  We have investigated whether the Scalar-Tensor-Vector Gravity theory (STVG)
may explain the kinematic of stars in dwarf spheroidal galaxies. STVG modifies
General Relativity by adding extra scalar and vector fields with the main aim
of replacing dark matter in astrophysical self-gravitating systems. The
weak-field limit of STVG brings a Yukawa-like modification to the Newtonian
gravitational potential. The modification is modulated by two parameters,
$\alpha$ and $\mu$, that represent a redefinition of the gravitational coupling
constant and the mass of the additional vector fields, respectively. Thus,
adopting the modified gravitational potential arising in the weak-field limit
of STVG, we have solved the spherical Jeans equation to predict the
line-of-sight velocity dispersion profiles of eight dwarf spheroidal galaxies
orbiting around the Milky Way. The predicted profiles are then compared to the
data using a Monte Carlo Markov Chain algorithm. Our results pointed out some
tensions on the $\alpha$ parameter within the data set, while comparison with
previous analysis shows the effectiveness of STVG in replacing dark matter with
extra massive fields. Further improvements will require more sophisticated
modelling of the line-of-sight velocity dispersion which will be possible as
soon as high-precision astrometric data in dwarf spheroidals will become
available.
