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Homework Help: Geosynchronous satellite

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Calculate the total energy of a geosynchronous satellite (one that orbits over a fixed spot) with a mass of 1500kg, orbiting Earth at a height of 325km with an orbital speed of 5000m/s

    2. Relevant equations
    Et= Ek-Ep
    Et= -1/2(GMem)/r

    3. The attempt at a solution
    im guessing the answer should be negative, using the mass of earth being 5.98*10^24, but its wielding an incorrect answer constantly ,im getting Et= 8.9*10^10J ( i calculated radius being... r= radius of earth + height= 6.7*10^6 m, am i suppose to use a different mass instead of the mass of earth, thank you
  2. jcsd
  3. Feb 8, 2010 #2
  4. Feb 8, 2010 #3
    how would you find orbital height? quite confused thank you for the help
  5. Feb 8, 2010 #4
    At a geosynchronous orbit you can figure the required orbital velocity to match the Earth's rotation, one orbit every 24 hours. We want the centripetal force equal the force of gravity,

    F = GmM/R^2 = mv^2/R
  6. Feb 8, 2010 #5
    yes , its orbiting earth at 325km or 3.25*10^5m
    Et= kinetic + potential energy= (mv^2/r- GMem/r^2) is that correct?
  7. Feb 8, 2010 #6
    sorry, kinetic is 1/2(mv^2)
  8. Feb 8, 2010 #7
    Looks good except the potential energy goes as 1/r.
  9. Feb 8, 2010 #8
    oh , so it would be Et= 1/2(mv^2) - (GMem/r) and thank you for the help
    im getting the total energy is -1.82*10^12j
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