  It is well known that, from the Newtonian point of view, the Lagrangian point
$L_4$ in the circular restricted three body is stable if $\mu<
\frac{1}{18}(9-\sqrt{19})\approx 0.03852$. In this paper we will provide a
formula that allows us to compute the eigenvalues of the matrix that determines
the stability of the equilibrium points of a family of ordinary differential
equations. As an application we will show that, under the relativistic
framework, the Lagrangian point $L_4$ is also stable for the Sun-Earth system.
Similar arguments show the stability for $L_4$ not only for the Sun-Earth
system but for systems coming from a range of values for $\mu$ similar to those
in the Newtonian restricted three body problem.
