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Basalts are understood to be derived by partial melting from the mantles of their planets, and properties of the basalt samples we have been able to obtain (from Earth, the Moon, and the parent planets of the basaltic achondrite meteorites) have been an invaluable source of information about the composition and nature of the mantles of these bodies (Chapter 3). There is little doubt that basaltic volcanism has also been active on the planets that we have not been able to sample; in several cases, the surface morphologies and photometric properties of these planets strongly indicate the action of basaltic volcanism (Chapters 5 and 2). The purpose of this chapter is to infer as much as we can, by means other than sampling, about the compositions of planetary mantles. Our estimates of mantle compositions provide a basis for experimental petrologists to project the possible compositions of basalts that would be erupted on unsampled planets (Chapter 3). The clues we have to mantle compositions, apart from directly sampling them and the basalts that issue from them, are (I) the gross geophysical properties of the planets in question and (2) our estimates of their bulk compositions. Fragmentary chemical information comes to us from sources such as spectral studies of planetary atmospheres and surface regoliths, but most of our chemical constraints are based on broader considerations of the overall composition of the solar system and the early processes that appear to have caused the terrestrial planets to incorporate varying proportions of the elements. The geophysical constraints are reviewed in section 4.2, below; the admittedly speculative question of chemical processes that affected the origin and bulk compositions of the planets (cosmochemistry) is treated in section 4.3. Section 4.4 describes the process of planetary modelling by which the most probable mantle compositions, or compositional profiles, are derived from these inputs. Finally, section 4.5 carries out thi

A world-wide estimate of the gravity field, based on all available gravimetry and extended by Markov analysis using correlation with elevation, was combined with an estimate of the geoid based on astro-geodetic data covering 19% of the earth and with secular and long period variations of the 1957 Beta and 1958 Beta satellite orbits, into a generalization of least-squares adjustments taking correlation into account. The value obtained for the quadratic sum indicated that the estimates of variance and covariance should be increased about 44%. The results obtained include: Equatorial radius, 6378163 + or - 21 m; Flattening, 1/298.24 + or - 0.01; Equatorial gravity, 978043.6 + or - 1.2 milligals (Potsdam system); Datum shifts (with three-dimensional standard deviation) for the Americas system, + or - 35 m; Europe-Africa-Siberia-India system, + or - 38 m; Japan-Korea-Manchuria system, + or - 68 m; Coefficients in the spherical harmonic expression of the gravity field up to the 8th degree; and World-wide geoid heights, with standard deviations varying from + or - 10 m to + or - 22 m. (Author)

Mathematical developments of the gravitational effects of the sun and moon on a close satellite were made. The developments were made as a result of attempts to adapt to a form convenient in analyzing close satellite orbits for terrestrial gravitational field variations. The disturbing functions are expressed in osculating Keplerian elements for use in equations of motion. (Author)