In this paper, we investigate the existence of p : q resonant orbit for the dissipative spin–orbit problem of the celestial mechanics. Our result is the generalization of the work (Biasco and Chierchia in J Differ Equ 246(11):4345–4370, 2009) from \(C^{\infty }\) topology to analytic and finitely differentiable topology. Moreover, our result gives the existence condition of p : q resonance solutions for concrete dissipative spin–orbit model under arbitrary potential frequency \(\mu \) , which can reduce to result in work (Biasco and Chierchia in J Differ Equ 246(11):4345–4370, 2009) when \(\mu =2\) . It is also a generalization from low-order resonance to arbitrary-order resonance. Our proof is based on Lyapunov–Schmidt decomposition, the contraction mapping principle on Sobolev space \(H^s\) and \(H^{\rho , s}\) and perturbation theory.
