  Using stellar structure calculations in the Hartle-Thorne approximation, we
derive analytic expressions connecting the ellipticity of the stellar surface
to the compactness, the spin angular momentum, and the quadrupole moment of the
spacetime. We also obtain empirical relations between the compactness, the spin
angular momentum, and the spacetime quadrupole. Our formulae reproduce the
results of numerical calculations to within a few percent and help reduce the
number of parameters necessary to model the observational appearance of
moderately spinning neutron stars. This is sufficient for comparing theoretical
spectroscopic and timing models to observations that aim to measure the masses
and radii of neutron stars and to determine the equation of state prevailing in
their interiors.
