hˈɪɹ wiː ʃˈoʊ ðˌæɾə nˈɛsᵻsɚɹi kəndˈɪʃən fɔːɹ stˈeɪbəl, ɛɡzˈæktli klˈoʊzd nˈɑːnsˈɜːkjʊlɚɹ ˈɔːɹbɪts ɪz ɐn ɪnvˈɜːsskwˈɛɹ fˈoːɹs ɔːɹ ɹˈeɪdɪəl hɑːɹmˈɑːnɪk ˈɑːsɪlˌeɪɾɚ pətˈɛnʃəl.
Here we show that a  necessary condition for stable, exactly closed non-circular orbits is an inverse-square force or radial harmonic oscillator potential.