  Stellar radial velocities play a fundamental role in the discovery of
extrasolar planets and the measurement of their physical parameters as well as
in the study of stellar physical properties. We investigate the impact of the
solar activity on the radial velocity of the Sun using the HARPS spectrograph
to obtain measurements that can be directly compared with those acquired in the
extrasolar planet search programs. We use the Moon, the Galilean satellites,
and several asteroids as reflectors to measure the radial velocity of the Sun
as a star and correlate it with disc-integrated chromospheric and magnetic
indexes of solar activity that are similar to stellar activity indexes. We
discuss in detail the systematic effects that affect our measurements and the
methods to account for them. We find that the radial velocity of the Sun as a
star is positively correlated with the level of its chromospheric activity at
about 95 percent significance level. The amplitude of the long-term variation
measured in the 2006-2014 period is 4.98 \pm 1.44 m/s, in good agreement with
model predictions. The standard deviation of the residuals obtained by
subtracting a linear best fit is 2.82 m/s and is due to the rotation of the
reflecting bodies and the intrinsic variability of the Sun on timescales
shorter than the activity cycle. A correlation with a lower significance is
detected between the radial velocity and the mean absolute value of the
line-of-sight photospheric magnetic field flux density. Our results confirm
similar correlations found in other late-type main-sequence stars and provide
support to the predictions of radial velocity variations induced by stellar
activity based on current models.
