orbiting spacecraft, for example, by radio tracking and laser altimetry. The relationship between gravity and topography and their connection to geologic features can be exploited to provide information on internal structure and dynamics and surface tectonics. Most importantly, it will enable better constraints on the thickness of the outer water ice-liquid shell and determination of variations in this thickness. The nonhydrostatic contributions to the gravity field will be characterized and internal mass anomalies identified. Modes of compensation for surface loads can be determined, thereby constraining the rheology of the ice shell.

The periodic distortion of Europa as it revolves around Jupiter produces variations in Europa's shape and gravitational field with a period equal to Europa's period of orbital revolution (3.55 days). The distortion of Europa is caused by the forced eccentricity of its orbit and the consequent variation in the tidal force from Jupiter with Europa's orbital position. Also contributing is the small periodic motion in the position of the sub-jovian point on Europa's surface. Europa's periodic changes in shape redistribute its mass and result in periodic changes in the gravitational field. These periodic variations in Europa's shape and gravity field are superimposed on the permanent and much larger ellipsoidal shape and degree-two gravitational field that result from Europa's rotation and Jupiter's tidal force, already measured by Galileo.

Measurements of the time-varying shape and gravity field of Europa can readily be taken by an orbiting spacecraft with a minimum lifetime of a few tens of europan orbital periods. If Europa has a global liquid-water ocean, the surface of its icy shell will rise and fall by about 30 m during a revolution around Jupiter. If there is no ocean, the periodic displacement of the surface will be only a few meters. The tidal response of a patchy shell will be intermediate between these two limits, with its exact amplitude determined by the degree to which the icy shell is decoupled from Europa's interior.

Determination of the topography will make it possible to distinguish easily between these possibilities. Radio tracking of the orbiting spacecraft could measure periodic changes in the gravitational field. The detection of the periodic variations in the gravitational field of the larger mass redistribution that would occur if Europa has an ocean would also readily determine if indeed there was an ocean. Comparison of the periodic changes in the topography and gravity could provide information on the ice thickness and rheology.

MAPPING OF ICE THICKNESS AND INTERNAL STRUCTURE OF THE ICY SHELL

In explorations of Europa, spatial patterns of ice thickness and the internal structure of the ice shell are first-order scientific objectives. Thickness patterns reveal information about present dynamics, the origin of surface structures, and the relationship of the ice cover to the underlying ocean and/or the ocean floor. The internal structure of the shell also may hold clues to past dynamics as well as provide information on the geologic evolution of the shell since its formation.

The relatively simple dielectric behavior of pure ice means that high-frequency radar waves penetrate great thicknesses of cold ice with relatively little attenuation, allowing for the application of radar technologies to subsurface exploration. Geophysical applications of radar technology for subsurface exploration have been demonstrated on Earth over the past 30 years. Although there is a wealth of experience in the use of ground-and airborne-radar systems of this type, the technique has not yet been successfully used by Earth-orbiting spacecraft, let alone a spacecraft orbiting another planetary body.

Sounding radars with average powers of less than 200 watts have penetrated deep ice on the Greenland ice sheet.3 Indeed, the ice in some locations studied is greater than 3000 m thick. Earlier observations conducted in Antarctica with more powerful but less sophisticated radars successfully sounded ice approaching 5000 m in thickness.4 These techniques have been used to determine the locations of subsurface structures to an accuracy of 10 m, as has been verified experimentally with boreholes drilled through the ice to bedrock.5

The reason sounding-radar techniques work so well is that the wave velocity (or, equivalently, dielectric constant) depends most strongly on the density of the ice sheet, and there are well-established mixing formulas for estimating velocity given an ice density. For most parts of Greenland and Antarctica, important density variations are confined to the upper 100 or so meters of ice, and the shape of the densification curve is well understood. Consequently, small uncertainties in density with depth tend to be unimportant in the determination of ice thickness from radar data.



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