The one-parameter family of Kepler ellipses is considered, which originates when mass points are released with the same initial velocity but in all directions at a point which has a finite distance from the attractive center. It is found that (a) the locus of the second foci is a circle whose center is the point of release, (b) the directrices of the ellipses have as envelope a conic which can be an ellipse or a hyperbola, (c) the envelope of the orbital ellipses is itself an ellipse, whose two foci are the attractive center and the point of release, and (d) that, if the particles are released at the same instant, they will return to the point of release simultaneously.