Taking his 8km/sec speed and 100km height as accurate, the energy to lift one kilogram that high on a ballistic arc (ignoring air resistance and the motion of the Earth’s surface) is mgh = 1kg100km \ (1000m/km) * (10 m/s^2) =1e6 J. The energy to accelerate it to orbital speed is 0.5mv^2 = 0.5*1kg*(8000m/s)^2 = 32e6 J. First pass, then, his reasoning seems accurate. Am I oversimplifying? What is your calculation?
You’d probably have greater success challenging the “XKCD guy’s” assumptions if you adopted a less belligerent tone. I don’t know nearly enough to verify who’s right here, but some things that strike me as questionable:
The most fuel is spent relatively low in the atmosphere.
This is consistent with most fuel going into producing kinetic energy.
1 - accelerate to the Moon—from 8 to 10 km/s
Generate a delta-v a fraction of the one you needed to reach orbit, in vacuum, with an engine with a higher specific impulse than that of the Saturn V’s first stage, for a small fraction of the launch mass. Yep, shouldn’t take that big of a rocket.
Taking his 8km/sec speed and 100km height as accurate, the energy to lift one kilogram that high on a ballistic arc (ignoring air resistance and the motion of the Earth’s surface) is mgh = 1kg100km \ (1000m/km) * (10 m/s^2) =1e6 J. The energy to accelerate it to orbital speed is 0.5mv^2 = 0.5*1kg*(8000m/s)^2 = 32e6 J. First pass, then, his reasoning seems accurate. Am I oversimplifying? What is your calculation?
The most fuel is spent relatively low in the atmosphere. For Saturn V or for Space Shuttle, doesn’t matter.
With just a fraction of the whole Saturn V mass in Earth’s orbit, Apollo managed to:
1 - accelerate to the Moon—from 8 to 10 km/s
2 - decelerate to Moon orbit—from 10 to 2 km/s
3 - land on the Moon
4 - orbit the Moon again
5 - accelerate to 10 km/s again
6 - re-orbit the Earth
7 - break for the reentry
The ideal numbers this guy is still using are useless.
You’d probably have greater success challenging the “XKCD guy’s” assumptions if you adopted a less belligerent tone. I don’t know nearly enough to verify who’s right here, but some things that strike me as questionable:
This is consistent with most fuel going into producing kinetic energy.
Generate a delta-v a fraction of the one you needed to reach orbit, in vacuum, with an engine with a higher specific impulse than that of the Saturn V’s first stage, for a small fraction of the launch mass. Yep, shouldn’t take that big of a rocket.
It is seriously more complicated than that. Same for returning to Earth orbit.
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
So, in other words, you’ve just discovered a fascinating physical law that says bodies of higher mass require more energy to accelerate?
The key point here is the delta-V budget, not fuel expenditure.