I hope to never stop learning - that is why I pursued this. My deductive reasoning seemed so logical and direct.
While i appreciate and don't dismiss your reply, I'm having trouble rationalizing why the lighter weight vehicle then is more efficient. Is is simply that the interior contents are part of the computation of mass, thereby maintaining the validity of the axiom?
The energy needed to move mass, m, at velocity, v, = mv^2. So, to move an object with twice the mass requires twice the energy.
At the surface of the Earth, mass and weight are directly proportionate, therefore the two concepts are often confused for each other.
To lift an object that is experiencing gravity, you not only have to put energy to move the object (mv^2), you have to also put energy into it to raise it to height, h. That energy = mgh, where g is the acceleration due to gravity. To lift a rocket from the Moon, mv^2 would be the same as on Earth. However, g on the Moon is 1/6 that of g on the Earth, so less energy is needed to lift objects on the Moon.
Weight is a force. F=ma (force = mass times acceleration), so W=mg (weight = mass times acceleration due to gravity). Once again, g on the Moon is 1/6 g on the Earth, so objects are easier to lift on the Moon. They are still just as hard to push, since you are not fighting gravity, so g does not enter into the calculation.
Now, I know I went six ways from Sunday on that answer, but I wasn't sure where the disconnect was. I threw the whole pot of pasta at the wall to see what would stick.
