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The source's tangential arrows $a,c$ respectively point along and against the original motion; $b,d$ point radially outward and inward. Write $r_0$ for the initial orbital radius, $v_c=\sqrt{GM/r_0}$ for the circular orbital speed, and $\delta >0$ for the small added speed. The resulting trajectories follow the velocity kick on a circular Kepler orbit formulas. Here orbital energy includes kinetic energy and gravitational potential energy; angular momentum refers to the central object.

Adding tangential velocity along the existing motion increases both orbital energy and angular momentum:For a sufficiently small kick the Kepler orbit remains an ellipse. At the kick point its radial velocity vanishes and its tangential speed exceeds the circular orbital speed, so that point becomes the pericentre. The ellipse extends farther outward than the original circle.

For a small opposing tangential kick,The new tangential speed is less than the circular orbital speed, so the kick point is the apocentre of an ellipse. The orbit falls inward from the original circle. The signs assume $0<\delta \ll v_c$; a large velocity reversal is outside the stated small-impulse regime.