flyingpig said:
So nothing is really at rest if you are close to the Earth's orbital?
Well I have a sort of two-part answer to your question. The first part is sort of an indirect answer. Before we continue with any sort of discussion about motion, I feel the need to point out that there is no
absolute notion of what is "at rest" and what is "moving." All motion is relative. What I mean by that is, one observer could claim that a certain object was at rest, while another observer (who is in motion relative to the first one) could equally well claim that the same object was moving. It all depends on your reference frame. Providing that both observers are in
inertial reference frames, then their statements about the motion of the object are
equally valid. Formally, an inertial reference frame is one in which Newton's laws are obeyed. Practically speaking, what that means it that inertial reference frames move at a constant velocity relative to each other. So, just to drive the point home: if Observer A and Observer B have a constant velocity relative to each other, then considering the situation "from Observer A's reference frame" is equivalent to considering Observer A to be stationary, in which case Observer B is moving. HOWEVER Observer B can claim
with equal validity that he is the one who is at rest, and that it is Observer A who is moving.
The above discussion doesn't hold true for
accelerated reference frames. Accelerating reference frames are
non-inertial (meaning that Newton's laws do not hold within them). Typically, in order for an observer to be able to explain the motions that he/she sees while in an accelerating reference frame, and still have things make sense in the framework of Newton's laws, that observer must introduce so-called "fictitious forces." For example, if you're in a car that's going around a curve, you're in an accelerating reference frame. If you still want to "pretend" that you are stationary, you're going to have to introduce a fictitious force in order to explain what you experience. In this case, out of nowhere, there seems to be a "centrifugal" force that pushes on you in the direction towards the outside of the turn.
Now that we've clarified those points, here is a more direct answer to your question above: yes, all objects near Earth experience its gravitational pull. Therefore, these objects have a force acting on them and are accelerating.
By the way, you didn't answer my question! What is the orbital speed of an object in a circular orbit 100 km above the surface of the Earth? Here's a hint: the object is moving in a circle, therefore it must have a
centripetal force acting on it. In this case, the centripetal force is provided by Earth's
gravity (which, after all, pulls towards the centre of the orbit). That last statement gives you all the information you need to work out the object's speed, and if you do, you'll find that whoever wrote your sci-fi series came up with quite a plausible value for the orbital speed of the space junk.
flyingpig said:
What would FBD look like? I can't draw it out. Can you draw fictitious forces on FBD? It's not really a temporarily G-field right? They said "G-field" which is physically wrong right?
I don't know what a "G-field" is, that's not really a proper physics term, and it is probably something the sci-fi writers made up. But, to answer your question: you are right. There is NO actual gravity involved here. Rotating the space station merely allows the effects of gravity to be simulated. From a FBD point of view, the situation is similar to above. A person in contact with the outer wall of the rotating space structure is in circular motion, and therefore he has a centripetal force acting on him. Due to his inertia, at any instant that person wants to "fly out" of the circle in the tangential direction. But the inward-pointing centripetal force prevents him from doing so. In this case, the centripetal force is due to the normal force exerted by the wall on the person. He feels a normal force pushing upward on his feet in just the same way that a person on Earth (in a gravitational field) feels such a normal force. If you get the station spinning fast enough, you can get it so that that normal force is
equal to the typical force that a person feels pushing up on his feet when he is on Earth (i.e. mg). See the attached figure.
EDIT: I should point out that science fiction writers seldom use this plausible way of simulating the effects of gravity in space, because it is too restrictive from a story-telling standpoint (esp for TV). They often just invent a futuristic (and conveniently unexplained) new technology that
can somehow generate "artificial gravity" (just like in Star Trek, for example). So, I wouldn't spend too much time scratching my head over the "physics" used in this sci-fi show you were watching if I were you. Scientific accuracy is not exactly the writers' top priority.
