A noncircular \b[ellipse with $r_0$ at pericentre has $\boxed{1<k<\sqrt2}$]. Its energy is negative. Merely specifying $k<1$ would make the stated closest-approach point an apocentre, so it is excluded by the geometry; the circular case is listed separately.

Solution

Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / Section E / E15 / ii / Solution

 Solution (source code)