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Problem using Newtonian Gravity... Will you check my work?

  1. Mar 18, 2017 #1
    1. The problem statement, all variables and given/known data
    The space shuttle is in a 300 km-high circular orbit. It needs to reach a 520 km - high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 6.5 E4 kg. Mass of the Earth = 5.98 E24 kg. Radius of Earth = 6.37 E6 m.

    How much energy is required to boost it to the new orbit? Express your answer with the appropriate units.

    2. Relevant equations
    The specific orbital energy of an object in a circular orbit is:
    -epsilon = (1/2) (mu/r)

    E = epsilon * m
    E = -GMm/2r

    Also can use:

    E = GMm/2 * (1/ri - 1/rf)

    3. The attempt at a solution

    E(300,000m) = -GMm/2r = -1.943 E12 J
    E(520,000m) = -GMm/2r = -1.881 E12 J
    E(520,000m)-E(300,000m) = 6.20566 E 10 J
     
    Last edited: Mar 18, 2017
  2. jcsd
  3. Mar 18, 2017 #2

    gneill

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    Staff: Mentor

    Your problem statement doesn't actually state what it is you need to determine...
     
  4. Mar 18, 2017 #3
    Oh, sorry about that.

    How much energy is required to boost it to the new orbit? Express your answer with the appropriate units.
     
  5. Mar 18, 2017 #4

    gneill

    User Avatar

    Staff: Mentor

    Okay! :smile: Your work method looks good. You might want to check that you don't quote more significant figures than is warranted by the given data.
     
  6. Mar 18, 2017 #5
    Thank you :D
     
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