In this paper, we analyse the chaotic satellite system using dissipativity, equilibrium points, bifurcation diagrams, Poincare section maps, Lyapunov exponents and Kaplan–Yorke dimension. We obtain the equilibrium points of chaotic satellite system and at each equilibrium point, we obtain the eigenvalue of Jacobian matrix of the satellite system to verify the unstable region.We calculate the Kaplan–Yorke dimension, which ensures the strange behaviour of the system. We observe closely the three-dimensional (3D) phase portraits of the satellite system at different parameter values. We plot the Lyapunov exponent graphs corresponding to every 3D phase portrait of satellite systems, to verify the chaoticity of satellite systems. We establish time-delay synchronisation for twoidentical satellite systems. The simulated and qualitative results are in an excellent agreement.