Comment on: “The photolytic stability of the Martian atmosphere” by R. C. Whitten and J.S. Sims

It is pointed out that the models given contain internal contradictions: they produce more O₂ than they destroy by factors of 100 or more.     

The occultation of Mariner 10 by Mercury

An analysis of the Mariner 10 dual frequency radio occultation recordings has yielded new information on the radius and atmosphere of Mercury. The ingress measurements which were conducted near 1.1° North latitude and 67.4° East longitude on the night side of the planet, gave a value for the radius of 2439.5 ± 1 km. Egress near 67.6° North latitide and 258.4° East longitude in the sunlit side yielded a radius of 2439.0 ± 1 km. The atmospheric measurements showed the electron density to be less than 10³ cm^?3 on both sides of the planet. From the latter result one may infer an upper limit to the dayside surface gas density of 10⁶ molecules per cm³.     

Comparison of calculational approaches for structural deformation in jointed rock

Results from five different computer models for structural deformation in jointed rock are compared for a problem involving stress-wave loading of a lined circular tunnel in a jointed medium. The computer models include two discrete element codes, The Direct Interacting Block Systems (DIBS) and The Universal Distinct Element Code (UDEC), and three finite element codes, The Finite Element Code for Largely Explicit Calculation (FLEX), The Explicit Calculations of Interacting Bodies Under Rapid Loading Code (EXCALIBUR), and PRONTO. The finite element codes used either slidelines or joint elements to simulate the motion on joints. All codes had some difficulties with a sequence of preliminary problems solved to ‘shake down’ the computer codes. However, most of the shortcomings of each code were readily overcome. Results showed that three codes could obtain similar answers for tunnel closure, stress around the tunnel and slip on the joints.     

Correlations between global features of terrestrial fields

Studies of correlation coefficients between different sets of global geophysical data may lead to useful inferences concerning their relationship or independence. If one data set is allowed to rotate with respect to another, the statistical theory is complicated and extra care is required before one can conclude that there is any statistical significance to a maximized correlation coefficient. If, for some relative rotation, two spherical harmonic fields are significantly correlated, then their individual degree component harmonics of dominant power must also be significantly correlated. Rotations can be found that result in high correlations between the dominant low-degree spherical harmonics of the geomagnetic and tertestrial gravity field potentials, but rotations can also be found that result in equally high, yet meaningless, correlations if the lunar gravity field is substituted for the geomagnetic field. To explain such high correlations, the theoretical correlation distribution function between normally distributed component harmonics is derived and then verified for lowdegree harmonics by using a Monte Carlo technique which takes into account the three-dimensional rotation group. Some curious properties surface: (1)the correlation distribution function for all possible relative orientations is almost the same between identical and uncorrelated fields; and (2)a system for determining the correlation distribution function from randomly selected fields or from randomly rotated fields is almost ergodic.     

A comparative study of Newtonian,Kustaanheimo/Stiefel,and Sperling/Burdet optimal trajectories

An optimal trajectory problem is formulated in each of three sets of equations, and the resulting solutions are numerically compared. The three formulations are the classical Newtonian (N), the Kustaanheimo/Stiefel (K/S), and the Sperling/Burdet (S/B). The last two solutions are first regularized by the classical Sundman technique and the K/S solution is transformed before the optimization problem is posed. A novel technique is developed for generating initial control vectors for each solution. Numerically generated derivatives (central differences) are used by a type of gradient, Newton-Raphson iterator to converge the two-point boundary value problems. The results indicate that, although the K/S and S/B formulations are more difficult to express mathematically than the Newtonian formulation, the transformed solutions are significantly more numerically stable than the Newtonian solution when the perturbing acceleration is less than a minimum value (T/W _o=0.05 for the particular example problem treated).     

Displaced mass,depth, diameter,and effects of oblique trajectories for impact craters formed in dense crystalline rocks

Empirical formulae are presented for calculating the displaced mass, depth, diameter, and effects of oblique trajectories for impact craters formed in dense crystalline rocks. The formulae are applicable to craters with diameters from approximately 10^?3–10³ cm that require, respectively, impact kinetic energies of approximately 10 to 10¹⁶ ergs for their formation. The experimental results are in poor agreement with Öpik’s theoretical calculations and raise questions on the validity of his theoretical model.