C/2013 US10 CATALINA FINSON-PROBSTEIN DIAGRAM

The motion of dust particles in a cometary environment is a complex process, and a precise description of the trajectories of grains within the coma requires adavnced hydrodynamic models, taking into account the interaction between gas and dust released from the surface. In the tail, dust and gas are decoupled and the only significant forces affecting the grain trajectories are the solar gravity and radiation pressure. Both forces depend on the square of the heliocentric distance but work in opposite directions. Their sum can be seen as a reduced solar gravity, and the equation of motion is simply m*a=(1-beta)*solar_gravity, where beta is the ratio radiation_pressure/solar_gravity, and is inversely proportional to the size of the grains for particles larger than 1 micron. From this relation, Finson & Probstein (1968) proposed a model which describes the full tail geometry with a grid of synchrones and syndynes; lines representing respectively the locations of particles released at a same time, or with the same beta. This model is simple because it considers only particles released in the orbital plane of the comet, and with zero initial velocity, but it provides a very good approximation of the shape of the tail, and has been used successfully to study many comets. One of the many strengths of this model is the possibility to date events in the tail. For instance, one can understand if regions of higher density are related to outbursts of the nucleus, or are a result of fragmentation of large chunks of material within the trail. It can also be used to disentangle between continuous activity, short outbursts, or impacts, when all these events produce a feature which at first look like a normal cometary tail.