1) A geosynchronous communications satellite experiences an accidental engine misfire that imparts an unwanted velocity change. This causes the satellite's orbit to change from circular to elliptical. 2) If the velocity change is small (β < 1), the satellite enters a new elliptical orbit around Earth. The parameters of this orbit, including semi-latus rectum, eccentricity, perigee and apogee distances, and period, are calculated in terms of the initial orbit parameters and β. 3) If the velocity change is large enough (β = escβ), the satellite will escape from Earth's gravity. The minimum β to escape and the satellite's closest approach distance are determined. 4