you are. Thus, a clock placed at the top of Mont Blanc advances relative to a clock at sea level by about 10 nanoseconds per day. This gravitational shift is the third prediction of the theory of general relativity, after the advance of the perihelion of the planet Mercury and the deflection of light, all verified experimentally. It follows directly from one of the foundations of modern physics: the principle of equivalence.
The measurement of the gravitational shift is essential because, like the space mission Microscope or the detection of gravitational waves, it allows to test the limits of Einstein’s theory of gravitation. Indeed, there are other theories of gravitation that do not respect the equivalence principle: the most famous are the string theory and the quantum loop gravitation, which aim to unify gravitation and quantum mechanics. By improving our measurements of time, we hope to challenge general relativity and thus discover a new physics.
In 1977, the first atomic clock was put into orbit in the NAVSTAR GPS satellite NTS-2, and confirmed a gravitational shift of about 20 microseconds per day. Thereafter, the GPS constellation allows to verify this shift with a relative uncertainty of 1%. The main limitation of this measurement comes from the circular orbits of the satellites of the constellation. In a historic experiment called "Gravity Probe A" (GP-A), conducted in 1976, Robert Vessot and Martin Levine (Harvard University) send an atomic clock in a rocket. The rocket climbed to an altitude of 10,000 kilometers before falling into the Atlantic Ocean, and the Einstein effect was verified with a relative uncertainty 100 times better than ever before (1).
Doresa and Milena, the eccentric satellites
Galileo is the European navigation satellite constellation. Currently 26 satellites are in orbit around the Earth. On August 22, 2014, the launch of satellites 5 and 6 (Doresa and Milena) is partly failed: a design flaw leads to partial freezing of the fuel and the engines responsible for controlling the orientation of the fourth stage of the rocket do not activate. Result: the rocket takes a bad orientation at the time of the last phase of setting on orbit. Doresa and Milena end up in very eccentric orbits: each satellite rises and falls 9000 km twice a day.
- GREAT
- L’altitude des deux satellites Galileo excentriques varie d’environ 9000 km deux fois par jour. La théorie de la relativité générale prédit alors que la variation du décalage temporel gravitationnel des horloges de ces satellites par rapport aux horloges terrestres est d’environ 400 ns, ce que l’on a mesuré avec une incertitude relative de 25 millionièmes .
This is a boon for relativity tests! A preliminary study conducted by SYRTE shows that it is possible, with more than one year of data from these two eccentric satellites, to improve the test of the gravitational shift made by GP-A in 1976 (2). Indeed, the Galileo satellites contain passive hydrogen maser (PHM) atomic clocks, which have an unequalled stability among space clocks. Moreover, these clocks are compared with the best clocks on the ground permanently by about a hundred ground receivers.
The European Space Agency, through their Galileo Navigation Science Office at ESAC, decided to fund and participate in two parallel studies to carry out this experiment, named GREAT (Galileo gravitational redshift experiment with eccentric sATellites). One of these studies is entrusted to SYRTE, Observatoire de Paris and the other to ZARM, University of Bremen. After three years of measurements and data analysis, the results of the study by SYRTE researchers and their collaborators have just been published in the scientific journal Physical Review Letters (3). They confirm the predictions of general relativity with a relative uncertainty of 2.5x10-5, an improvement of a factor of 5.6 compared to the results of GP-A.
Many collaborators
In order to achieve this result, the systematic effects of the experiment had to be understood, evaluated and corrected. This required the help of many experts. In order to evaluate the systematic errors associated with the orbit modeling, a satellite laser ranging (SLR) campaign was conducted by the International Laser Ranging Service (ILRS) station network during 2016/2017 (4). The laser telemetry station of the Observatoire de la Côte d’Azur, a partner in the project, has strongly contributed to this campaign, which has allowed to disentangle systematic errors coming from orbit errors and onboard atomic clocks.
European Space Agency experts at ESAC, ESOC and ESTEC provided decisive support for the modeling of systematic errors thanks to their knowledge of the Galileo system. The European Space Agency’s navigation office, ESOC, also generated accurate orbit and clock products using the best available satellite models. For other systematic errors potentially affecting onboard clocks, conservative upper limits were calculated through ground testing of clocks and onboard controls.
The future: an atomic fountain on the ISS
Finally, the GREAT experiment is now limited by the knowledge of the effects of magnetic fields on the onboard clocks. The ACES space experiment, a project led by the French and European space agencies, has the ambition to send an atomic fountain (with Caesium) on board the International Space Station. This should allow to improve the test of the gravitational shift of an order of magnitude (5).
Contact : Pacôme Delva
SYRTE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, LNE, 61 avenue de l’Observatoire 75014 Paris
Références
[1] R. F. C. Vessot and M. W. Levine. « A test of the equivalence principle using a space-borne clock », Gen. Relativ. Gravit. 10, 181 (1979)
[2] P. Delva et al. « Test of the gravitational redshift with stable clocks in eccentric orbits: application to Galileo satellites 5 and 6 », Class. Quantum Grav. 32, 232003 (2015).
[3] P. Delva et al. « A gravitational redshift test using eccentric Galileo satellites », Phys. Rev. Lett. 121, 231102 (2018)
[4] P. Delva et al. « An SLR campaign on Galileo satellites 5 and 6 for a test of the gravitational redshift – the GREAT experiment », Proceedings of the ILRS Technical Workshop, Matera, Italy, October 26-30, 2015 (2016)
[5] F. Meynadier et al. « Atomic clock ensemble in space (ACES) data analysis », Class. Quantum Grav., 35:3, p. 035018 (2018)
[6] Delva, Pacôme, Neus Puchades, Erik Schönemann, Florian Dilssner, Clément Courde, Stefano Bertone, and others, "A New Test of Gravitational Redshift Using Galileo Satellites: The GREAT Experiment", Comptes Rendus Physique, URSI-France 2018 Workshop/Journées URSI-France 2018 Geolocation and navigation / Géolocalisation et navigation, 20.3 (2019), 176–82