In this work we study some numerical results about a family of periodic orbits of the Restricted Three Body Problem (RTBP). The family considered is one of the Lyapunov families related to the equlibrium point $L_5$. More concretely, we deal with the family related to the vertical oscillations around this point. Here we present a study of the normal behaviour of this family for several values of the mass parameter $\mu$. We focus on the case in which $\mu$ tends to zero (note that $\mu=0$ is a degenerate case), and we identify the orbits for $\mu=0$ (they are Keplerian orbits around the primary) that give rise to the vertical family when $\mu\ne 0$.