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Satellite rotation

  1. Apr 11, 2008 #1
    Suppose we want a satellite to revolve around the Earth 5 times a day. What should the radius of its orbit be? (Neglect the presence of the moon.)


    Found the number of second in 24 hours and divided it by 5 to get the period. Then rearranged the gravitational equation with T^2=((4pi^2)/(GM))r^3 and solved for r. I came up with 1.44 × 10^7 m but its wrong. Any insight?
  2. jcsd
  3. Apr 11, 2008 #2


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    That seems pretty reasonable to me. Why do you think there is something wrong with it?
  4. Apr 11, 2008 #3
    My teacher calculated 7.78 x 10^7 m. The difference is our calculations of the period. He did 5 x 12 x 3600 for the period while I did (24 x 60 x 60)/5. I don't understand where he came up with 12. Could someone help me see where my teacher or I made a mistake.
  5. Apr 11, 2008 #4


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    (24*60*60)/5 is 5 times a day. 5*12*3600 is once every 60 hours. If you are reading the same problem I don't see how he could interpret that as '5 times a day'.
  6. Apr 14, 2008 #5
    Yea I don't know why he did it either. Can any else find a reason for it?
  7. Apr 14, 2008 #6
    I think you are right
    5 times a day means 0.2 day for a complete revolution...
  8. Apr 14, 2008 #7


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    Here's an online calculator I made. It does the unit conversions for you. Choose units of days, Earth masses, and seconds. Plug in 0.2 for period (1/5 of a day), 1 for Mass, and it will compute seconds for you: 1.44E7. Your teacher is wrong. You are right.

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