Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is a free ballistic path a parabola or a cycloid?

  1. May 24, 2005 #1
    Feynman says that the path of projectile in a uniform gravitational field is a parabola, but the bottom of this page says it's a cycloid. My calculation shows a parabola. Which is correct?

    If parabola, why does a hypothetical Big Bang to Big Crunch scenario (a closed Friedmann model) plot, for the distance over time for a pair of galaxies, a cycloid? Is that because in GR in this scenario the galaxies are in free fall in signficiant expanding space (the expanding space paradigm) whereas for the projectile the expanding space is negligible?
     
  2. jcsd
  3. May 24, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    In Newtonian physics is neither of them.It's an arch of en ellipse,with the center of the earth in the closest focus.

    Daniel.
     
  4. May 24, 2005 #3
    An arc of an ellipse is a parabola, no?
     
  5. May 24, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Nope,an arch of an ellipse is just an arch of an ellipse (pardon the tautology).

    Daniel.
     
  6. May 24, 2005 #5
    You mean "arc"? What is the difference between arc and arch as you're using it? An arc of an ellipse looks like a parabola to me. How is it different? Feynman didn't know what he was talking about?
     
  7. May 24, 2005 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I dunno what he was talking about.Yes,"arc",if you prefer.

    Give me a reference on Feynman to check him out.

    Daniel.
     
  8. May 24, 2005 #7

    EL

    User Avatar
    Science Advisor

    Yes.

    By uniform gravitational field he means a field with the same amplitude and direction at all points.

    The Earth's gravitational field is directed towards its centre (i.e. different directions at different points), and is getting weaker further away.
     
  9. May 24, 2005 #8

    Garth

    User Avatar
    Science Advisor
    Gold Member

    That link states "The "altitude" vs time of an object in gravitational free-fall is a cycloid"; that is not the same as the plot of altitude vs distance, which is a parabola on a flat Earth. As we are not on a flat Earth, although the real Earth can be approximated as such for small distances, the trajectory is part of an ellipse as stated by Daniel.

    Garth
     
    Last edited: May 24, 2005
  10. May 24, 2005 #9
    That makes sense, thanks. Except, isn't part of an ellipse a parabola?
     
    Last edited: May 24, 2005
  11. May 24, 2005 #10
    From Six Not-So-Easy Pieces, pg. 140: “...a parabola—the same curve followed by something that moves on a free ballistic path in the gravitational field”
     
  12. May 24, 2005 #11

    EL

    User Avatar
    Science Advisor

    Nope. An ellipse closes itself. For a parabola, say y=x^2, y goes to infinity when x does.
     
  13. May 24, 2005 #12
    Ah but wait--I had thought before about the altitude/time vs. altitude/distance difference. I thought they were synonymous plots because the horizontal velocity is constant. What am I missing?
     
  14. May 24, 2005 #13
    OK. Is the path of the projectile an arc of a parabola on a (hypothetical) flat Earth and an arc of an ellipse on a round Earth? Edit: Never mind, I see that is just what Garth said. Maybe I'm getting this now.
     
  15. May 24, 2005 #14
    Looks like Feynman is correct, because he was talking about a uniform gravitational field. You are correct about a nonuniform field.
     
  16. May 24, 2005 #15

    EL

    User Avatar
    Science Advisor

    You sure are!
     
  17. May 24, 2005 #16

    Garth

    User Avatar
    Science Advisor
    Gold Member

    The round Earth?

    Garth
     
  18. May 24, 2005 #17

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Incidentally,"ballistic" trajectories should keep account on many subtleties,on of them being the Earth's curvature,hence elliptical shape of orbit,neglecting rotatation & air motion & viscosity.

    You know,ballistical missiles (so caled "strategical weapons") have ranges in thousands of kilometers...To assume earth's flat is insanity.

    Daniel.
     
  19. May 24, 2005 #18
    Can you elaborate? Given a flat Earth, I'm thinking that if the horizontal velocity is 1 km/s, say, then a curve of altitude/time will be the same shape as altitude/distance. Given a paraboloidal curve for altitude/distance, I don't see how altitude/time will be cycloidal.
     
  20. May 24, 2005 #19

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Garth's point is that absent atmosphere, on a spherical earth the arc would be a section of an ellipse with a focus at the earth's center. Geometrically if you allow that focus to move away "to infinity", i,.e. so far way the error is below your maxiumum accuracy, then the arc of the ellipse is indistinguishable from an arc of a parabola.
     
  21. May 24, 2005 #20
    Thanks, that agrees with what I learned above. What I'm asking now is, for a hypothetical uniform gravitational field, why is the path paraboloidal for an altitude/distance plot but cycloidal for an altitude/time plot (as told by the link in the first post in this thread)? Given that the horizontal velocity is constant, I would think these plots would have the same shape.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Is a free ballistic path a parabola or a cycloid?
  1. Photon paths. (Replies: 1)

  2. Path of an object (Replies: 4)

Loading...