Secular dynamics around small bodies with solar radiation pressure

•New results on the stability of terminator and heliotropic orbits.•First global study of dynamics around asteroids with SRP and the C20 term.•Influence of the asteroid’s orbit eccentricity on the secular stability is studied. This study focuses on the secular dynamics of orbital motion around asteroids with joint effects of C20 term and solar radiation pressure (SRP). With their combined influences, two specific orbits are firstly studied, namely the solar terminator orbit (STO) and the heliotropic orbit. Then, the global orbital motion other than the two specific ones is investigated. Finally, the influence of the asteroid’s orbital eccentricity around the Sun on the secular dynamics is discussed.