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Oribital Speed of a Satellite

  1. Aug 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Two satellites are in circular orbits around a planet that has radius 9.00x10^6 m. One satellite has mass 65.0kg , orbital radius 6.10×10^7m , and orbital speed 4800 m/s. The second satellite has mass 95.0kg and orbital radius 3.20×10^7m .


    2. Relevant equations

    v = sqrt(GMplanet/r)
    Mplanet = rv^2/G

    3. The attempt at a solution

    I tried solving for the mass of the plant with the details of the first satellite:

    Mplanet = (9x106 + 6.10x107)(4800 m/s)2/ (6.67x10-11)
    M = 2.41799x1025 kg

    I then used this mass to calculate the speed of the second satellite:

    v2 = sqrt(((6.67x10^-11)(2.41799x1025))/(4.1x107)

    v = 2.2489x103 m/s
     
  2. jcsd
  3. Aug 5, 2012 #2
    This cannot be correct: the second satellite's orbit is lower, so its speed must be higher.

    I suggest that you get a formula that connects speeds and radii symbolically, and then plug in the numbers.
     
  4. Aug 5, 2012 #3

    TSny

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    Gold Member

    "Orbital radius" is usually interpreted as the radius of the circular orbit. So, there is no need to add the radius of the planet.
     
  5. Aug 5, 2012 #4
    I ran the calculation again using v=sqrt(GM/r) with just the orbital radius of the satellite not including the radius of the planet.

    Using the first satellite I solved for the mass of the planet:

    Mplanet = ((6.10x107)(48002))/(6.67x10-11)
    M = 2.10711x1025

    Therefore the speed of the second satellite is:

    v = sqrt(((6.67x10-11)(2.10711x1025))/(3.2x103)
    v = 6.63x103 m/s

    6.63x103 m/s is the correct answer.
     
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