  In order to understand the orbital history of Galactic halo objects, such as
globular clusters, authors usually assume a static potential for our Galaxy
with parameters that appear at the present-day. According to the standard
paradigm of galaxy formation, galaxies grow through a continuous accretion of
fresh gas and a hierarchical merging with smaller galaxies from high redshift
to the present day. This implies that the mass and size of disc, bulge, and
halo change with time. We investigate the effect of assuming a live Galactic
potential on the orbital history of halo objects and its consequences on their
internal evolution. We numerically integrate backwards the equations of motion
of different test objects located in different Galactocentric distances in both
static and time-dependent Galactic potentials in order to see if it is possible
to discriminate between them. We show that in a live potential, the birth of
the objects, 13 Gyr ago, would have occurred at significantly larger
Galactocentric distances, compared to the objects orbiting in a static
potential. Based on the direct N-body calculations of star clusters carried out
with collisional N-body code, NBODY6, we also discuss the consequences of the
time-dependence of a Galactic potential on the early- and long-term evolution
of star clusters in a simple way, by comparing the evolution of two star
clusters embedded in galactic models, which represent the galaxy at present and
12 Gyr ago, respectively. We show that assuming a static potential over a
Hubble time for our Galaxy as it is often done, leads to an enhancement of
mass-loss, an overestimation of the dissolution rates of globular clusters, an
underestimation of the final size of star clusters, and a shallower stellar
mass function.
