Diffusion-deposition patterns in Martian streaks

The spreading angle of a number of light and dark Martian streaks is determined from selected Mariner 9 images. The resulting frequency distributions of spreading half-angles have maxima at ～5° for light, and ～7° for dark streaks; however the dark streaks have a secondary maximum spreading angle at ～14°. The smaller values, which include most streaks, are interpreted as crater-wake spreading phenomena. The larger value, found in only a few dark streaks or “tails,” may result from atmospheric diffusion and subsequent deposition of material from isolated sources such as vents or blowouts. An atmospheric diffusion-deposition analysis is presented, assuming this streak origin, from which it is possible to deduce the eddy diffusivity, K, in Mars' boudary layer. Calculated K values are found to agree with various theoretical estimates. They lie in the range 10⁷ and 10⁹ cm² sec^?1 and exhibit the proper scale dependence. Thus it appears that, in addition to streak-derived wind direction patterns and speed information, it is possible in a few cases to derive information on Mars' boundary-layer turbulence from streak-spreading measurements.     

Thermal structure of the Martian atmosphere during the dissipation of the dust storm of 1971

The secular variation of the thermal structure of the Martian atmosphere during the dissipation phase of the 1971 dust storm is examined, using temperatures obtained by the infrared spectroscopy investigation on Mariner 9. For the latitude range ?20° to ?30°, the mean temperature at the 2mbar level is found to decrease from approximately 220 K in mid-December 1971 to about 190 K by June 1972 while for the 0.3mbar level a decrease from 203 K to 160 K is observed. Over the same period, the amplitude of the diurnal temperature wave also decreased. Assuming a simplified radiative heating model, the dust optical depth is found to decrease approximately exponentially with an e-folding time of about 60 days at both the 0.3 and 2mbar levels. Stokes-Cunningham settling alone cannot account for this behavior. Sedimentation models which include both gravitational settling and vertical mixing are developed in an effort to explain the time evolution of the dust. Within the framework of a model which assumes an effective vertical diffusivity K independent of height, a mean dust particle diameter of ～2 μm is inferred. To provide the necessary vertical mixing, K ? 10⁷ cm²sec^?1 is required in the lower atmosphere.     

Velocity-space maps and transforms of tracking observations for orbital trajectory state analysis

The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction. External observations of orbital vehicles, such as provided by optical and radar sensors of tracking systems, are transformable into corresponding velocity state maps, as presented in this paper. These transformations and the consequent state maps are essential for development of the orbit observation matrix used with the unified state matrix, in recursive estimators such as the Kalman filters. Line-of-sight rays and range spheres (or hemispheres) of observations map conformally into orthogonal spherical surfaces in velocity space, as the result of the point-contact transformations. In bispherical coordinates, the field of observation maps for a ground-based tracking system site is shown to be a reduced (or degenerate) form of the general field of observation maps for a satellite-based tracking site. These orbital state maps and transforms are directly useful in development of observation matrices for candidate observation sets, such as range only, angle only, or range plus range-rate tracking schemes. Also, surface coverage patterns can be generated for proposed new tracking systems, in mission analysis and system synthesis studies.