Mars physical parameters as determined from Mariner 9 observations of the natural satellites and Doppler tracking

Abstract

Spherical harmonic coefficients of the Mars gravity field to degree 6, mass, spin‐axis direction, and the orbits of Phobos and Deimos were determined from radio and optical data obtained by the Mariner 9 spacecraft. The optical data consist of 62 TV photographs of Phobos and Deimos. The radio data are in the form of apoapsis state vectors obtained from 195 one‐revolution fits of the Doppler data. A first‐order analytical theory was used to model the motion of both the satellites and the spacecraft. However, the resonance arising from the fact that the orbital period of Mariner 9 was very close to ½ day necessitated development of a partial second‐order theory to model the long‐period perturbations by even‐order tesseral harmonics. Results for the spherical harmonic coefficients are in good agreement with those previously published from Mariner 9 Doppler data. The value obtained for the gravitational constant of Mars (42,828.1±0.5 km3/s2) is in excellent agreement with prior determinations from Mariner flyby trajectories. The direction of Mars' rotational pole relative to the earth's mean equinox and equator of 1950 is given by α = 317.3°±0.1°, δ = 52.7°±0.1°. The longitudes for Phobos and Deimos at the time of Mariner 9 Mars orbit insertion were found to be 0.2° less and 0.3° greater, respectively, than the longitudes predicted for this epoch by A. T. Sinclair (1972) on the basis of a recent processing of earth‐based data obtained for the satellites during 1877–1969.

Effect of resonance-oblateness coupling on a satellite orbit

“…This agrees well with Born (1974). On the other hand the indirect effect from Equation (13) is calculated as:…”

“…This amplitude is somewhat greater than the amplitude of the periodic part of the resonant-resonant interaction (Born, 1974). It also appears to be sufficient to explain the remaining discrepancy of the Mariner 9 theory (for the node) with numerical integration.…”

“…These effects are entirely analogous to those here. Born (1974) has worked out coupling effects of order (Jtm n// )2 from the interaction of periodic resonant terms with themselves. This was done for the analytic theory of the Mariner 9 Mars orbiter (n ~-2 revs/day) which had a shallow resonant period of 18 days.…”

Strength of Martian lithosphere beneath large volcanoes

“…Several spherical harmonic models of the surface topography of Mars have been presented in the last two decades or so. Using Earth-based radar ranges, Mariner 9 occultation timing, and photogrammetry data, Christensen [1975] As more Doppler data became available, spherical harmonic models of the Martian gravity field that included harmonics of degree and order up to 9 were developed using different procedures [Lorell et al, 1973;Born, 1974;$jogren et al, 1975;Gapcynski et al, 1977]. After the two Viking spacecraft, gravity field models were derived on the basis of both Mariner 9 and Viking measurements that included harmonics of degree and order shows that the conclusion is also valid for Martian topography which is 3-4 times more dynamic than the lunar topography.…”

The atmosphere of Mars

“…The figure of Mars' equipotential surface is complex enough (Born, 1974). Besides that, the heights of the different parts of the physical surface vary both on a large and a small scale relative to the equipotential surface.…”