We estimate that the moment of inertia of star A in the recently discovered double pulsar system PSR J0737-3039 may be determined after a few years of observation to ~10% accuracy. This would enable accurate estimates of the radius of the star and the pressure of matter in the vicinity of 1-2 times the nuclear saturation density, which would in turn provide strong constraints on the equation of state of neutron stars and the physics of their interiors.
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