# Why does the torque due to a reaction wheel shift to the center of mass of the spacecraft?

In a spacecraft, even if a reaction wheel is placed at some distance from the center of mass, the satellite always rotates through an axis which passes through its CoM? What is the reason behind this? Why is the torque vector treated as free vector?

• What do you mean by a "free vector?"
– user687
Jul 28, 2016 at 13:32

The reason for this is Newton's first law of motion:

When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force

(from here). This is the version for point-like objects. For extended objects, the law applies to the center of mass.

When it activates its reaction wheel, the satellite is not acted upon by external forces (ignoring gravity): the wheels only create an internal force, which cannot impact the trajectory of the center of mass.

"Because Newton's first law says..." is an answer but it's not really a "because" type answer. Newton's laws of motion are observations. He noticed these things about how the world seems to work and wrote them down. They are not explanations.

Asking why does an object's center of mass tend not to move (or change velocity) when there is no external force, and answering because objects tend not to move (or change velocity) when there is no external force - and we call that Newton's Law is not really an answer to why?

Richard Feynman sometimes got a little prickly when asked "the why question" in physics himself. He is usually very careful to remind us over and over "we don't know why" something happens, but it just does.

So in my alternate answer, I've expressed Newton's first law in more familiar rather than formal terms. But really, no matter how you look at it, it's simply an observation of how the world appears to work. Every time we check, no matter how we check, it keeps happening this way. Most people call it a law, but this is only because we haven't found a case yet when it doesn't happen.

We should really call these Newton's observations. He noticed it and noted his observations, and he couldn't find exceptions, and it helped him predict more complicated things and those thinks also always seem to happen the way he predicted. For humans, a law is something we should or must do. But, in physics, a law is no more than an observation that something seems to keep happening and no exceptions have been seen yet.

Very good question! I had to think about it. The center of mass can't suddenly move on its own, without an external force - like thrust from it's rocket or somebody pushing on it. Floating there in space, if you don't see it interacting with anything, not thrust or magnetic fields or beams of light or solar wind, then it's gotta just stay right there. That's what Newton sez in this excellent answer.

If something (symmetric like a wheel around its axis) is turning inside the spacecraft - even a tape recorder - the whole thing can rotate in place, but it can't move from one place to another.

If something moves (translates) inside, then the whole spacecraft can appear to move from the outside, but its center of mass will still be in the same place.

• I totally agree with you that the answer to the question is "that's the way things seem to work", and that any "why" question on the fundamental principles of physics can be answered the same way. Jul 29, 2016 at 11:58