I want someone to comment on my reasoning here, whether it can be considered valid or not.

We have Shuttle Tydirium orbiting around earth. The gravitational pull is always pointing from the shuttle's centre of gravity towards Earth's centre of gravity. The "nose" of the shuttle is always pointing perpendicular to that pull, ie, "forward". The shuttle is following a geodesic, a "straight line" through space. Now, during orbit, is the shuttle considered to be rotating around it's own axis while it goes one revolution around Earth? Does it have any angular momentum?
I figured it hadn't, and also that the same could be said for the moon. It is constantly facing the Earth as it goes around and I want to know if it is actually rotating at the same rate as it is orbiting, or that it is simply facing the same side towards Earth because it is following a geodesic, a "straight line" in space?

I proposed this in another forum, but I was called an idiot. I guess he was right, but I'd like to know how I've misinterpreted GR in the sense that orbiting objects is following a geodesic, a path that is often referred to as a "straight line" through space because of space-time curvature.

There is no such thing as a silly question. -- Well, almost ;)

If a shuttle ("Tydirium" ???) is orbiting a planet and always has the same side facing the planet, then it is rotating around an axis of its own, with a revolution period identical to its orbital period. Just like the Moon.

Because of tidal pull, a small body orbiting a large body will usually act this way.

Hans

OK, thanks. I can fully appreciate what you're saying. Then stating that the moon is going in "a straight line" around earth must be an erraneous simplification.

Oh, and Shuttle Tydirium is from Star-Wars :)

Anders, whoever it was who told you that you are an idiot for asking a question ought to be shot. In order to get anywhere in science you need to ask questions. Anyone who thinks otherwise should become a politician.

The answer depends on the reference frame. Where are we watching the shuttle from?

Originally posted by AndersHermansson
The "nose" of the shuttle is always pointing... ..."forward".Is this a thought experiment, or is this actually the case.




Originally posted by AndersHermansson
The shuttle is following a geodesic...I don't want to make any assumptions about your interpretation, but, from the looks of it, there is a logical flaw here.

An "orbit" is definitely a geodesic, but only in the abstract, academic, mathematical sense. No, I'm not trying to be a crackpot, here. But, an orbit in this sense is an infinitesimally thin curve, which is not realized in practice. The shuttle has finite extension (so it sweeps out a hyper "cylinder" in 4-space, as opposed to simply a curve with no thickness). Gravity curves space-time. What this means for an orbiting shuttle is that the geodesics of the constituent particles of the shuttle are <i>not</i> parallel (they either converge or diverge with proper time).

I would suggest that you not consider the shuttle, as a whole, to be following <i>a</i> geodesic. In this sense, the orbit <i>of the shuttle</i> is <i>not</i> a geodesic, even though there may be at least one particle of the shuttle that is on a geodesic.

<i>edit</i>: Actually, you can probably get away with approximating the orbit of the shuttle as a geodesic for <i>most</i> practical purposes.




Originally posted by AndersHermansson
Now, during orbit, is the shuttle considered to be rotating around it's own axis while it goes one revolution around Earth? Does it have any angular momentum?If all previous statements are true, then yes. (And the answers to both of these questions should agree.)




Originally posted by AndersHermansson
the same could be said for the moon. It is constantly facing the Earth as it goes around and I want to know if it is actually rotating at the same rate as it is orbiting, or that it is simply facing the same side towards Earth because it is following a geodesic, a "straight line" in space?Just like the shuttle (but to a <i>much</i> more pronounced degree), the orbit is not a geodesic, unless you use the terms sloppily. Consider mercury. It has an orbit about the sun very similar to the moon about the earth, but also a rather observable "wobble" caused by tidal forces.




Originally posted by AndersHermansson
...I'd like to know how I've misinterpreted GR in the sense that orbiting objects is following a geodesic, a path that is often referred to as a "straight line" through space because of space-time curvature. Well, hopefully what I said above answers the misinterpretation. But, here, I see evidence of yet another misinterpretation.

I will venture that the curvature of space-time is not as closely related as you think to the common sense idea that orbits are elliptical, and therefore curved. The curvature is much deeper than that. Worldlines may be curved in <i>flat</i> space-time. The curvature is of the space-time itself. This manifests most directly in the tidal force, <i>not in the fact that orbits are curves</i>.

Imagine two streets running N-S in your home town that you consider parallel (i.e. ave A and ave B). Now imagine that they go all the way to the north pole. Are they still parallel there? No. Why? Because they exist on a <i>curved</i> 2 dimensional manifold (the earth's surface). The analogy is more pronounced for lines of longitude separated by several degrees. At the equator (let's say that they arbitrarily "start" there), they seem parallel. But at the poles, they are very much <i>not</i> parallel (in fact, they INTERSECT!).