Secular behavior of a pair of coplanar planets

This chapter is a review of the secular dynamics of two coplanar planets. The first section presents the development of the secular model. We use both analytical and semi-numerical approaches, which employ an averaging of the short period gravitational interaction of the planets. We apply the secular analysis to the case of the two outer planets, c and d, of the ν Andromedae system. Assuming an edge-on orbital configuration of the planets, we obtain the general structure of its secular phase space, and the boundaries of its secular stability.