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Homework Help: Energy required to move an object in orbit?

  1. Jan 4, 2010 #1
    The International Space Station, with a mass of 370,000 kg, is orbiting the Earth at a height 335 km and needs to be boosted to an orbit of 352 km. Calculate the energy needed to boost the ISS to its new height.

    m = 370,000 kg
    M = 5.98 x 10^24 kg
    G = 6.67 x 10^-11 Nm^2/kg^2
    Initial distance from earths center = (6.38 x 10^6m) + 335000m
    Final distance form eath's center = (6.38 x 10^6m) + 352000m


    Using Ep = GMm/r

    I calculated
    Epi = (6.67x10^-11)(5.98x10^24)(370000)/((6.38x10^6)+(335000)) = 2.316682247E13

    and

    Epf = (6.67x10^-11)(5.98x10^24)(370000)/((6.38x10^6)+(352000)) =2.316676064E13

    I found the difference of the two, and took it as my answer, 6.2x10^7 J

    I feel I'm doing something wrong, Thanks in advance for any help!
     
  2. jcsd
  3. Jan 4, 2010 #2

    mgb_phys

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    Have you considered the difference in speed (and so Kinetic energy) for the two orbits?
     
  4. Jan 6, 2010 #3
    Hmmm, so I would have to find the total energy,

    Et = Ep + Ek = G Mm/r + .5mv^2

    ok I think I got it now.
     
  5. Jan 6, 2010 #4

    mgb_phys

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    Remember that V is also a function of r and M (there is a fixed speed for each orbital height)
     
  6. Jan 6, 2010 #5
    yes, v = sqrt(MG/r)

    so figuring out the difference in total energy, would that give me the amount of energy needed to boost the space station to its new height?
    what I mean is, does difference in total energy = amount of energy required to boost to new height?
     
  7. Jan 6, 2010 #6

    mgb_phys

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    Yes actualy thats the minimum energy, assuming you want it to orbit in the same direction
     
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