Gravity in space and the dimensions and mass of the Earth

Closed formulas for the gravity field of a rotating triaxial ellipsoid have not heretofore been computed, although approximate formulas containing terms which are functions of the longitude have been derived. Using data from satellites we have computed the ellipticity of the earth's equator (supposed elliptic) and also the longitudinal terms of the outer gravity field. Adopting the Pizzetti-Somigliana method we have obtained the field of a triaxial rotating ellipsoid in closed form using elliptic integrals and also to the first order of the equatorial flattening without the use of these integrals. On the basis of these results and the recent gravity data taken around the equator between the longitudes 50° to 100°E, 155° to 180°E, and 145° to 180°W, we question the advantage of using a triaxial gravity formula in geodesy. Closed formulas for the field of a rotating biaxial ellipsoid are also derived in polar coordinates and the parameters are specialized to give the International Gravity Formula values on the International Ellipsoid. By means of these formulas, and using the present gravity information, we obtain MG = 3.98603 × 1020 g cm sec.