>Consider the "Tyranny of Rockets" problem: if you want to send a rocket up 1 km, you need X fuel. But to get to 2 km, you need way more than 2X fuel- because you first have to carry all that extra fuel up 1 km, which takes more energy/fuel, before you can use it to go the other km. And if you want 3 km up... well, you get the idea. It's exponential in cost.

Is this correct? I know how the Tyranny of the Rocket Equation relates to mass, but I've never heard it used in terms of altitude before. Using the kinematic equations, it seems the initial velocity required to reach height 2X would actually be less than double of that for just X. However, I'm not sure if that also applies to rocket launches and if it does how it relates to fuel requirements.

Feel free to correct me if I'm on the completely wrong track here.