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ACK! Kepler's 3rd + Newton

  1. Nov 13, 2006 #1
    Okay, so I get the concept behind Newton's version of Kepler's 3rd law, but everytime I go to do a problem with it, I get totally lost. This may be because I have never seen one done in a way that did not totally confuse me... I think it might be best if I just ask one of the questions that's bothering me...

    "The distance of closest approach of Halley's comet to the Sun is 8.9X10^10 m. Its period is 76 yr. Calculate the following: a) semimajor axis (b) eccentricity (c) aphelion distance (dist. farthest from sun)"

    So, here's what I know, semimajor axis = a = (Rmin +Rmax)/2, eccentricity = e = (Rmax - Rmin)/2a
    and of course Kepler's law T^2 is proportional to R^3, or newton's
    T^2/R^3 = 4(pi^2)R^3/GM

    So... I don't expect (or want) to be given the answer... i want to finally understand this stuff so that I dont have to continue struggling with it. Maybe there's some basic aspect of this that I've missed every time I've seen it...or maybe it's the continual use of different letters for variables that confuses me. I dont know... Any help would be appreciated.
     
  2. jcsd
  3. Nov 13, 2006 #2
    p.s. the "ACK!" in the subject was just an onomatopoeiatic exclamation of dismay... i realized after that it could be mistaken for some part of a formula or something.
     
  4. Nov 13, 2006 #3

    OlderDan

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    What do you mean by R?
     
  5. Nov 13, 2006 #4
    distance from the sun i think
     
  6. Nov 13, 2006 #5

    OlderDan

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    For a comet, the distance from the sun is constantly changing. What do you use for R then?

    http://www.go.ednet.ns.ca/~larry/orbits/kepler.html
     
  7. Nov 13, 2006 #6
    yeah...R is constantly changing, it's the distance from one of the focii in the ellipse to the body that's orbiting... sooo yeah, I dont know.
     
  8. Nov 13, 2006 #7

    OlderDan

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    For elliptical orbits the period is related to the semi-major axis. Take a look at the link I posted near the bottom.
     
  9. Nov 13, 2006 #8
    Hmm...but i can't use p^2 = a^3 because it shouldn't be an equality, I thought that's why newton had to develope the equation that's below that one... but that one relies on masses which are not given to me in the problem. Arg... I think i'm giving up for the night, I have to head off to bed. Thanks for the help though - Feel free to respond to me again, I'll check it in the morning.
    Thanks again.
     
  10. Nov 14, 2006 #9

    OlderDan

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    Don't worry about the Newton refinement. You only need that if the masses of the two objects are comparable. The mass of the sun is huge compared to a comet, so only the mass of the sun is needed.
     
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