  Using a phenomenological form of the equation of state of neutron matter near
the saturation density which has been previously demonstrated to be a good
characterization of quantum Monte Carlo simulations, we show that currently
available neutron star mass and radius measurements provide a significant
constraint on the equation of state of neutron matter. At higher densities we
model the equation of state using polytropes and a quark matter model, and we
show that our results do not change strongly upon variation of the lower
boundary density where these polytropes begin. Neutron star observations offer
an important constraint on a coefficient which is directly connected to the
strength of the three-body force in neutron matter, and thus some theoretical
models of the three-body may be ruled out by currently available astrophysical
data. In addition, we obtain an estimate of the symmetry energy of nuclear
matter and its slope that can be directly compared to the experiment and other
theoretical calculations.
