1. 1 GNSS-R concept extended by a fine orbit tuning Jaroslav KLOKOČNÍK a, Aleš BEZDĚK a, Jan KOSTELECKÝ b,c a Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-251 65 Ondřejov, Czech Republic, Tel.:+420323620158, jklokocn@asu.cas.cz, bezdek@asu.cas.cz, b CEDR – Research Institute for Geodesy, Topography and Cartography, CZ-250 66 Zdiby, Czech Republic, c Department of Advanced Geodesy, Czech Technical University, CZ-166 29 Praha 6, Thákurova 7,Czech Republic, kost@fsv.cvut.cz jklokocn@asu.cas.czkost@fsv.cvut.czjklokocn@asu.cas.czkost@fsv.cvut.cz 2 nd CNES CCT workshop on passive reflectometry using radiocom space signals, Space Reflecto2011, Calais, France 27 and 28 Oct 2011

2. 2 Outline  Definitions  Orbit tuning for altimetry mission ERS 1, DGFI 1989  GRACE and GOCE  Inspiration for GNSS-R  Examples for GNSS-R, second satellite  Instead of Conclusion  References

3. 3  Definitions

4. 4 Orbital resonances Orbital resonance β/α takes place, if:  Groundtracks are exactly the same after β nodal revolutions and α nodal days  Equivalent names: repeat orbit, resonant orbit  Density of ground tracks at equator D = o/β, where the circumference o = 40 075 km (for the Earth)  Number of single-satellite crossover points (among the ascending and descending tracks)  where u = 1 for I < 90 and u = –1 for I > 90 deg (see, e.g., Farless 1986 or Kim 1997).

5. 5 mean motion vs semi-major axes, 1 st order analytical theory Recalling the exact resonance β:α; the phase in LPE at the exact resonance becomes. The relevant satellite mean motion n: (1) Now we have to put the LPEs for the orbital elements Ω, ω, and M 0 into (1); we get: where the minus sign is valid for the normal rotation and the plus sign for the retrograde rotation of the planet. Finally we arrive at (2) where for and for, the former case for the normal rotation, the latter for the retrograde rotation. Note that Klokočník, J., Kostelecký, J., and Gooding, R. H., “On fine orbit selection for particular geodetic and oceanographic missions involving passage through resonances”, Journal of Geodesy, Vol. 77, No. 1, 2003, pp. 30–40. doi: 10.1007/s00190-002-0276-3

6. 6  Historical notes - altimetry and GRACE

7. 7 History: orbit tuning for altimetry missions: oceanography vs space geodesy

8. 8 D = 932 km

9. 9 D = 80 km

10. 10 future

11. 11 Motivation to study resonance regimes for freely decaying GRACE: dramatic changes in the accuracy of monthly solutions for variations of the geopotential near low-order resonances (here the case of 61/4 in Autumn 2004): Courtesy of S. Bettadpur (2004, 2006, priv. commun.) Note logarithmic scales on the y-axes.

12. 12  GOCE (pre)-selected orbits with high-order resonances for measuring phases with the onboard gradiometer, orbit keeping by means of the ion motor to ± 5m

13. 13

14. 14 D=2505 km D=41 km

15. 15 GNSS-R small demonstration satellite piggybacked to another satellite to sun-synchronous, retrograde, dawn-dusk (SSO) orbit (6 am and 6 pm are times of equator crossings) at height 500–800 km. Later the operational satellite again on SSO orbit but at height 1300–1500 km both orbits sun-synchronous, I = 98–101 deg, revisit time about 3 days for the former and about 2 days for the latter mission. Swath is 900 km or 1500 km, respectively, spatial resolution not worse than 10×100 kmxkm

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21. 21 Example of possible orbit tuning for GNSS-R satellite

22. 22 243/17872/61 h=788.0 km, D = 165 km h=787.7 km, D = 46 km

23. 23 Table 1. Density of the ground tracks and number of the cross-over points for different repeat orbits D = o/β, u = 1 for I < 90 and u = –1 for I > 90 deg

24. 24

25. 25 The Fine Orbit Tuning for (the second) ESA’s GNSS-R satellite  Step 1 standard orbit selection (already done by ESA) SSO orbits 500–800 km and 1300–1500 km, I = 98–101 deg,  Step 2 suggestion for possible fine orbit tuning (done now & here)  Step 3 the definitive, more specific orbit selection (by ESA), to be aware of possibility of the fine orbit tuning  Step 4 definitive fine orbit tuning for the final orbit selection

26. 26  Case of GOCE we are ready to repeat something like that for any satellite

27. 27 Orbits with no syubcycles, orbits with subcycles, the basic difference…

28. 28 GOCE groundtrack pattern animation for a hypothetical free fall

29. 29 actual 61-day orbit planned 61-day orbit 20/21-day subcycles 41-day subcycle 62-day orbit

30. 30 Temporal evolution of an orbit – with/without a subcycle  Repeat orbit with no subcycles → gradually filling up two large equatorial gaps  Repeat orbit with a subcycle → groundtracks laid down in two (or more) almost homogeneous grids

31. 31 Analytical vs. numerical modelling  So far, graphs based on simple theory with only the zonal term J2 (flattening of Earth)  What happens when all other orbital perturbations (geopotential, lunisolar, tides, radiation, …) are added?  Peaks in histograms widened  Repeat character is kept  Earth coverage graphs almost the same (0.02° ↔ 2 km)

32. 32 Orbits near the actual 61-day orbit of GOCE  Equator with groundtracks after 65 days  Different mean altitudes Repeat orbits:  61-day (selected for MOP1)  41-day subcycle  62-day orbit compared with 61-day  has more regular groundtrack grid  is only by 200 m higher 6262 6262 41 6161 6161 6161 6262

33. 33 Proposal for the 145-day orbit with 62 or 83 day subcycles Planned 2327:145 repeat orbit  node spacing ≈ 17.2 km Nearest repeat orbits  62-day, lower by 30 m  83-day, higher by 23 m Ion thruster performance ±50 m 145-day repeat is a good choice → node spacing at least  40.3 km for 62-day repeat  30.1 km for 83-day repeat Resonant orbits ordered by height DRh (km) 1653103255,062 99562255,105 2327145255,135 133283255,158 1669104255,19 2006125255,211 2343146255,226 83 145 6262

34. 34 Instead of Conclusion Analyses done for GRACE and GOCE can be repeated for GNSS-R satellite(s). Number of measuring points (nadir and off-nadir) for a bistatic altimetry with the fine orbit tuning may increase by 1-2 orders, in comparison with the number of monostatic (nadir) altimetry (sub-satellite) points in a “general” orbit (ignoring any fine orbit tuning). Additional costs for the inclusion of the fine orbit tuning and orbit keeping are theoretically zero.

35. 35 Thank you for your attention

36. 36 More information: jklokocn@asu.cas.czjklokocn@asu.cas.cz www.asu.cas.cz/~jklokocn, ~bezdek References Klokocnik et al. 2003: On Fine Orbit Selection for Particular Geodetic and Oceanographic Missions Involving Passage Through Resonances, J. GEOD., Vol. 77, No. 1, 30–40, doi:10.1007/s00190-002-0276-3 Wagner et al. 2006: Degradation of Geopotential Recovery from Short Repeat-Cycle Orbits: Application to GRACE Monthly Fields, J. GEOD.,Vol. 80, No. 2, 94–103, doi:10.1007/s00190-006-0036 Klokocnik et al. 2008: Variations in the Accuracy of Gravity Recovery due to Ground Track Variability: GRACE, CHAMP, and GOCE, J. GEOD, Vol. 82, No. 12, 917–927, doi:10.1007/s00190-008-0222-0 Bezděk et al. 2009: Simulation of Free Fall and Resonances in the GOCE Mission, J. GEODYN., Vol. 48, No. 1, 47–53, doi:10.1016/j.jog.2009.01.007 Klokocnik et al. 2010: Orbit Tuning of Planetary Orbiters for Accuracy Gain in Gravity-Field Mapping, JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS, Vol. 33, No. 3, May– June, doi: 10.2514/1.46223.