  The moment of inertia of the pulsar A in the neutron star binary J0737-3039
will soon be measurable through detailed measurements of the periastron
advance. We present the calculation of the moment of inertia of neutron stars
with the masses of the components of the binary J0737-3039 for a broad range of
equations of state of dense matter and discuss the implications of such
measurement for constraining the equation of state. An observational
determination of the moment of inertia of the pulsar A in J0737-3039 with the
accuracy of 10% shall narrow down considerably the range of viable equations of
state. We also show that limits on maximal mass of a neutron star provide a
complementary set of constraints on the properties of dense nuclear matter.
