Question

I wonder if because the coordinate system in a space ship is operating in a vacuum space, is there any factors weighing against the control inputs? Meaning, in an airplane, every input action has to weigh against gravity, drag, etc. In space, there's no gravity and drag to work against. Does this make the orthogonality equation simpler?

Answer 1

As you have said that if the spacecraft is in vacuum space which means it is out of the atmosphere and which results in no drag consideration.

But in the space, the main factor is gravitational force. It is not only due to a non-spherical planet(say earth) around which it is rotating but other masses which are either huge or really close to the spacecraft.

After launching a satellite we have to spent millions of dollars to keep that satellite in the same operating orbit around the object of interest. And this destabilization of the orbit occurs due to differential gravitational forces only. This differential gravitational force is due to stars, planets, comets, plate tectonics, tide etc.

In short we can say that in space the gravitational forces complicates the orthogonality equation rather simplifying it. After all it is rocket science.