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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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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The size makes no difference, the mass does. The size and shape would only matter for other reasons such as maintaining a rotational section for artificial gravity, going into atmospheres, or keeping the drive section segregated from the rest of the craft. The mass is what defines the momentum change required to move.

No energy is needed to keep it moving the way its already going. If you want to change its direction, slow down, or go faster, you need energy. The heavier something is the more energy you need to move it.

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.

F=ma.

Force = mass times acceleration.

Reworking that, acceleration = force divided by mass.

Thus, the acceleration gets smaller and smaller as the mass gets bigger.

So, if you want a bigger spaceship to accelerate as much as a smaller spaceship, you need more force–which means you need to push it with more energy.

I’ll add a technical detail, but an important one. You don’t need energy for something to move in space, you need it to change the velocity of movement.

If something in space is going at the certain velocity, doesn’t matter if it’s double the mass or not, it will keep going at it’s speed. It’s only if you want to slow it down or accelerate it that you need energy.