Change in trajectory by velocity impulses

The effect of velocity kicks on the flight path of an object is investigated theoretically for the case of the smaller of two bodies in an idealized restricted two-body problem. Velocity kicks coplanar with the conic-section trajectories are considered. The effects described include the change in the semimajor axis, the eccentricity after the impulse, and the rotation of the conic-section path. Trajectory changes from ellipse to different ellipse, hyperbola, or parabola; from hyperbola to different hyperbola or parabola; and from parabola to different parabola are analyzed.