Resonant motion of Echo I: a case study of SRP and J2 coupling

In this paper, we explore the resonant behaviour exhibited by the historical NASA’s Echo I satellite. It is well known that the coupling between the SRP and the geopotential (second zonal harmonic 𝑱2) perturbations leads to a resonance effect in eccentricity under certain orbital conditions. Here, we revisit the orbital motion of Echo I in light of the recently published phase space theory for spherical spacecraft subject to the SRP-𝑱2 resonance. We first demonstrate that our modelling is in very good agreement with the recorded Two Line Element (TLE) data of the spacecraft. We then derive the first ( 𝒋 = 1) resonance model associated with the motion of Echo I by using the Hamiltonian formulation of the satellite dynamics, which we use to interpret its observed behaviour. Finally, we extrapolate the resonance model of Echo I for two imagined extreme scenarios: the motion near a stable equilibrium, and the motion under the strongest resonance possible. The results provide a new understanding of the orbital motion of Echo I and offer new insights into the SRP-𝑱2 resonance phenomenon.