  We give an effective bound on how much time orbits of a unipotent group $U$
on an arithmetic quotient $G/\Gamma$ can stay near homogeneous subvarieties of
$G /\Gamma$ corresponding to $\mathbb Q$-subgroups of $G$. In particular, we
show that if such a $U$-orbit is moderately near a proper homogeneous
subvariety of $G/\Gamma$ for a long time it is very near a different
homogeneous subvariety. Our work builds upon the linearization method of Dani
and Margulis.
  Our motivation in developing these bounds is in order to prove quantitative
density statements about unipotent orbits, which we plan to pursue in a
subsequent paper. New qualitative implications of our effective bounds are also
given.
