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Re question 1: I believe the amount of rocket fuel required to maintain constant thrust will increase linearly with the rockets velocity.
The thrust is proportional to the mass flow rate of the exhaust times the change in momentum. It becomes more difficult to change the moment (out the back of rocket) when it already has so much forward velocity
Said more simply is in general a prolonged rocket burn is probably not a constant force event
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18 Cayman GTS
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