A numerical technique for two-way radio occultations by oblate axisymmetric atmospheres with zonal winds

The Ultra Stable Oscillator aboard the Cassini spacecraft failed in late 2011, which means that all radio occultations after that date have to be done in two-way mode, using a ground-based signal transmitted to the spacecraft as the frequency reference. Here we present the numerical technique we use to analyze the data from the two-way atmospheric radio occultations of both Saturn and Titan that have occurred since the Ultra Stable Oscillator (USO) failure, along with the theoretical reasons behind this technique. Since our two-way technique is based upon our earlier one-way technique which used the USO as the frequency reference, we also present our one-way technique which we used for Saturn occultations prior to the loss of the USO.