How does the mass and size of a spacecraft influence the amount of energy needed for it to move through the vacuum of space?
In: 2
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.
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.
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.
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.
Distance in space is measured in terms of “delta v”, which is the change in velocity to go from one place to another.
For example, going from low earth orbit to geosynchronous earth orbit takes approximately 6000 meters/second of delta v.
We can then figure out how to get that much delta v, using the rocket equation:
delta-v = 9.8 * Isp * ln(starting mass / ending mass)
Isp is the efficiency of the engine/fuel combination.
starting mass is how much the vehicle masses at the start
ending mass is how much the vehicle masses at the end – it’s the starting mass minus the ending mass.
I’ll skip the math, but if we are using an engine with an Isp of 310 (typical for probes), it turns out the starting mass / ending mass must be 7.2. That means that 88% of your vehicle mass must be 12%, and that 12% includes the vehicle plus the payload.
So, if you know how much your rocket masses, you can calculate how much fuel it will take to get a specific amount of delta v for a specific payload.
Latest Answers