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[asterroc]

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Comments

[q10.livejournal.com]

it's not that it's not measurable by normal force - it's that it's not there at at all in the frame that takes the orbiting station to be stationary. if you adopt such a frame, i'm pretty sure you can do all the computations for the mechanics of objects in the station in a way that does not once mention gravity (or, at least, does not mention the Earth's gravitational pull - the objects bouncing about the station are of course interacting with each other gravitationally, but i assume it's customary to ignore this). and it ought to be a pretty well-behaved inertial frame in other respects, if i remember this right (it has, admittedly, been a while).

of course, i don't think most people are thinking about it like this, but the point is that, for the movements of objects aboard the station relative to the station, if we do all our math as if there is no gravity involved, we ought to get the right results, and even people who aren't up to doing the math probably have an intuitive grasp of that.

[zandperl.livejournal.com]

for the movements of objects aboard the station relative to the station, if we do all our math as if there is no gravity involved, we ought to get the right results,

Well, technically it would still be a non-inertial reference frame, so if the station is large enough then an assumption of no gravity and an inertial reference frame would not be correct.

If you care about the details, if the station is large enough in the radial direction, objects floating in the station closer to or farther from the Earth would appear to drift forward or backwards in orbit (respectively, I think). If the station is large enough in the other direction perpendicular to travel (i.e., for an East-West orbit, long in the North-South direction) you would be able to measure the Coriolis force.

[q10.livejournal.com]

thanks - this is quite illuminating.

[zandperl.livejournal.com]

Whew! I'm never sure which things you already know and which you don't, so I'm glad this one came out as useful rather than talking down. :-P

[q10.livejournal.com]

well, i mean, you're clearly entitled to risk talking down if i seem not to know what i'm talking about. in some cases, when i perceive things as talking down, i get snippy, but even in those cases that's an issue with me, but a sign that you've done anything wrong.

[sildra.livejournal.com]

It sounds like you're mixing up Special and General Relativity. Special Relativity can be invoked when everything can be done assuming something is stationary in an inertial reference frame, i.e. there is no acceleration involved relative to any other inertial reference frame. It's usually used for objects moving at significant fractions of the speed of light relative to each other. Gravity, however, being force-like (and therefore appearing to cause acceleration) is necessarily non-inertial. In General Relativity, to deal with gravity as a not-force, rather than treating an object as stationary in some frame, we treat spacetime as warped and an object as moving along a geodesic of spacetime's new geometry (it's been a long time and I forget whether we pick the largest object or the center of mass of the entire system of objects to be the stationary reference frame, probably the latter). A geodesic through spacetime can only be stationary in space when spacetime is completely flat--that is, there is nothing with mass around (so in that case, it reduces back to Special Relativity).

[q10.livejournal.com]

you're right, of course, that i was mixing things up and/or being sloppy.

i was mainly remembering being taught to think of an elevator in free-fall as a canonical inertial frame, which is, i'm sure, wrong in the details, but which is really good enough a lot of the time.

[sildra.livejournal.com]

Well, it is true that if you decide to invoke curvature of spacetime rather than gravity, you can redefine inertial to mean anything moving along a geodesic in your curved spacetime, and it won't contradict the Special Relativity definition of inertial (just expand on it). In that case, an elevator in free-fall is an inertial frame, yes. It's an either-or thing, though. If you call it "gravity" instead, then it's an accelerating frame, which is not inertial. But the basic argument in favor of General Relativity (ignoring, of course, that now that the framework has been built up, GR was shown to predict new phenomena which have since been discovered) is that an object in freefall looks, in a lot of ways, more like an object in an inertial frame than like an object with a force applied to it.