  We determine an `empirical' kaon dispersion relation by analysing and fitting
recent experimental data on kaon production in heavy-ion collisions. We then
investigate its effects on hadronic equation of state at high densities and on
neutron star properties. We find that the maximum mass of neutron stars can be
lowered by about 0.4$M_\odot$, once kaon condensation as constrained by our
empirical dispersion relation is introduced. We emphasize the growing interplay
between hadron physics, relativistic heavy-ion physics and the physics of
compact objects in astrophysics.
