To precisely calculate the motion of dust particles in a cometary environment 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. The resulting force is equivalent to a reduced solar gravity, and the equation of motion of a grain is simply:
beta is the ratio radiation_pressure/solar_gravity, and is inversely proportional to the size of grains 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 only considers particles released in the orbital plane of the comet with no initial velocity, yet provides a very good approximation of the shape of the tail, and has been used successfully to study many comets.
One of its many strengths is the possibility to date events in the tail, for instance to determine if tail structures are related to outbursts or impacts on the nucleus, vs coninuous emission.
Vincent et al (ACM, 2014).
Finson, M. L., Probstein, R. F., 1968, A theory of dust comets. I. Model and equations, AJ, 154, 353–380
Vincent, J.-B., Comet-toolbox: numerical simulations of cometary dust tails in your browser, Asteroids Comets Meteors conference, 2014, Helsinki, (pdf).