How much fuel?Classical Mechanics Level 3
Consider a rocket engine that burns liquid hydrogen with liquid oxygen as the oxidizer, so that water is produced as the exhaust. One can extract around 150 mega-Joules of energy from 1 kg of liquid hydrogen. If all of this energy goes into putting a payload into the orbit in the previous problem, what is the minimum number of kilograms of liquid hydrogen needed for the rocket? (In real life this number is much higher as you need to push quite a bit of the fuel itself up into space. i.e. the rocket is a lot more than just the payload on the ground.)
Hint: this number is actually pretty close to the pre-launch mass of modern rockets and payloads. For example, the total space shuttle + rocket system has a pre-launch mass of roughly 2 million kg, most of it fuel.