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Centripetal Acceleration Problem

  1. Oct 21, 2008 #1

    C^2

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    1. The problem statement, all variables and given/known data
    Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational accleration at the Earth's surface.

    Known Variables:

    time(t)= 5400seconds
    centripetal acceleration(a)= ?
    radius(r)=400,000 meters


    2. Relevant equations
    v=2pir/t
    a=v^2/t
    g=9.8 m/s^2

    3. The attempt at a solution

    So, what I thought I was supposed to do was use the first equation and plug in the numbers:

    v= 2(3.14)(400,000)/5400s

    =465.2 m/s

    then I plugged the result into the second equation:

    a= (465.2)^2/5400

    =.084 m/s^2

    and since they ask to express the answer in terms of g,

    .084 m/s^2 * 9.8 m/s^2

    =.844 m/s^2

    but the book says the answer should be .9g's. I dont know if I'm just splitting hairs here, but .844 does not round up to .9.
    Can someone point out where I went wrong?
    Thanks in advance
     
  2. jcsd
  3. Oct 21, 2008 #2
    Hi,

    where did you get a = v^2 / t ?

    v is a velocity in metres per second
    t is a time in seconds
    a is an acceleration in metres per second squared

    the dimensions (units) do not add up!

    Hope that helps cheers
     
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