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