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Physics

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  • $\begingroup$ Pedantic comment: "stable" meaning "not doomed" rather than the usual "stable against small perturbations". Nice answer, though. +1 $\endgroup$
    – Mark Mitchison
    Commented Mar 30, 2013 at 21:33
  • $\begingroup$ @MarkMitchison: Good point, I've updated my answer accordingly. $\endgroup$
    – Keith Thompson
    Commented Mar 30, 2013 at 21:55
  • $\begingroup$ I get everything you said but my question was: shouldn't the distance the ball travels toward the earth during the next iteration be larger since it is accelerating? $\endgroup$
    – mtanti
    Commented Mar 31, 2013 at 2:23
  • $\begingroup$ @mtanti: If you stay in the original frame of reference, the distance the ball moves "down" is larger. But the Earth is no longer straight "down"; it's now below and a little bit "behind" the Moon's new position. Over a short time span, the Moon's motion approximates the parabola it would follow in a uniform gravitational field; the Earth is at the center of the circle that's tangent to that parabola. $\endgroup$
    – Keith Thompson
    Commented Mar 31, 2013 at 6:27
  • $\begingroup$ @mtanti The point here is that the moon does not speed up. It is accelerating because its direction is changing. A change of velocity can be a change in speed, or a change in direction, or both. $\endgroup$
    – Harry Weston
    Commented Apr 3, 2013 at 19:13