Resonances and GOCE orbit selection

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Resonances and GOCE orbit selection
EGU Vienna 2008 G2 A 03305 Monday 14 April

• J. Klokocník (1), A. Bezdek (1), J. Kostelecký
  (2),
• R. Floberghagen (3), Ch. Gruber (1)
• Astron. Inst. Czech Acad. Sci., CZ 251 65
  Ondrejov (jklokocn_at_asu.cas.cz),
• Research Institute of Geodesy, Topography and
  Cartography,
• CZ 250 66 Zdiby 98 (kost_at_fsv.cvut.cz),
• (3) ESTEC/EOPPGM, ESTECKeplerian 1, NL 2200 AG
  Noordwijk (Rune.Floberghagen_at_esa)

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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)

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courtesy Bettadpur 2004
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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
2005. Courtesy M. Weigelt 2008
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exact resonance 61/4 at mid Sept 2004
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future
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GRACE A density history for estimated band
limited resolution in unconstrained solution for
gravity field parameters or their time
derivatives
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What have we learnt from GRACE for GOCE?

• The orbit choice must avoid low order repeat
  orbit to avoid low density of ground tracks
  (16th-order resonance for GOCE)
• For given inclination and eccentricity small
  tuning in semimajor axis provides very diverse
  scenarios for measuring phases of GOCE
  gradiometer

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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 de?nition of the overall
  gravity ?eld mapping pro?le, in particular
  because the solar activity is expected to raise
  substantially during 2008. Baseline mission
  pro?les de?ned during Phase A must therefore be
  revisited

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• repeat orbit D km
• _________________________________
• 16/1 2500
• 49/3 818
• 65/4 616
• 81/5 495
• 97/6 413
• .
• 451/28 89
• 974/61 41
• 975/61 41
• 2513/156 16
• ..

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Example 1Measuring phase 975/61 repeat orbit,
altitude272.9 km
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Example 2Measuring phase 974/61 30d repeat
orbit, altitude277.4 km
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Evolution of the ground-track patterns

• Note the different time evolution between 272.9
  km (61d) and 277.4 km (61d 30d) repeat orbits.

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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.
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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 de?nition of the overall
  gravity ?eld mapping pro?le, in particular
  because the solar activity is expected to raise
  substantially during 2008. Baseline mission
  pro?les de?ned during Phase A must therefore be
  revisited

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

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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

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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

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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

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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

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• 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.
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• PPT_EGU08_GOCE.ppt
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• The end