The role of solar apsidal resonance in the evolution of geostationary transfer orbits

Subjected to multiple perturbations and their complex interplay, the dynamical evolution of geostationary transfer orbits (GTOs) is sensitive to initial conditions and model parameters. As one of the most remarkable outcomes of multiple perturbations, the solar apsidal resonance, i.e., the 1:1 resonance between the solar orbital motion and the rotation of the orbital apsidal line caused by Earth's oblateness, is an important feature of the GTO evolution. It occurs when the semi-major axis is reduced by the atmospheric drag to the critical value, with which the rotation of the orbital apsidal line is commensurate with the solar orbital motion. In the present paper, we show that the solar apsidal resonance plays an important role in the evolution and decay of GTOs. To do so, we first explain the underlying dynamical mechanism of the solar apsidal resonance, which is the U-turn of the solar azimuth with respect to the orbital apsidal line and the resulting monotonic increase or decrease of the eccentricity. The resonance is then classified into three kinds, and their causes and effects are analyzed. Previous studies have regarded the solar apsidal resonance as a mechanism extending the orbital lifetime. However, we find that in most cases the GTO will re-enter Earth's atmosphere soon or only several years after the resonance, and so the solar apsidal resonance can be regarded as the prelude to the GTO final re-entry. Finally, the sensitivity of orbital dynamics is studied through numerical simulations. It is shown that the high sensitivity of the dynamics can be attributed to the resonance, which is difficult to predict or manage. With the initial state, it is possible to predict the orbit evolution of GTO only before the solar apsidal resonance. To predict the lifetime of GTO, new measurements on the orbit after the resonance are required.