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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By definition, mass is the ratio of momentum and velocity. Adding or removing kinetic energy to the system changes momentum, velocity changes relative to the change in momentum and the constant (or changing) mass.
Mathematically, it gets written as p=mv.
This is a possible formulation of Newton’s third law, though this is commonly expressed as force and acceleration. Special relativity changes it a little, but it’s the underlying building block of a gigantic chunk of physics. It applies.
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