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Is there a specific starting point and direction where the ball will travel in a circle or ellipse and perhaps never cross the equator? Presumably the ball keeps moving indefinitely, so what would these path's look like? Obviously without the force, any perpetually moving ball across the surface would move in a great circle, inevitably crossing the equator or riding perfectly along the equator, but with the Coriolis effect the path gets more complicated.

I imagine the path would be dependent on velocity, direction and starting place, so it might be a lot to explain or diagram. The Coriolis force increases with velocity too from what I've read.

I'm keeping this to velocities that would keep the ball on the surface of the Earth. No escape velocity or orbital velocity paths please. Also, lets ignore any spin from the ball (Friction-less Earth should cover that).

Thanks. An answer with pictures and logical explanation would be preferred over pure math, which would probably be over my head.

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    $\begingroup$ First, we assume a bowling ball is a sphere..... $\endgroup$ – Jim Jun 29 '16 at 18:27
  • $\begingroup$ @Jim, yes, my mistake. We assume both are perfect spheres, (which a bowling ball obviously isn't), and perfectly balanced weight, not off-center. $\endgroup$ – userLTK Jun 29 '16 at 18:37
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    $\begingroup$ For the record, I was being facetious. Obviously a bowling ball is a sphere. I was trying to be funny by suggesting that assuming it is a sphere (like we do in many cases) would simplify the problem. Of course, now that I've explained it, it isn't funny..... ::awkward silence:: $\endgroup$ – Jim Jun 29 '16 at 18:42
  • $\begingroup$ Funny is always welcome. $\endgroup$ – userLTK Jun 29 '16 at 18:44
  • $\begingroup$ i thought it was funny! $\endgroup$ – jmh Nov 1 '18 at 21:02
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Possible Example: Since the earth is frictionless, we can consider the inertial frame (instead of the rotating frame where there is the complicated Coriolis), place the ball anywhere below or above the equator, and at rest with respect to the inertial frame. enter image description here

In the rotating frame, it will seem that it has traveled a circular path at equal latitude.

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