Abstract
This work presents a study on how techniques provided by the algebraic manipulation software Mathematica can be used in planetary dynamics investigations. The discovery of extra-solar planets orbiting other stars has been one of the major breakthroughs in astronomy of the past decades, changing our view on the features of planetary systems, mainly drawn from the observation of the Solar System. Today, over 1000 exoplanets are known and the Kepler satellite has recently identified over 3000 additional candidates, most of them still waiting for confirmation. We have learned that exoplanets are much more diverse when compared to our own Solar System. Thus, the implementation of advanced manipulation techniques can be of great importance for the investigation of such unusual configurations of these new worlds. We chose Mathematica, a software that has been increasingly used worldwide due to its great analysis power. The case that we focus is the 2/1 mean-motion resonance in the two-planet systems. Based on the Mathematica platform, we present animations of the orbits of the Neptune-Pluto system and exoplanets in the 2:1 mean-motion resonance over a short-period of time. The visualization of this problem can be very important to an initial understanding of dynamical proprieties of resonant planetary systems and their stability.
