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Planetary motion please help?

  1. Nov 24, 2008 #1
    Compare the orbital speeds of satellites that orbit at the following altitudes.
    (a) One Earth radius above the surface of the Earth (in km/s)

    (b) Two and a half Earth radii above the surface of the Earth.

    Here is the equation to be used,

    orbital speed is v=(sqrt)(GM/r)
    G is the universal gravitational constant
    M is the mass of the thing in the middle
    r is the distance from the center of the thing in the middle to the center of the thing in orbit.

    V=(sqrt) [(6.67E-11)(5.97E24 kg)/ (6378000 m]

    ...and yet, my answer is incorrect.
     
  2. jcsd
  3. Nov 24, 2008 #2

    LowlyPion

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    Welcome to PF.

    Aren't the distances they give you above the surface?

    Where is the first Earth radius to get to the surface?
     
  4. Nov 24, 2008 #3

    mgb_phys

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    Those units will give you an answer in m/s, the question asks for km/s
     
  5. Nov 24, 2008 #4
    the distances are what i know...

    earth's mass is 5.97E24...whereas its radius is 6378 km...

    the answer i got in km/s was 249866.38...which is wrong..and idk why.
     
  6. Nov 24, 2008 #5

    mgb_phys

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    v = sqrt ( GM/r )
    gm = 399 000 km3s-2 for earth, r = 6400km

    (a) One Earth radius above the surface of the Earth (in km/s)
    So r = 2 * earth radius,
    v = sqrt( 399 000/ (2*6400)) km/s =

    (b) Two and a half Earth radii above the surface of the Earth.
    So r = 2.5 * earth radius,
    v = sqrt( 399 000/ (3.5*6400)) km/s =
     
  7. Nov 24, 2008 #6
    thank you...but where did you get 399,000? isn't GM 3.98E14??

    and also, i'm confused on why the radius is 2 and 3.5...?
     
    Last edited: Nov 24, 2008
  8. Nov 24, 2008 #7

    mgb_phys

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    The question says one earth radius ABOVE the surface - which is 2 Earth radii from the centre.

    GM = 6.674E−11 m^3 kg-^1 s^-2 * 5.97E24 Kg = 3.986 E 14 m^3 s^-2 = 398600 km^3 /s^2

    edit - GM comes up a lot in orbital calcs and has an inconveniently large and small value, it's easier to remember that it's about 400,000 (in km and s), or just remember - a bit less than 1/2M (km^3/s^2)
     
    Last edited: Nov 25, 2008
  9. Nov 24, 2008 #8
    thanks.
     
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