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LEO cannon ball

  1. Feb 29, 2012 #1
    How long would it take a cannon ball to orbit the earth given that the radius of the
    earth is 4000 miles and the height of the (quite fictitious) mountain is 800 miles?

    Me = mass of earth
    Mc = mass of cannon ball
    R = earth's radius
    v = 2piR/T
    4000 mi = 6437200 meters
    a = acceleration of cannon ball
    G = 6.67e-11
    Using an applet for a previous question, I found Vo to be 15468 miles/hr. But I didn't use Vo... Instead I used Fnet = GMeMc/r^2 as follows.

    Fnet = GMeMc/r^2 = Mca = (Mc(2piR/T)^2)/R -->
    GMe/r^2 = (4pi^2*R^2)/RT^2 -->
    r^2/GMe = T^2/(4pi^2*R) -->
    sqrt(4pi^2*R^3)/GMe = T

    my result was 5138s, which is about 85.6 minutes.
    Does my work and result look all right?? thanks in advance
     
  2. jcsd
  3. Feb 29, 2012 #2
    well, the International Space Station is in Low Earth Orbit and it takes about 90 minutes to orbit the Earth once, so you're in the right ballpark ;)

    it's about 200 miles up for comparison, and has an orbital velocity of about 7,000 m/s
     
  4. Feb 29, 2012 #3
    thanks!
     
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