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Hartle formalism for rotating Newtonian configurations

We apply the Hartle formalism to study equilibrium configurations in the framework of Newtonian gravity. This approach allows one to study in a simple manner the properties of the interior gravitational field in the case of static as well as stationary rotating stars in hydrostatic equilibrium. It is shown that the gravitational equilibrium conditions reduce to a system of ordinary differential equations which can be integrated numerically. We derive all the relevant equations up to the second order in the angular velocity. Moreover, we find explicitly the total mass, the moment of inertia, the quadrupole moment, the polar and equatorial radii, and the eccentricity of the rotating body. We also present the procedure to calculate the gravitational Love number. We test the formalism in the case of white dwarfs and show its compatibility with the known results in the literature.