In this work, we present an approach taking into account the single-averaged equations and unaveraged equations to investigate the dynamics of artificial satellites on the effect due to the non-spherical shape of the planet Mercury. An analysis considering the long-period terms and another taking into account the short-period terms is presented. The numerical integrations of the equations developed are performed using the Maple software. We consider the numerical values of the most updated spherical harmonic coefficients in the literature. Emphasis is given to analyze the effect of the C22 term in the dynamics of the spacecraft. We show that the two techniques are in agreement (average or not average). We found orbits that librates around an equilibrium point with small variation of the orbital elements, in particular the eccentricity and argument of the pericenter. We also note that the C22 term contributes to reduce the growth of the orbital eccentricity.