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How much more energy does it take to orbit an object vs. just lifting it?

How much energy does it take to lift a 1000kg mass to 100km altitude (straight up), vs putting that same mass into orbit around the Earth at 100km?

What about at 400km altitude?

2 Answers

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  • 8 years ago
    Favorite Answer

    I have a spreadsheet that gives me those numbers. For 1 kg (multiply by 1000 to get numbers for 1000 kg):

    at 100 km, 1e5 meters, orbital velocity is 7850 m/s, energy to gain altitude is 97 MJ, KE from it's speed is 3080 MJ, total energy is 3178 MJ

    at 400 km, 4e5 meters, orbital velocity is 7674 m/s, energy to gain altitude is 370 MJ, KE from it's speed is 2945 MJ, total energy is 3314 MJ

  • ?
    Lv 7
    8 years ago

    d(GPE) = G*M*m[1/R - 1/D] where R is the radius of the earth and D is the radius of the orbit. This is the energy just to lift to orbital height.

    The KE in orbit = ½m*V² = ½m[GM/D]

    Remember that orbital height above the surface H = D - R

    As I recall, KE = GPE/2; you may want to check that.......

    12/26/12:

    Oops, I checked it myself and it's really KE = GPE*[R/2H]

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