Galileo gravitational Redshift test with Eccentric satellites (GREAT)

Galileo gravitational Redshift test with Eccentric satellites (GREAT) P. DELVA and N. PUCHADES SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 6, LNE Rencontres de Moriond Gravitation La Thuile, Italy, March 25 April 1, 217 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 1 / 24

Outline 1 Galileo satellites 21 and 22 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 2 / 24

Galileo satellites 21 and 22 Outline 1 Galileo satellites 21 and 22 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 3 / 24

Galileo satellites 21 and 22 The Galileo system 24 satellites + 6 spares in medium Earth orbit on three orbital planes [actually 18]; A global network of sensor stations receiving information from the Galileo satellites; Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 4 / 24

Galileo satellites 21 and 22 The Galileo system 24 satellites + 6 spares in medium Earth orbit on three orbital planes [actually 18]; A global network of sensor stations receiving information from the Galileo satellites; The control centres computing information and synchronising the time signal of the satellites; Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 4 / 24

Galileo satellites 21 and 22 The story of Galileo satellites 21 & 22 Galileo satellites 21 & 22 were launched with a Soyuz rocket on 22 august 214 on the wrong orbit due to a technical problem Launch failure was due to a temporary interruption of the joint hydrazine propellant supply to the thrusters, caused by freezing of the hydrazine, which resulted from the proximity of hydrazine and cold helium feed lines. Paco me DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 5 / 24

Galileo satellites 21 and 22 Galileo satellites 21&22 orbit Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 6 / 24

Gravitational redshift test Outline 1 Galileo satellites 21 and 22 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 7 / 24

Gravitational redshift test Gravity Probe A (GP-A) (1976) Test of the gravitational redshift on a single parabola [Vessot and Levine, 1979, Vessot et al., 198, Vessot, 1989] Continuous two-way microwave link between a spaceborne hydrogen maser clock and ground hydrogen masers Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 8 / 24

Gravitational redshift test Gravity Probe A (GP-A) (1976) Test of the gravitational redshift on a single parabola [Vessot and Levine, 1979, Vessot et al., 198, Vessot, 1989] Continuous two-way microwave link between a spaceborne hydrogen maser clock and ground hydrogen masers Frequency shift verified to 7 1 5 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 8 / 24

Gravitational redshift test Gravity Probe A (GP-A) (1976) Test of the gravitational redshift on a single parabola [Vessot and Levine, 1979, Vessot et al., 198, Vessot, 1989] Continuous two-way microwave link between a spaceborne hydrogen maser clock and ground hydrogen masers Frequency shift verified to 7 1 5 Gravitational redshift verified to 1.4 1 4 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 8 / 24

Gravitational redshift test Why Galileo 21 & 22 are perfect candidates? An elliptic orbit induces a periodic modulation of the clock bias at orbital frequency ( τ(t) = 1 3Gm ) 2ac 2 t 2 Gma c 2 e sin E(t) + Cste.4.3.2.1 Very good stability of the on-board atomic clocks test of the variation of the redshift -.1 -.2 -.3 -.4 Jul 31 Aug 1 Aug 2 Aug 3 Aug 4 215 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 9 / 24

Gravitational redshift test Why Galileo 21 & 22 are perfect candidates? An elliptic orbit induces a periodic modulation of the clock bias at orbital frequency ( τ(t) = 1 3Gm ) 2ac 2 t 2 Gma c 2 e sin E(t) + Cste.4.3.2.1 -.1 -.2 Very good stability of the on-board atomic clocks test of the variation of the redshift Satellite life-time accumulate the relativistic effect on the long term -.3 -.4 Jul 31 Aug 1 Aug 2 Aug 3 Aug 4 215 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 9 / 24

Gravitational redshift test Why Galileo 21 & 22 are perfect candidates? An elliptic orbit induces a periodic modulation of the clock bias at orbital frequency ( τ(t) = 1 3Gm ) 2ac 2 t 2 Gma c 2 e sin E(t) + Cste.4.3.2.1 -.1 -.2 -.3 -.4 Jul 31 Aug 1 Aug 2 Aug 3 Aug 4 215 Very good stability of the on-board atomic clocks test of the variation of the redshift Satellite life-time accumulate the relativistic effect on the long term Visibility the satellite are permanently monitored by several ground receivers Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 9 / 24

Gravitational redshift test Galileo gravitational Redshift test with Eccentric satellites Two parallel studies funded by ESA: SYRTE/Observatoire de Paris and ZARM/University of Bremen Improvement of the orbit/clock solution by ESA/ESOC using enhanced models Improvement of Solar Radiation Pressure (SRP) modelling with finite element method Dedicated Laser ranging campaign launched with ILRS community to disentangle clock and orbit radial errors Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 1 / 24

Gravitational redshift test Galileo gravitational Redshift test with Eccentric satellites Two parallel studies funded by ESA: SYRTE/Observatoire de Paris and ZARM/University of Bremen Improvement of the orbit/clock solution by ESA/ESOC using enhanced models Improvement of Solar Radiation Pressure (SRP) modelling with finite element method Dedicated Laser ranging campaign launched with ILRS community to disentangle clock and orbit radial errors Processing more data from the 2 Galileo eccentric satellites (GAL-21 & 22) so to further improve the statistics Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 1 / 24

Data analysis Outline 1 Galileo satellites 21 and 22 2 Gravitational redshift test 3 Data analysis Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 11 / 24

Data analysis Flowchart for the time approach Satellite orbits (sp3 files) Clock Bias (clk files) SLR residuals (res files) Coordinate to proper time transformation Pre-processing Model of systematics Theoretical clock bias Corrected clock bias Clock bias systematics Test of gravitational redshift Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 12 / 24

Data analysis Data availability GAL-21 sp3 time: 618. days clk time: 615.86 days GAL-22 sp3 time: 592. days clk time: 59.99 days Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 13 / 24

Data analysis Transformation from ITRS to ITRF: GAL-21 Use of SOFA routines Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 14 / 24

Data analysis Theoretical clock bias: contributions (GAL-21).4.2 2 1-5.3.15 1.5.2.1 1.1.5.5 -.1 -.5 -.5 -.2 -.1-1 -.3 -.15-1.5 -.4 Jul 31 Aug 1 Aug 2 Aug 3 Aug 4 215 -.2 Jul 31 Aug 1 Aug 2 Aug 3 Aug 4 215-2 Jul 31 Aug 1 Aug 2 Aug 3 Aug 4 215 x = [ 1 GM rc 2 v 2 2c 2 GMR2 J 2 ( 1 3 cos 2 2r 3 c 2 θ ) ] dt; Note: for a keplerian orbit, gravitational (GM) and velocity contributions are equal for the periodic part. Here the maximum difference is 2 ps. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 15 / 24

Data analysis Clock bias drift: GAL-21 1 1.5 8 1 6.5 4 2 -.5-1 -2 Jul 214 Jan 215 Jul 215 Jan 216 Jul 216 Jan 217 Jul 217-1.5 Jul 214 Jan 215 Jul 215 Jan 216 Jul 216 Jan 217 Jul 217 The clock bias drift is 34 µs.d 1 ( 3.9 1 1 ). Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 16 / 24

Data analysis Systematic effects in clock residuals.3 5 4.2 3.1 2 1 -.1-1 -2 -.2-3 -4 Jul 214 Jan 215 Jul 215 Jan 216 Jul 216 Jan 217 Jul 217 -.3 Aug 1 Aug 2 Aug 3 Aug 4 Aug 5 Aug 6 Aug 7 215 We remove one linear fit per day: x= X i ( 1 for day i fi (t)(ai + bi t), fi (t) = otherwise Paco me DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 17 / 24

Data analysis Fit of the GR deviation model.3 5 Data minus daily linear fits Fitted GR deviation Data minus daily linear fits Fitted GR deviation 4.2 3.1 2 1 -.1-1 -2 -.2-3 -4 Jul 214 Jan 215 Jul 215 Jan 216 Jul 216 Jan 217 Jul 217 x= X i -.3 Aug 1 Aug 2 Aug 3 Aug 4 Aug 5 Aug 6 Aug 7 215 Z GM GMR2 J2 2 fi (t)(ai + bi t) + α 1 3 cos θ dt 2 rc 2r 3 c 2 Paco me DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 18 / 24

Data analysis Limitations: systematic errors [Delva et al., 215] 1 Effects acting on the frequency of the reference ground clock can be safely neglected 2 Effects on the links (mismodeling of atmospheric delays, variations of receiver/antenna delays, multipath effects, etc...) very likely to be uncorrelated with the looked for signal, averages with the number of ground stations 3 Effects acting directly on the frequency of the space clock (temperature and magnetic field variations on board the Galileo satellites) 4 Orbit modelling errors (e.g. mismodeling of Solar Radiation Pressure) are strongly correlated to the clock solution Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 19 / 24

Data analysis Limitations: systematic errors [Delva et al., 215] 1 Effects acting on the frequency of the reference ground clock can be safely neglected 2 Effects on the links (mismodeling of atmospheric delays, variations of receiver/antenna delays, multipath effects, etc...) very likely to be uncorrelated with the looked for signal, averages with the number of ground stations 3 Effects acting directly on the frequency of the space clock (temperature and magnetic field variations on board the Galileo satellites) 4 Orbit modelling errors (e.g. mismodeling of Solar Radiation Pressure) are strongly correlated to the clock solution Condidering systematic errors, simulations have shown that Galileo 5 and 6 can improve on the GP-A (1976) limit on the gravitational redshift test, down to an accuracy of (3 4) 1 5 with at least one year of data. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 19 / 24

Data analysis Systematic effects in clock residuals Orbital frequency: 1.855 d 1 ( 13 hours period) July 216: Change of clock from PHM B to PHM A... Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 2 / 24

Data analysis Systematic effects in clock residuals: PHM B Orbital frequency: 1.855 d 1 ( 13 hours period) β = in June 215 figure from Steigenberger et al, AdSR 55, 215. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 21 / 24

Data analysis Systematic effects in clock residuals: modulation 1.2 1.5 1 1.8.5.6.4 -.5.2-1 -1.5 Jan 215 Jul 215 Jan 216 Jul 216 1.845 1.85 1.855 1.86 1.865 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 22 / 24

Data analysis Systematic effects in clock residuals: modulation 1.2 1.5 1 1.8.5.6.4 -.5.2-1 1.845-1.5 Jan 215 Jul 215 Paco me DELVA (SYRTE/Obs.Paris) Jan 216 1.85 1.855 1.86 1.865 Jul 216 GREAT 217 Moriond GR 22 / 24

Data analysis Systematic effects in clock residuals: modulation 1.2 1 Data Model.8.6.4.2 1.845 1.85 1.855 1.86 1.865 Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 22 / 24

Data analysis Conclusion Opportunity to improve gravitational redshift constraint thanks to the launch failure of Galileo satellites 21 and 22 Two ESA GREAT projects: SYRTE and ZARM Without taking into account systematics, current constraint is around the level of Gravity Probe A Investigation of systematic effects is on-going: dedicated one-year ILRS/SLR campaign Paco me DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 23 / 24

Data analysis Literature I Delva, P., Hees, A., Bertone, S., Richard, E., and Wolf, P. (215). Test of the gravitational redshift with stable clocks in eccentric orbits: Application to Galileo satellites 5 and 6. Class. Quantum Grav., 32(23):2323. Vessot, R. F. C. (1989). Clocks and spaceborne tests of relativistic gravitation. Advances in Space Research, 9:21 28. Vessot, R. F. C. and Levine, M. W. (1979). A test of the equivalence principle using a space-borne clock. General Relativity and Gravitation, 1:181 24. Vessot, R. F. C., Levine, M. W., Mattison, E. M., Blomberg, E. L., Hoffman, T. E., Nystrom, G. U., Farrel, B. F., Decher, R., Eby, P. B., and Baugher, C. R. (198). Test of relativistic gravitation with a space-borne hydrogen maser. Phys. Rev. Lett., 45:281 284. Pacôme DELVA (SYRTE/Obs.Paris) GREAT 217 Moriond GR 24 / 24