Resonances and GOCE orbit selection J. Kloko č ník (1), A. Bezd ě k (1), J. Kostelecký (2), R. Floberghagen (3), Ch. Gruber (1) (1)Astron. Inst. Czech Acad. Sci., CZ ­ Ond ř ejov (2)Research Institute of Geodesy, Topography and Cartography, CZ ­ Zdiby 98 (3) ESTEC/EOP­PGM, ESTEC­Keplerian 1, NL 2200 AG Noordwijk EGU Vienna 2008 G2 A Monday 14 April

Outline What we have learnt from GRACE GOCE orbit choice to avoid low order resonances GOCE orbit fine tuning of semi-major axis for various scenario of ground tracks evolution Free fall of GOCE due to atmospheric drag from injection orbit to orbits for measuring with gradiometer (MOPs)

courtesy Bettadpur 2004

Dimensionless RMS error degree variances of fully-normalized geopotential coefficients of the monthly gravity field solutions (calibrated errors, CSR, Release 4), from May 2004 to March Courtesy: M. Weigelt 2008

exact resonance 61/4 at mid Sept 2004

future

GRACE A density history for estimated band limited resolution in unconstrained solution for gravity field parameters or their time derivatives

What have we learnt from GRACE for GOCE? The orbit choice must avoid low order repeat orbit = to avoid low density of ground tracks (16 th -order resonance for GOCE) For given inclination and eccentricity small “tuning” in semimajor axis provides very diverse scenarios for measuring phases of GOCE gradiometer

Orbit scenario & constraints - launch date provided by launcher authority determines length of MOPs - launch date drives selection of satellite and orbit configuration, and therefore location of long eclipse phase within the year (dawn-dusk vs dusk-dawn orbit) - solar activity determines decay rate from safe injection altitude down to gravity field sampling altitude - current case: launch early August 2008, dusk-dawn configuration, MOP1 duration about 6 months duration The orbit decay phase has been analyzed for different solar activity and drag scenarios. Such analysis is of key interest to the GOCE mission analysis and to the definition of the overall gravity field mapping profile, in particular because the solar activity is expected to raise substantially during Baseline mission profiles defined during Phase A must therefore be revisited

repeat orbit D [km] _________________________________ 16/ / / / /6 413 …. 451/ / / / …..

Example 1: Measuring phase: 975/61 repeat orbit, altitude=272.9 km

Example 2: Measuring phase: 974/61 ≈ 30d repeat orbit, altitude=277.4 km

Evolution of the ground-track patterns Note the different time evolution between km (61d) and km (61d ≈ 30d) repeat orbits.

The orbits from the bough closest to 16/1 resonance have no sub-cycles and create denser ground tracks from the beginning of the repeat cycle, but slowly. The orbits from higher boughs have at least one sub-cycle and create ground track loops quickly but with a lower density. After the interval of the repeat period the ground track patterns are nearly the same from both methods but distribution of gaps in ground tracks differ case by case.

Orbit scenario & constraints - launch date provided by launcher authority determines length of MOPs - launch date drives selection of satellite and orbit configuration, and therefore location of long eclipse phase within the year (dawn-dusk vs dusk-dawn orbit) - solar activity determines decay rate from safe injection altitude down to gravity field sampling altitude - current case: launch early August 2008, dusk-dawn configuration, MOP1 duration about 6 months duration The orbit decay phase has been analyzed for different solar activity and drag scenarios. Such analysis is of key interest to the GOCE mission analysis and to the definition of the overall gravity field mapping profile, in particular because the solar activity is expected to raise substantially during Baseline mission profiles defined during Phase A must therefore be revisited

Solar activity: 11-yr cycles no. 23 (measured) and 24 (predicted)

Simulation software NUMINT used for GOCE free-fall Simulation calculated using our „home-made“ program for numerical integration, NUMINT. The perturbing forces used in NUMINT for this long-term prediction are: gravity: EGM96, degree and order 50 direct lunisolar perturbations solid Earth tides atmospheric drag: DTM2000 direct solar radiation pressure We modified the spacecraft characteristics relevant for atmospheric drag, namely Cd and the spacecraft frontal area according to the discussion with ESA experts, e.g. we augmented the frontal area due to the 15-degree tilt. It is clear that the ability to change the cross-sectional area using the pitch angle is a flexible way to control the time of free fall during the commissioning phase.

Simulation of GOCE free-fall: How long from the 295-km initial orbit to the orbit for measuring with the gradiometer? „nominal“ – no tilt in the satellite attitude „15° tilt“ – tilting the satellite in order to increase the atmospheric friction to shorten the time of free fall „max“/ „min“ – level of predicted solar activity

Conclusions 1 clear correlation: diminished accuracy of solutions for gravity field parameters and occurrence of short repeat (resonance) orbits In a low order repeat orbit – one may have the same number and quality of observations for gravity parameter recovery – but the space distribution of the data due to the repeat condition is inevitably sparser Over a long mission, encompassing many such repeat orbits, the density variations may be large both in time and also in geographic latitude. This was not so critical for pre-CHAMP models

Conclusions 2 To achieve the maximum accuracy and resolution in recovery for unconstrained solutions the orbit design must avoid short repeat cycles as much as possible either by – (1) station keeping in an orbit with suitably dense tracks or – (2) by manoeuvering to avoid undesirable orbits (in an otherwise 'free fall') For GOCE it means to avoid the orbit choice in the close vicinity to the 16/1 resonance during the measuring phases with the gradiometer

Conclusions 3 Various fine orbit tuning regimes in SMA are possible leading to different ways of creation of ground tracks The orbits from the bough closest to 16/1 resonance have no sub-cycles and create denser ground tracks from the beginning of the repeat cycle, but slowly The orbits from higher boughs have at least one sub- cycle and create ground track loops quickly but with a lower density After the interval of the repeat period the ground track patterns are nearly the same from both methods but distribution of gaps in ground tracks differ case by case

Acknowledgments Support of CEDR, grant LC 506, of the Ministry of Education of Czech Republic for the Czech co-authors, and by grants A3407 from the Grant Agency of the Academy of Czech Republic and PECS/ESA C 98056, are highly appreciated. Anonymous ftp: sunkl.asu.cas.cz pub/jklokocn PPT_EGU08_GOCE.ppt or The end