Context : Increasing our knowledge of the interior structure , composition and density distribution of exoplanets is crucial to make progress in the understanding of exoplanetary formation , migration and habitability .
However , the directly measurable mass and radius values offer little constraint on interior structure , because the inverse problem is highly degenerate .
Therefore there is a clear need for a third observable of exoplanet interiors .
This third observable can be the k _ { 2 } fluid Love number which measures the central mass concentration of an exoplanet .

Aims : The aims of this paper are ( i ) to develop a basic model to fit the long-term radial velocity and TTV variations caused by tidal interactions , ( ii ) to apply the model to the WASP-18Ab system , and ( iii ) to estimate the Love number of the planet .

Methods : Archival radial velocity , transit and occultation timing data are collected and fitted via the model introduced here .

Results : The best model fit to the archival radial velocity and timing data of WASP-18Ab was obtained with a Love number of the massive ( \sim 10 M _ { \mathrm { Jup } } ) hot Jupiter WASP-18Ab : k _ { 2 ,Love } = 0.62 ^ { +0.55 } _ { -0.19 } .
This causes apsidal motion in the system , at a rate of \sim 0.0087 \pm 0.0033 ^ { \circ } / \mathrm { days } \approxeq 31.3 \pm 11.8 arcseconds/day .
When checking possible causes of periastron precession , other than the relativistic term or the non-spherical shape of the components , we found a companion star to the WASP-18 system , named WASP-18B which is a probable M6.5V dwarf with \sim 0.1 ~ { } M _ { \odot } at 3519 AU distance from the transit host star .
We also find that small orbital eccentricities may be real , rather than an apparent effect caused by the non-spherical stellar shape .

Conclusions :