An improved model of Martian global topography has been obtained by fitting a sixteenth-degree harmonic series to occultation, radar, spectral, and photogrammetric measurements. The existing observations have been supplemented in areas without data by empirical elevation estimates based on photographic data. The mean radius is 3389.92 4-0.04 km. The corresponding mean density is 3.9331 4-0.0018 g cm -8. The center of figure is displaced from the center of mass by 2.50 4-0.07 km toward 62 ø 4-3øS, 272 ø 4-3øW. The geometric flattening (fs = (6.12 4-0.04) X i0 -8) is too great and the dynamic flattening (fd • (5.22 4-0.03) X 10 -8) is too smal I for Mars to be homogeneous and hydrostatic. It is confirmed that the low-degree gravity harmonics are produced primarily by surface height variations and only secondarily by lateral density variations. Maps of the data distribution, global topography, and Bouguer gravity anomaly are presented. These are interpreted in terms of a crustal thickness map which is consistent with gi'avity, topography, and recent preliminary Viking seismic results. From plausible density contrasts and an assumed zero crustal thickness at Hellas, the inferred minimum mean crustal thickness is 28 4-4 km. DATAThe basic data used in this analysis are identical to those used by Christensen [1975]. They consist of occultation and spectral measurements from Mariner 9 and earth-based radar data. The occultation measurements yield absolute distances of surface points from the center of mass. All the other data are only relative. Christensen [1975] solved for and minimized the biases between the various reference surfaces and thus produced a unified data set. Figure 1 indicates the approximate distribution of this data, summarized according to 5 ø X 5 ø tesserrae or bins. An important aspect of this distribution is its uneven character. Only 1381 of the 2592 bins, representing 68.5% of the total surface area, contain any data. Even among these the number and quality of measurements vary widely, from only one measurement per bin in some high-latitude regions, to over a hundred measurements per bin in the low southern latitudes. Carlson and Helmsen [1969] have shown that it is the unevenness, rather than the sparsity, of the data distribution which causes the greatest difficulty in obtaining reliable estimates of harmonic coefficients. It is primarily in our treatment of this problem that our analysis differs from Christensen's. In a similar analysis of lunar topography [Bills and Ferrari, 1977a] we have relied on a linear autoregressive interpolation scheme to obtain estimates in the regions without data of the most probable elevations and associated errors, consistent with the known statistical characteristics of the available data.This process minimizes the expected mean square error of the estimates, but unfortunately, it totally ignores the actual topography in the unmeasured regions. Fortunately, in the case of Mars we can do better.Wu [1977] has used essentially the same data set, in conjunction wi...

Abstract.A

Doppler tracking data from Lunar Orbiter 4 have been combined with laser ranging data from lunar retroreflectors to yield a number of geophysical and geodetic parameters for the earth and moon. This joint solution gives values of (1) the lunar principal polar moment C/MR2 = 0.3905 ± 0.0023, (2) GME = 398600.461 ± 0.026 km3/s2, and (3) an earth/moon mass ratio at 81.300587±0.000049. Also determined are the harmonics of a complete lunar gravity field through degree and order 5, the obliquity of the lunar pole, selenocentric coordinates of the lunar retroreflectors, geocentric coordinates of the McDonald Observatory, and the lunar secular acceleration. The lunar potential Love number is weakly determined at 0.022±0.013, and a surprisingly large dissipation of rotational energy is inferred, though either solid body tidal dissipation or liquid core mantle interactions could be causes.

No abstract

An improved model of lunar global gravity has been obtained by fitting a sixteenth‐degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface. To compensate for the irregular selenographic distribution of these data, the solution algorithm has also incorporated a semi‐empirical a priori covariance function. Maps of the free‐air gravity disturbance and its formal error are presented, as are free‐air anomaly and Bouguer anomaly maps. The lunar gravitational variance spectrum has the form V(G; n) = O(n−4), as do the corresponding terrestrial and martian spectra. The variance spectra of the Bouguer corrections (topography converted to equivalent gravity) for these bodies have the same basic form as the observed gravity (V(ΔG; n) = O(n−4)), and, in fact, the spectral ratios σn (ΔG )/σn(G) are nearly constant throughout the observed spectral range for each body. Despite this spectral compatibility, the correlation between gravity and topography is generally quite poor on a global scale.