The gasdynamic convected magnetic field model for predicting solar wind flow past a planetary magnetoionopause obstacle has been extended to three dimensions to apply to obstacles of nonaxisymmetric shape. The need for such an extension is of first-order importance for Jupiter and Saturn because the effects of rapid spin, large size, and substantial ring current phenomena are believed to cause the magnetospheres of these planets to be significantly broader near the planetary equatorial plane than near the noon-midnight polar meridian plane. Direct observational determination of such asymmetries for Jupiter and Saturn has not been possible, however, because only a limited amount of data are available from four spacecraft at Jupiter and three at Saturn, all of which followed flyby trajectories at fairly low latitudes. With the aid of the new three-dimensional model, it is now possible to infer the degree of flattening of the magnetospheric cross sections from a knowledge of the locations of the low-latitude magnetopause and bow shock crossings. In this paper, the computational procedures of the new model are described, and calculated results are presented for a number of magnetospheres of elliptic cross sections with values ranging from 1 to 2 for the ratio a/b of major (equatorial) to minor (polar) axes. This range is sufficient to include values appropriate to both Jupiter and Saturn. Comparisons of the model results with the locations of observed crossings of the magnetopause and bow shock directly provide an estimate of the degree of equatorial broadening of the magnetospheric cross section for each of these planets.

For Jupiter, the results indicate a broadening to a/b~1.75, a value consistent with previous estimates determined from independent calculations of the three-dimensional magnetosphere shape formed by adding to the planetary dipole field the magnetic field of an equatorial current sheet selected so as to match the observed Jovian magnetic field near the equatorial plane. For Saturn, a similar comparison indicates a smaller broadening to a/b~1.25. The determination is less certain than for Jupiter, however, because of the smaller amount and greater scatter of the available data. ¿ American Geophysical Union 1989