The Structure of Rotating Stars. I

A successive perturbation theory is established for the structure of stars in uniform rotation with a known law of energy generation. The first-order structure is computed for a rotating Cowling model with a law of energy generation $$\epsilon \,\propto \,\rho {T}^{17}$$ The results from a first-order model indicate that with the distribution of rotation velocities observed, rotation can produce a spread in luminosity of order half a magnitude in a mass-luminosity diagram, and of order half a magnitude for a given spectral type in a colour-magnitude array, this figure being for the most rapidly rotating Be stars.