In this paper I deal with the WD0137-349 binary system consisting of a white dwarf ( WD ) and a brown dwarf ( BD ) in a close circular orbit of about 116 min .
I , first , constrain the admissible range of values for the inclination i by noting that , from looking for deviations from the third Kepler law , the quadrupole mass moment Q would assume unlikely large values , incompatible with zero at more than 1-sigma level for i \lesssim 35 deg and i \gtrsim 43 deg .
Then , by conservatively assuming that the most likely values for i are those that prevent such an anomalous behavior of Q , i.e .
those for which the third Kepler law is an adequate modeling of the orbital period , I obtain i = 39 \pm 2 deg .
Such a result is incompatible with the value i = 35 deg quoted in literature by more than 2 sigma .
Conversely , it is shown that the white dwarf ’ s mass range obtained from spectroscopic measurements is compatible with my experimental range , but not for i = 35 deg .
As a consequence , my estimate of i yields an orbital separation of a = ( 0.59 \pm 0.05 ) R _ { \odot } and an equilibrium temperature of BD of T _ { eq } = ( 2087 \pm 154 ) K which differ by 10 \% and 4 \% , respectively , from the corresponding values for i = 35 deg .