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We calculate stationary configurations of rapidly rotating compact stars ingeneral relativity, to study the properties of circular orbits of testparticles in the equatorial plane. We search for simple, but precise,analytical formulae for the orbital frequency, specific angular momentum andbinding energy of a test particle, valid for any equation of state and for anyrotation frequency of the rigidly rotating compact star, up to themass-shedding limit. Numerical calculations are performed using precise 2-Dcodes based on multi-domain spectral methods. Models of rigidly rotatingneutron stars and the space-time outside them are calculated for severalequations of state of dense matter. Calculations are also performed for quarkstars consisting of self-bound quark matter. At the mass-shedding limit, therotational frequency converges to a Schwarzschildian orbital frequency at theequator. We show that orbital frequency for any orbit outside equator is alsoapproximated by a Schwarzschildian formula. Using a simple approximation forthe frame-dragging term, we obtain approximate expressions for the specificangular momentum and specific energy on the corotating circular orbits in theequatorial plane of neutron star, which are valid down to the stellar equator.The formulae recover reference numerical values with typically 1% of accuracyfor neutron stars with M > 0.5 M_sun. They are less precise for quark starsconsisting of self-bound quark matter.

Approximate analytic expressions for circular orbits around rapidly rotating compact stars