  We tentatively look at anthropic constraints on the Cosmological Constant
(CC) \Lambda at galactic scales by investigating its influence on the motion of
the Sun throughout the Milky Way (MW) for -4.5 <= t <=0 Gyr. In particular, we
look at the Galactocentric distance at which the Sun is displaced at the end of
the numerical integration of its equations of motion modified in order to
include the effect of \Lambda as well. Values of it placing our star at its
birth at more than 10 kpc from the Galactic center (GC) are to be considered
implausible, according to the current views on the Galactic Habitable Zone
(GHZ) on the metallicity level needed for stars' formation. Also values
yielding too close approaches to GC should be excluded because of the risks to
life's evolution coming from too much nearby supernovae (SN) explosions and
Gamma Ray Bursts (GRB). We investigate the impact on our results of the
uncertainties on both the MW model's parameters and the Sun's initial
conditions, in particular the Hubble parameter H_0 and the Local Standard Rest
(LSR) speed \Theta_0 accurate at 2% and 6.2% level, respectively. While
H_0=70.1 km s^-1 Mpc^-1, \Theta_0=254 km s^-1 and \Lambda <= 10^-55 cm^-2
locates the place of birth of the Sun at 19.6 kpc from GC, the same values for
H_0 and \Lambda, and \Theta_0^max=270 km s^-1, places it at the plausible
Galactocentric distance of 8.5 kpc. \Lambda = 10^-54 cm^-2 and \Lambda = 10^-53
cm^-2 place the Sun at 10.6 kpc and 18.7 kpc, respectively.

General Relativity and Quantum Cosmology;Astrophysics of Galaxies;High Energy Physics - Phenomenology;Space Physics