How does the mass and size of a spacecraft influence the amount of energy needed for it to move through the vacuum of space?
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Doubling the mass doubles the momentum so that accelerating requires double the change in momentum. As for energy, that depends on the exhaust velocity of your rocket motor. If you have the same exhaust velocity, doubling the mass means doubling the energy required to accelerate.
If you want an energy-efficient rocket you should throw out lots of mass at low velocity. The problem with that is that you run out of propellant very quickly. Doubling the exhaust velocity means the same amount of propellant gives you double the acceleration but it also quadruples your energy cost, so it’s less efficient.
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