genz :
Calvin, you attach a horizontally firing rocket to the ballon. At the gravity level present at 100km, and the complete lack of atmosphere you could use a relatively small one, as we all know 90% of the fuel of every rocket we've ever put in space has been spent escaping earths atmoshpere.
That would be possible theoretically. But you're overestimating the change in gravity and air density at those altitudes.
At 2000km, gravitational acceleration is still over half of what it is at sea level. Satellites aren't really trying to escape Earth gravity. They're in continuous free fall in fact. They just move at such a speed (over 7km/s ~= 15,658 mph) that they continuously fall beyond the curvature of Earth, balancing their inertia with gravity so that they don't drop in altitude and also don't fly off into space.
At 100km, the air density is much, much lower, but it's still over 4x as much as at actual satellite orbits. So it's still questionable that we can economically launch satellites with balloons, if we could even make them big enough to carry full-sized satellites + rockets and get them up to 100km.
In terms of fuel savings, the Saturn V used 38% of its fuel to get to 67km. But launching from that height wouldn't necessarily save you 38% of your fuel costs because a balloon's ascent adds very little to the inertia of your vehicle. In regular launches, that vertical inertia is built up by each stage of the rocket and then finally topped off and converted to horizontal orbital inertia by the final stage.
On top of that, you have to deal with the cost of expensive helium gas or use highly flammable hydrogen gas to inflate the balloon, which would have to be massive. And then there's the unpredictability of wind that may blow your balloon off-course.
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