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Juggling and orbital mechanics

  1. Jun 9, 2006 #1


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    This is really cool.


    I notice the balls change speeds proportionate to their height on the wall as they follow their elliptical paths. Does their speed follow Kepler's 2nd Law?
    Last edited by a moderator: Apr 22, 2017
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  3. Jun 9, 2006 #2


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    That is pretty cool!
  4. Jun 9, 2006 #3
    Newton showed that Kepler's laws were a consequence of the inverse square law for gravitational force. In this case, the balls are subject to a gravitational force and to a push from the walls of the cone. My guess (and it is a wild guess) is that the horizontal components of the wall's push are inconsequential to the speed of the balls. But if the walls impart a force with a component in the vertical direction, then Kepler's laws are not obeyed.

    Edit: I just realized that friction makes it unlikely that Kepler's laws apply.
  5. Jun 9, 2006 #4


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    Last edited by a moderator: Apr 22, 2017
  6. Jun 9, 2006 #5


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    The balls do follows kepler's second if you allow for friction (wich is pretty negligable in this case). Interestingly, I ocne heard a story that Kepler made this discovery by watching a chandeleer sway (and noticing that it took the same amount of time to complete one swing, no matter how big). This same principle is the reason pendulom clocks keep such excellent time, even though their magnetude of swing is not constant.
  7. Jun 9, 2006 #6
    Kepler made his discovery by careful analysis of Tycho Brahe's data. The chandelier story is about Galileo.

    The story I heard was that Brahe collected the data in order to prove that the orbits of the planets were circles with the Earth at the center.
    Last edited: Jun 9, 2006
  8. Jun 9, 2006 #7
    Also wrong. Here is the real skinny on Tycho's model.
  9. Jun 9, 2006 #8


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    If you watch the balls, they don't lose much height after several passes, so we can safely say that friction is a small enough factor to ignore over short distances and times.


    1] the balls clearly are accelerating as they drop, and decelerating as they rise

    2] the balls are moving fastest at their peri ... uh ... periGreg, and slowest at their apoGreg

    3] the balls are following an elliptical path (as any slice through a cone would be)

    So, if they are NOT following Kepler's 2nd law, they are doing something very similar.

    Which is probably what pervect is saying with those Latex hen-scratchings of his.
  10. Jul 14, 2006 #9
    its like those coin buckets at the mall, where you roll the coin down a ramp, which rolls the coin on its edge on the outside of a funnel. sometimes you can get it to follow an extremely elleptical path (the funnel isnt exactly cone shaped, usually curved toward the inside of the funnel)
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