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Homework Help: Velocity needed to maintain orbit

  1. Jan 27, 2010 #1
    An Earth satellite remains in orbit at a distance of 6104 km from the center of the Earth. What speed would it have to maintain? The universal gravitational constant is 6.67X10^-11 N m^2/kg^2. The mass of the earth it 5.88X10^24 kg. Answer in units of m/s.

    So again, missed the class. I'm crying. Most of my classmates are crying. (the few exceptions finding everything else to do in the world BUT help....) I tried this:
    I knew that it had to go into the equation:
    Vt=2piR/T
    since I didn't have T i used the equation:
    R= [(G x m x T^2)/(4pi)^2]^(1/3)
    sooo that became:

    6104000m=[(6.67X10^-11)(5.98X10^24kg)(T^2)/(4pi)^2]^(1/3)
    (2.274X10^20)= (3.98866X10^14)(T^2)/(4pi)^2
    T=9488.369sec
    so then plugging back in I got:

    Vt=(2pi)(6104000m)/9488.369sec
    thus the answer was 4042.06066 m/s

    guess what? That was wrong.

    If anyone has any ideas where I messed up or if I just had a "100% FAIL" moment, I would love to hear it.
     
  2. jcsd
  3. Jan 27, 2010 #2

    rl.bhat

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    Homework Helper

    Centripetal force on the satellite is
    G*M*m/(R+h)^2 = m*v^2/(R+h)
    S0 v=sqrt[GM/(R+h)]
    Now solve.
     
  4. Jan 27, 2010 #3
    Thank You!!
     
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