  In this paper we show two examples of numerical orbital integrations (Planar
Circular Restricted Three Body Problem) in which even though the conservation
of Jacobi's constant is near to 1 part in 10e8, the integration proves to be
wrong. That is, for some particular cases the Jacobi's constant is insensitive
to very important qualitative (not quantitative) changes in the integrated
orbit which are produced by numerical errors. We provide specific
recomendations to test and ensure that a numerical code is working properly,
regardless the numerical method employed.
