Gross-fragmentation of meteoroids and bulk density of Geminids from photographic fireball records

The explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid moving in any actual atmosphere was published several years ago. The solution yields the theoretical relation of l, the distance flown by the meteoroid in its trajectory, as a function of time, t, assuming that the height, h, is a known function of l. The photographic records of meteors and fireballs are coded by time marks, using a rotating shutter or a similar device to break the moving image. Time is, thus, the independent variable and for each time mark on a meteoroid trajector, the observed distance along the trajectory, l sub obs, as well as the double- or multiple- station photographs of the same meteoroid. Applying this solution to all available Prairie Network (PN) fireball-records, we recognized that the majority of them gave good solutions with standard deviations somewhat bigger than the intrinsic geometrical precision of the data. We also noticed that, on an average, previous methods of evaluation of the meteoroid velocities (interpolation polynomials, numerical differenciation of the observed l sub obs) used up to only several tens of percent of the intrinsic precision of the PN observational data. When residuals of these solutions, i.e. l sub obs - l sub com, were represented as a function of time for about 75 percent of solutions. The remaining 25 percent of residuals showed systematic changes with time exceeding one standard deviation. We tried to explain these systematic time course of residuals by using different meteoroids first computed theoretically and then analyzed by the same model as the natural PN fireballs were. The conclusion of these model computations is that systematic time changes of residuals in the nonfragmenting model exceeding one standard of deviation are caused by sudden gross fragmentation at one or more trajectory points. Thus, we generalized the explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid by allowing for one or more points, where sudden gross fragmentation can occur. Using this generalized solution, the distances along the meteoroid trajectory can be computed for any choice of input parameters and compared with the observed distances flown by the meteoroid. For the most precise and long fireball trajectories, the least-squares solution can, thus, yield the initial velocities, the ablation coefficients, the dynamical masses, the positions of gross-fragmentation points, and the t