  Aims. Observations of solar protons near comet 67P/Churyumov-Gerasimenko
(67P) by the Rosetta spacecraft can be modelled by the planar motion in an
effective magnetic field proportional to 1/r^2. We aim to provide a thorough
study of such dynamics, with a clear description of the behaviour of an
incoming flux of particles. We will be able, then, to calibrate the free
parameters of the model to Rosetta observations.
  Methods. Basic tools of dynamical analysis are used. They lead to a
definition of the relevant parameters for the system and a classification of
the possible types of trajectories. Using the so-obtained formalism, the
structures formed by a flux of particles coming from infinity can be studied.
  Results. All the trajectories are parametrised by two characteristic radii,
rE and rC, derived from first integrals. There are three different types of
motion possible divided by a separatrix corresponding to rE = rC. An analytical
expression of the trajectories, defined by an integral, is developed. Using
this formalism, the application to a flux of particles coming from infinity
(modelling the incident solar wind) gives one free parameter only, the radius
rE, which scales the problem. A circular cavity of radius 0.28 rE is created,
as well as an overdensity curve (analogous to a caustic in optics). At each
observation time, rE can be calibrated to Rosetta plasma measurements, giving a
qualitative understanding of the solar particle dynamics (incoming direction,
cavity and density map). We also deduce that, in order to properly capture the
essence of the dynamics, numerical simulations of the solar wind around a comet
must use simulation boxes much larger than rE and grids much finer than rE.
