Shape and Orientation of Mercury from Radar Ranging Data

Abstract

If Mercury's radius is expanded in Legendre functions to the second degree and order, the systematic error in radar ranging can be reduced significantly. We interpret the expansion coefficients in terms of a best-fit ellipsoid displaced with respect to the center of mass in the equatorial plane. The ellipsoid's principal axes are rotated in the equatorial plane such that the long axis is aligned with cartographic longitude 15.3° ± 2.9° (west). The pole location is consistent with the IAU pole, normal to Mercury's orbital plane. There is a significant equatorial ellipticity (a−b)/a= (540 ± 54) × 10−6. The center of figure is offset from the center of mass (C.F.–C.M.) by 640 ± 78 m in the equatorial plane in the direction of cartographic longitude 319.5° ± 6.9°. The magnitude of the equatorial center of figure offset implies an excess crustal thickness of 12 km or less, comparable to the Moon's excess. By comparing the equatorial ellipticity with the Mariner 10 gravity coefficientC22, and assuming Airy isostatic compensation, we conclude that Mercury's crustal thickness is in the range from 100 to 300km.