The detection of low-mass transiting exoplanets in multiple systems brings new constraints to planetary formation and evolution processes and challenges the current planet formation theories .
Nevertheless , only a mere fraction of the small planets detected by Kepler and K2 have precise mass measurements , which are mandatory to constrain their composition .
We aim to characterise the planets that orbit the relatively bright star K2-138 .
This system is dynamically particular as it presents the longest chain known to date of planets close to the 3:2 resonance .
We obtained 215 HARPS spectra from which we derived the radial-velocity variations of K2-138 .
Via a joint Bayesian analysis of both the K2 photometry and HARPS radial-velocities ( RVs ) , we constrained the parameters of the six planets in orbit .
The masses of the four inner planets , from b to e , are 3.1 , 6.3 , 7.9 , and 13.0 \mathrm { M } _ { \oplus } with a precision of 34 % , 20 % , 18 % , and 15 % , respectively .
The bulk densities are 4.9 , 2.8 , 3.2 , and 1.8 g cm ^ { -3 } , ranging from Earth to Neptune-like values .
For planets f and g , we report upper limits .
Finally , we predict transit timing variations of the order two to six minutes from the masses derived .
Given its peculiar dynamics , K2-138 is an ideal target for transit timing variation ( TTV ) measurements from space with the upcoming CHaracterizing ExOPlanet Satellite ( CHEOPS ) to study this highly-packed system and compare TTV and RV masses .