Recall that the condition equations for minimization of the distance is a pair of eighth-order bivariate polynomials, which we must solve to find the distance minima. The zeros of these equations yield distance maxima and saddle points in addition to the minima. The number of zeros cannot currently be determined, although one can (using algebraic geometry) place an upper bound of 16 for the orbit-orbit distance equations. To date, the maximum number of zeros found after searching many thousands of test cases is 12. The number of independent free parameters (quantities such as orbital eccentricities, inclinations, etc.) constitutes a six-dimensional search space, which is clearly impossible to explore systematically. However, it so happens that the computational method of genetic algorithms (GA) is well suited for exactly this type of problem. Hence, Murison is working on a numerical program that will use GA to find the regions of parameter space that yield large numbers of zeros. Thereby, he will test numerically the theoretical upper bound of 16 zeros, as well as (and more importantly) characterize the types of real-world orbits by their number and types of zeros.
With the rest of the AA department, Murison consumed a week or so moving offices to Bldg. 1.
Murison continues to work with the USNO FTS project in a mostly-advisory role.
Murison's duties as DDA Secretary have begun their annual pre-meeting ramp-up.
