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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
- billrussell42Lv 78 years agoFavourite 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
- SteveLv 78 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]
