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How fast must a satellite leave Earth's surface to reach an orbit with an altitude of

  1. Jan 18, 2009 #1
    How fast must a satellite leave Earth's surface to reach an orbit with an altitude of 895 km?

    Ek + Eg (earth) = 1/2 Eg

    (could you please show how to substitute to solve for v)

    this question is on the forum and it was suggested to add this v once calculated to 7404.5 m/s which was calculated from v= square root of GM/r.
     
    Last edited: Jan 18, 2009
  2. jcsd
  3. Jan 18, 2009 #2

    LowlyPion

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    Re: How fast must a satellite leave Earth's surface to reach an orbit with an altitud

    Welcome to PF.

    PE + KE = PE + KE

    What they want to know is the KE at launch to end in the PE and KE in orbit.
     
  4. Jan 18, 2009 #3
    Re: How fast must a satellite leave Earth's surface to reach an orbit with an altitud

    could you please show how to substitute for this equation? for 1/2mv squared i do not know what to use for mass.
     
    Last edited: Jan 18, 2009
  5. Jan 19, 2009 #4

    LowlyPion

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    Re: How fast must a satellite leave Earth's surface to reach an orbit with an altitud

    Your PE at any point is given by -GMm/r. We will shorten that to -μ*m/r

    μ = GMe is the standard gravitational parameter for Earth = 398,000 km³/s²
    http://en.wikipedia.org/wiki/Standard_gravitational_parameter

    This means that

    -μm/Rearth + 1/2*m*V2launch = -μm/Rorbit + 1/2*m*Vorbit2

    The mass of the object drops out.

    V2launch = 2*(μ/Rearth -μ/Rorbit) + Vorbit2
     
  6. Jan 19, 2009 #5
    Re: How fast must a satellite leave Earth's surface to reach an orbit with an altitud

    Thank-you so much!!
     
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