The search for a universal solution of the equations of motion for a satellite orbiting an oblate planet is a subject that has merited great interest because of its theoretical and practical implications. Here, a complete first- order perturbation solution, including the effects of the J2 terms in the planet's potential, is given in terms of standard orbital parameters. The simple formulas provide a fast method for predicting satellite orbits that is more accurate than the two-body formulas. These predictions are shown to agree well with those of a completely numerical code and with actual satellite data. Also, in an appendix, it is rigorously proven that a satellite having negative mechanical energy remains for all time within a spherical annulus with radii approximately equal to the perigee and apogee of its initial osculating ellipse. ... Perturbation solution, Oblate planet, Orbital parameters.