EFFECTS OF DISCRETE-SOURCE OUTGASSING ON MOTIONS OF PERIODIC COMETS AND DISCONTINUOUS ORBITAL ANOMALIES

Almost 300 determinations of the Style II nongravitational parameters A1 and A2 have been collected from published orbital solutions for 43 periodic comets observed at five or more apparitions. Upon integrating the law for the nongravitational forces (assumed to be symmetrical with respect to perihelion) over the orbital period of a comet, A2 and A1 measure, respectively, the total effects of these forces on the comet's mean motion and its longitude of perihelion. Interpreting the perturbations as products of the momentum transferred to the comet's mass by sublimation of water ice from a small, localized source on the rotating nucleus, isoline maps of A2 and A1 are presented for a baseline model as functions of the parameters of the inertially fixed spin vector and the source's location-dependent thrust angle. The baseline model assumes the absence of sublimation lags, in which case the perturbations are independent of the sense of nucleus rotation and the nongravitational parameters for any given values of the comet's mass, the outgassing area, and the outflow velocity can be scaled. Both the radial and the transverse components contribute, in general, significantly to the perturbation of the mean motion. Whether the comet is accelerated or decelerated is determined by the position of its spin vector and by the source's hemispherical location. An acceleration correlates with a greater production of water before perihelion and a deceleration with a greater production after perihelion, in substantial agreement with evidence presented by Festou et al. [Nature, 345, 235 (1990)] and [Asteroids, Comets, Meteors III (Uppsala University, Uppsala, 1990), p. 313] Contrary to their conclusions, however, no universal relationship is found between the magnitudes of the dynamical effect and the production asymmetry. The parameters A1 and A2 for a collection of sources are equal to the sum of their values for the individual contributors, thus depending upon the source distribution. The model is consistent with even the most extreme among the detected perturbations, including the instances of rapid temporal changes in A2 and the discontinuous orbital anomalies, which are interpreted as products of a sudden redistribution of the transferred momentum due to episodic activation of short-lived sources. It appears that lifetimes of active regions vary considerably from case to case and that forced precession of the nucleus strongly influences the comet's activity pattern.