1. V. Rudenko (SAI MSU), N. Bartel (York U.), L. Gurvits (JIVE), K. Belousov (ASC), M. Bietenholz (HartRAO), A. Biriukov (ASC), W. Cannon (York U.), G. Cimo’ (JIVE), A. Fionov (SAI MSU), A. Gusev (SAI MSU), C. Gwinn (UCSB), D. Duev (JIVE), M. Johnson (UCSB), V. Kauts (ASC), G. Kopelyansky (ASC), A. Kovalenko (PRAO), V. Kulagin (SAI MSU), D. Litvinov (SAI MSU), G. Molera (JIVE), S. Pogrebenko (JIVE), N. Porayko (SAI MSU), S. Sazankov (ASC), A. Skripkin (Comcon), V. Soglasnov (ASC), K. Sokolovsky (ASC) Probing the Gravitational Redshift Effect with the RadioAstron satellite Astro Space Center of the Lebedev Physical Institute (Russia) Lavochkin Scientific and Production Association (Russia) Sternberg Astronomical Institute (Russia) Keldysh Institute for Applied Mathematics (Russia) York University (Canada) Joint Institute for VLBI in Europe (the Netherlands) University of California in Santa-Barbara (USA) Hartebeesthoek Radio Observatory (South Africa) Rencontre de Moriond, 21–28 March 2015

2. Einstein obtained the gravitational redshift formula in 1906 considering the equivalence of homogeneous gravity field and inertia (accelerated reference system) a test of the grav. redshift effect is a test of the EP : measurement of the free fall acceleration of a photon RS astro test with Sirius B (W. Adams, 1925): light from massive stars arrives with decreased frequency

3. EP – fundamental basis of GR GR postulates  equivalence of gravity and inertia UFF – for test bodies ( ~ 10 -12 – 10 -13 ) UGR – for photons ( ~ 10 -4 ) LLI – for physical laws ( ~ 10 -4 ) PPN parameters curvature  – 1 ~ 10 -5 light-time delay light deflection nonlinearity  – 1 ~ 10 -4 perihelion shift red shift in 2 nd order

4. h~10 4 km  f/f=  /  ~gh/c 2 ~10 -9  v min ~ 6 cm/s  f/f) H  10 -13 ±0,01% GP-A, 1976

6. (P/Q) –  2 (R/S) [1+(N/M) 2 ] -1/2  0 Online compensation - Doppler shift - atmospheric shift

7. Gravitational red shift experiment with SRT “Radioastron” increase sensitivity due to the measurement repetition 10^{-4}  10^{-5}

9. Moon  highly evolving orbit Period: 8 – 10 day GRS modulation: 0.4∙10 -10 – 5.8∙10 -10 280,000 – 350,000 km 1,000 – 80,000 km 6.8∙10 -10 9.4∙10 -11 – 6.4∙10 -10 RadioAstron orbit Orbit determination accuracy Position: 100 m radio, 10 cm SLR Velocity: 1 mm/s

10. Radio links: 8.4 GHz down (tone) 15 GHz down (data) 7.2 GHz up (tone) S-band T&C Green Bank tracking station (USA) Pushchino tracking station (Russia)

11. Effelsberg (Germany)Yebes (Spain) Svetloe (Russia) GBT (USA)

12. VCH-1010 Hydrogen maser frequency standard of the space radio telescope “RadioAstron”

13. log  y (  ) log  Allan deviation: stochastic and systematic

14. VCH-1010 (RadioAstron) vs. VLG-10 (GP-A) Averaging time , s Allan deviation 

16. F REQUENCY METHOD : CLOCK MOTION meteo data + model, orbit

17. 1st-order Doppler effect 8.4 GHz link Frequency, Hz Date (January 2014) 1 st -order Dopplergeocentric distance Distance, 10 3 km

18. Gravitational redshift and 2nd-order Doppler effect 8.4 GHz link Frequency, Hz Date (January 2014) 2 nd -order Dopplergeocentric distancegravitational redshift Distance, 10 3 km

19. GRAVITATIONAL REDSHIFT EXPERIMENT WITH THE SRT “RADIOASTRON” Contributions to the total frequency shift of the 8.4 GHz signal. Puschino TS, Oct 2012

20. GRAVITATIONAL REDSHIFT EXPERIMENT WITH THE SRT “RADIOASTRON” A GREEMENT BETWEEN THEORY AND EXPERIMENT : 3% Residual frequency of the 8.4 GHz signal. Puschino TS, Oct 2012 Frequency, Hz geocentric distance residual frequency Date (October) Distance, 10 3 km

21. Gravity Probe A (1976)

22. RadioAstron radio links operating modes 1-way “H-Maser” mode2-way “Coherent” mode

23. RadioAstron radio links operating modes Mixed “Semi-Coherent” mode Biriukov et al. 2014, Astron. Rep. 58, N.11, p. 783 software processing

24. Spectrum of the 15 GHz signal, transmitted data is noise-like SRT RADIOASTRON ON-BOARD HARDWARE SYNCHRONIZATION: “SEMI-COHERENT” MODE Normalized spectral power density, dB Frequency, Hz

25. “Semi-Coherent” + “Test-2”  incompatibility with astronomy

26. Spectrum of the 15 GHz signal “Test-2” mode SRT R ADIO A STRON ON - BOARD HARDWARE SYNCHRONIZATION : “S EMI - COHERENT ” MODE

27. 2015/02/15 Onsala, 8.4 GHz, 2-way Recorded signal spectrum Normalized power (log scale) Frequency, Hz

28. 2015/02/15 Onsala, 8.4 GHz, 2-way Signal phase Phase, rad Session time, s

29. Normalized power (log scale) Frequency, Hz 2015/02/15 Onsala, 8.4 GHz, 2-way Stopped-phase signal spectrum  f  0.001 Hz

30. SRT RADIOASTRON ON-BOARD HARDWARE SYNCHRONIZATION: “SEMI-COHERENT” MODE Select components of the 15 GHz signal spectrum 31 Aug 2014, Puschino TS, 08:20:00 UTC, mode: “Test-2” 18 MHz

31. Geocentric distance, 10 3 km Number of observing telescopes near perigee in 2016

32. Geocentric distance, 10 3 km ~10 experiments at <10,000 km distance and Number of observing telescopes near perigee in 2016

33. Experiment accuracy Signal frequency instability at 1000 s 1  10 –14 to 2  10 –14 *) Systematic errors: space and ground clock drift over 1 experiment uncertainties due to orbit determination errors 2  10 –15  U/c 2 variation2  10 –10 to 4  10 –10 Experiment accuracy (15 sessions 1+1 hr, 2 telescopes on average) 2  10 –5 *) Work in progress

34. G RAVITATIONAL REDSHIFT TESTS Mission Launch/ status Frequency standard Achieved/ planned accuracy Gravity Probe A 1976 completed H-maser1.4∙10 -4 RadioAstron 2011 active H-maser2∙10 -5 ACES2016 Cs-fountain + H-maser 2∙10 -6 STE-Quest≥ 2026?2∙10 -8

35. Thanks for attention