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Circular Motion

  1. Mar 3, 2016 #1
    • Member advised to use the homework template for posts in the homework sections of PF.
    The problem is as follows. "NASA places communication satellites into earth orbit with a radius of 42000 km. If the centripetal acceleration of one of the satellite is 0.22m/s^2, how long, in hours, will it take this satellite to make one complete orbit?

    For this chapter, these are the following equations I can use. V(speed)=2πr(radius)÷T(period), Ac=V(speed)^2÷r(radius), and Ac(centripetal acceleration)=4π^2r÷T^2


    I used Ac=4π^2r÷T^2. Now I'm stumped because the attributes are straight forwarded, so when insert 0.22m/s=4π^2*4.2e4÷T^2 I know I need to rearrange the problem.

    I get T^2=4π^2r÷Ac. The answer is 24 hours and I don't come close to it. I just want to know if I'm setting up the problem correctly? If not, what am I doing wrong?

    Thanks! :)
     
    Last edited: Mar 3, 2016
  2. jcsd
  3. Mar 3, 2016 #2

    HallsofIvy

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    Your problem is that you used r in km when it should be in m because the acceleration is given in m/s^2.
    r= 4200 km which is 4200000 m. That is 4.2 x 10^6, NOT 4.2 x 10^4 as you have.
     
  4. Mar 3, 2016 #3
    I converted the m/s^2 to km/h/s. Haven't tried converting the radius to m.
     
  5. Mar 3, 2016 #4
    Either way works. My problem is that I didn't convert my time properly lol I got 24 hrs.

    T^2=4π^2*42000km÷0.792km/h/s, T^2=2093636, T=√2093636, T=1446.94 min÷60 T=24.11 or 24 hours
     
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