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.
Reaching orbital speed takes much more fuel than reaching orbital height.
Hogwash.
Explain. The XKCD guy is usually quite competent at what he does. Are you sure that you are talking about the same thing as he is? If so, what precisely is his mistake?
This XKCD guy, very popular here, is wrong again:
http://what-if.xkcd.com/58/
Hogwash.
Downvoted for calling math ‘hogwash’ without pointing out a math error.
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.
Explain. The XKCD guy is usually quite competent at what he does. Are you sure that you are talking about the same thing as he is? If so, what precisely is his mistake?