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MEASURING GANYMEDE’S TIDAL DEFORMATION BY LASER ALTIMETRY:APPLICATION TO THE GALA EXPERIMENT
GREGOR STEINBRÜGGE, HAUKE HUSSMANN, ALEXANDER STARK AND JÜRGEN OBERSTINSTITUTE OF PLANETARY RESEARCH, DLR, BERLIN, GERMANY ([email protected])
BACKGROUNDMeasurements of Ganymede’s induced magneticfield suggest a salty water layer under the icycrust [1]. However interior structure modelsconsistent with Ganymede’s moment of inertiaand total mass cannot constrain the ice thick-ness or ocean depth. In order to reduce theambiguity of the structural models, it has beenproposed to measure the dynamic response ofGanymede’s ice shell to tidal forces exerted byJupiter characterized by the Love numbers h2
and k2. The h2 value depends on the tidal fre-quency, the internal structure and the rheology,in particular on the presence of fluid layers andthe thickness and rigidity of an overlaying iceshell. Combined with measurements of k2, whichcan be inferred from radio science experiments,and a simultaneous determination of linear com-binations of h2 (laser altimetry) and k2 (radioscience) the obtained data would significantlyreduce the ambiguity in structural models [2].
Figure 1: Maximal double amplitudes if an ocean ispresent.
THE INSTRUMENT
The Ganymede LaserAltimeter (GALA)will perform glob-ally distributed alti-tude measurementsfrom a low circular500 km and 200 kmorbit. It contains a17 and 2.8 mJ laser.
METHODSA way to determine tidal effects in Ganymede’stopography and therefore the h2 value by aspacecraft in orbit is the crossover method:Different orbit tracks will intersect at cer-tain surface locations at different timesso that the tidal signal can be extractedfrom a differential altimetry measurement.
Figure 2: The map shows the maximal measurable tidalamplitudes in a grid with a resolution of 1◦ derivedfrom the current JUICE orbit scenario.
The accuracy of the tidal measurement is depen-dent on the amount of cross-overs available forthe analysis and therefore dependent on the mis-sion and operational scenario. We consider thefollowing possible operational scenarios:
• S1 GALA continuous operation except 8hper day reserved for downlink
• S2 GALA operating every third orbit - 8h re-served for downlink
Both scenarios have been analysed us-ing the JUICE trajectory SPICE kernel.
NUMERICAL SIMULATIONS
Figure 3: Flowchart of the numerical modelThe environmental factors influencing the instru-ment accuracy are the altitude and the slope. Alsoorbit and pointing errors as well as interpolationerrors between the cross-over points have to betaken into account. Since all measurement errorsare of statistical nature, a consolidated statisticalanalysis is necessary. All single error componentsare evaluated for each individual shot. After av-eraging over all cross-over points the average er-ror defines our mean measurement error.
CONCLUSIONS
We compared a set ofinterior models cov-ering a large range ofpossible layer thick-
nesses and materialproperties but consis-tent with Ganymede’smass and moment ofinertia to their h2 andk2 value. From thescatter and the pre-dicted h2 error onecan estimate the con-straints for the ice-Ithickness as resultingfrom the tidal mea-surement.
Figure 4: h2 values of interior models in dependence ofdifferent ice thicknesses.
The measurement uncertainties of 1-4% are suffi-ciently small to unambiguously confirm the exis-tence (or to prove the non-existence) of an oceanunder Ganymede’s ice shell. Further the thick-ness of the ice-I layer can be constrained by the h2
value to an order of 10-20 km. Note that this con-strain can be even further improved when usinga linear combination of h2 and k2.
REFERENCES AND CONTACT[1] M. Kivelson et al., The permanent and induc-tive magnetic moments of Ganymede, Icarus, 157,507-522, 2002.[2] J. Wahr et al.,Tides on Europa and the thick-ness of Europa’s icy shell, Journal of geoph. re-search, vol 11, 2006.Contact:Tel: +49 (0) 30 67055 [email protected]
RESULTSFor the full operation scenario S1, the estimatederror of the h2 value would be 1.3% while thereduced case S2 (every 3rd orbit) would give anerror of 4.0%. For a typical value (e.g. h2 = 1.50)as derived from models of the tidal response ofGanymede (compare Fig. 1) we get
h2 = 1.50± 0.02 for S1 andh2 = 1.50± 0.06 for S2
