Invading FFP with a distance parameter and a mass m_FFP = m_J. Panel a: temporal evolution of Jupiter’s semi-major axis a_J, given θ = θ^* = 249° (see Eq. (13)). The sudden increase of a_J happens just around the timing of the FFP’s perihelion passage, that is t^* = 251 yr. Panel b: the migration amplitudes Δa_J of Jupiter against different values of θ. An upper limit of Δa_J is defined by the condition that Jupiter’s eccentricity e_J is smaller than its current value of ~0.05.