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It is demonstrated that, for the recently introduced classical magnetizedKepler problems in dimension $2k+1$, the non-colliding orbits in the "externalconfiguration space" $\mathbb R^{2k+1}\setminus\{\mathbf 0\}$ are all conics,moreover, a conic orbit is an ellipse, a parabola, and a branch of a hyperbolaaccording as the total energy is negative, zero, and positive. It is alsodemonstrated that the Lie group ${\mr {SO}}^+(1,2k+1)\times {\bb R}_+$ actstransitively on both the set of oriented elliptic orbits and the set oforiented parabolic orbits.

On the Orbits of the Magnetized Kepler Problems in Dimension 2k+1