  We derive analytic approximations for the neutrino luminosities and the heat
capacities of neutron stars with isothernal nucleon cores as functions of the
mass and radius of stars. The neutrino luminosities are approximated for the
three basic neutrino emission mechanisms, and the heat capacities for the five
basic combinations of the partial heat capacities. The approximations are valid
for for a wide class of equations of state of dense nucleonmatter. The results
significantly simplify the theoretical interpretation of observations of
cooling neutron stars as well as of quasistationary thermal states of neutron
stars in X-ray transients. For illustration, we present an analysis of the
neutrino cooling functions of nine isolated neutron stars taking into account
the effects of their magnetic fields and of the presence of light elements in
their heat blanketing envelopes. These results allow one to investigate the
superfluid properties of neutron star cores.
