| Summary: | <p>The solutions of the equations of motion for a point mass particle under a conservative force field are generally constrained by a basic set of integrals of motion, which depend on the knowledge about the potential function and on time and space properties and symmetries satisfied by the dynamical system. The epicycle approximation is a particular case of integration of the equations of motion under a minimum set of hypotheses, such as symmetry plane and axial symmetry, allowing to obtain solutions for nearly circular orbits in the three dimensional space. Under this approach, any orbit projected onto the symmetry plane describes an ellipse with origin at a guiding centre or epicentre, which moves uniformly in a circular orbit around the centre of the system. The approach is easy to model and allows to visualise the contribution of several parameters to the shape of the orbits, being an excellent example of how education and learning of science can take profit of mathematical modelling.</p>
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