Resonant Orbits due to Evection Resonance

. Depending on the frequency of the mean motion of the third body, some secular resonances involving this frequency and the frequencies of the longitude of the pericenter or longitude of the ascending node of the satellite, can appear in this problem. In this case, averaging in the mean motion of the Sun can not be applied, while single averaging in the mean longitude of the satellite is always recommended since it greatly simplifies the calculations. We developed the equations to calculate the resonant semimajor axis due to the evection resonance considering the J 2 and C 22 terms. With these equations, we show some examples of the resonant semimajor axis for the planets Earth and Mercury and of the dwarf planet Haumea. Using the single-averaged model (keeping only J 2 and third body perturbation), we draw some simple curves (Contour Plots) to identify resonant orbits due to evection resonance.