Determine true orbital inclinations for secular mode analysis in multi-planet systems

Determine the real values of orbital inclinations (relative to the invariable plane) associated with the secular normal modes used in the nodal precession analysis of the selected multi-planet systems, so that the eigenvector amplitudes are physically quantified rather than treated as a unit vector and the dynamical strength of potential spin–orbit resonances can be accurately assessed.

Background

In analyzing potential secular spin–orbit resonances in ten multi-planet systems, the paper computes nodal precession frequencies via Laplace–Lagrange theory and compares them to planets’ spin precession constants. A secondary resonance criterion relies on the eigenvector component associated with each planet exceeding a threshold.

Because the absolute orbital inclinations that scale these normal-mode eigenvectors are not available from current observations (particularly in multi-transit systems where inclinations to the invariable plane are not directly measurable unless precession is detected), the authors treat the eigenvectors as unit vectors. This limits their ability to quantify the dynamical strength of the identified resonances and motivates determining the true inclinations.