Abstract: This paper studies the reachable domain of a satellite after a coplanar single impulse with fixed magnitude applied. On the assumption that all of the generated trajectories are ellipses due to the small amplitude impulse, the reachable domain is bounded. According to the definition of the envelope of the curve family in a plane, the boundary of reachable domain is revealed respectively for three situations, namely, the point to apply impulse is fixed and the direction is arbitrary, the point to apply impulse is arbitrary and the direction is fixed, both the point to apply impulse and the direction are arbitrary. The simulation results verify the validity of the present approach. The conclusion has no restriction on the eccentricity of the initial elliptic orbit, and fits for the situation of initial elliptic orbit with large eccentricity.

Key words: satellite trajectory, impulse, reachable domain, envelope