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Average speed of earth in its orbit of sun

  1. Apr 20, 2007 #1
    1. The problem statement, all variables and given/known data
    The earths orbit around the sun is very nearly circular, with an average radius of 1.5x10^11 m. What is the average speed of the earth in orbit around sun.


    2. Relevant equations

    d/t= 2pi/t


    3. The attempt at a solution

    2pi*1.5x10^11/ 31556926
    it comes out to be 29865.95
    answer is supposed to be v=28,886 m/s
    so can anyone tell me what i did wrong

    31556926 is a year so thats why i used it in the equation
     
    Last edited: Apr 20, 2007
  2. jcsd
  3. Apr 20, 2007 #2

    hage567

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    Your t value is a little off. Can you explain how you got it?

    Hmm, I get the same answer you do though.
     
    Last edited: Apr 20, 2007
  4. Apr 20, 2007 #3
    I used google to find t, lol.
     
  5. Apr 20, 2007 #4

    chroot

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  6. Apr 20, 2007 #5

    hage567

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    Try calculating it yourself! I'm inclined to believe the book's answer is wrong.
     
  7. Apr 20, 2007 #6

    D H

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    The relevant data are
    a=1.00000011 au
    e=0.01671022
    T=365.242190 days (tropical year)

    Using Ramanujan's approximation of the circumference of an ellipse,

    [tex]C=\pi a \left(3\left(1+\sqrt{1-e^2}\right)-\sqrt{\left(3+\sqrt{1-e^2}\right)\left(1+3\sqrt{1-e^2}\right)}\right)[/tex]

    the Earth's orbital velocity is 0.01720159 au/day, or 29.7838 m/s

    From http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html, the Earth's minimum orbital velocity is 29.29 km/s, larger than the supposedly correct answer. (In other words, the book is wrong.)
     
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