Abstract: This paper studies the reachable domain of a satelliteafter a coplanar single impulse with fixed magnitude applied. On theassumption that all of the generated trajectories are ellipses due to thesmall amplitude impulse, the reachable domain is bounded. According to thedefinition of the envelope of the curve family in a plane, the boundary ofreachable domain is revealed respectively for three situations, namely, thepoint to apply impulse is fixed and the direction is arbitrary, the point toapply impulse is arbitrary and the direction is fixed, both the point toapply impulse and the direction are arbitrary. The simulation resultsverify the validity of the present approach.The conclusion has no restriction on theeccentricity of the initial elliptic orbit, and fits for the situation ofinitial elliptic orbit with large eccentricity.