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However, if you're modeling the part of the Earth in which (for example) the airlines operate, the geocentric model is quite effective. It allows you to ignore forces like the Coriolis effect, and the gravitational pulls of the moon and sun, which are inconsequential in flight calculations. You even ignore the Earth's rotation, and consider the sun to be in orbit around the Earth, because this greatly simplifies your equations.

I was mostly agreeing with what you said until you said that flight calculations can omit things like the Coriolis effect and the Earth's rotation; in point of fact, both of these play a major role in calculating trajectories for long distance flights. For example, check out this page, which has some great animations of the Coriolis effect, along with this quote (that directly contradicts you): "In reality, pilots take the Coriolis effect into account so they do not miss their targets."

Similarly, in scientific study of the molecular mechanics of our bodies (medicine), the orbits of the earth, moon, etc. are rarely if ever mentioned. Their effects are unmeasurable at the molecular level, so there's no point in taking them into account.

Rarely? Try never. The notion that tidal forces somehow affect our bodies internally has been largely discredited, and while it's true that some organisms respond to lunar cycles, this has more to do with cycles of luminosity and responses to ocean tides going on around them.

Your point is well taken, but... erm... it's kind of stating the obvious to anyone with a background in the physical sciences. And I have a background in the physical sciences, incidentally. :-) Case in point:

Part of such an approach is recognizing that you're not really dealing with "the Truth" in any philosophical sense. Rather, you are dealing with the equations, and including in your model only the motions and forces that are required to explain the parts of the system that you're dealing with.

Thank you, Captain Obvious! Yes, we do this all the time to reduce the number of free variables we have to consider in any mathematical model. You don't throw stuff in your model that will only have a miniscule or immeasureable effect. (The trick comes in trying to figure out what things can truly be ignored and what things can't. Sometimes, that isn't so obvious.)

As for philosophical "Truth," I believe that is what science and religion are both seeking, ultimately... but they do it in their own, very different ways. (I won't say "equally valid," because that's a whole other kettle of fish, and I personally don't think the two approaches are equally valid, not even for the domains in which they are meant to be applied.) I think, though, scientists don't get as hung up on philosophy because they're more focused on empirical evidence than on being in love with ideas for their own sake and spinning complex notions that have zero grounding in concrete reality. Maybe that's because most of the physical sciences focus on a philosophically materialist world view, but it happens to be a very useful viewpoint to have if you're in the business of doing science.

Personally, I find it absurd to state with a straight face that heliocentrism and geocentrism are totally equivalent and that heliocentrism is "merely" a computational convenience, for many of the reasons you yourself mention. This is where starry-eyed philosophers get a smack-down from reality, and where I have to tip my hat to another philosopher... if you're going to invoke philosophy, then I have to invoke Occam's Razor, and point out that the real win of heliocentrism (and follow-on theories that mark the advent of modern physics) isn't the convenience of being able to do orbital calculations simply! No, the real win is having a single set of rational, co

I just got an interactive whiteboard for my room, and I've been looking around for useful animations for the kids. Classzone has a number of these, you just have to select the right textbook. I'm teaching in Maryland with the "Algebra 2 2007" book. If you choose a different book, you may wind up with the older version of their site. That's just a bunch of PDF's of the supplemental workbooks. Animations of concepts are the way to go I think. This is especially true when kids can manipulate the process themselves. Classzone has these in Shockwave format. There's one for slope where you can move either of two points on a 2d line, and the slope computation appears, the rise and run are shown, the line is redrawn, etc. You could certainly do the same lesson with a chalkboard or overhead projector but for visual learners, seeing the change will make a big difference. That's my hope anyway.

The best approach seems to be like one of the other posters said: don't think of it as "what can I present with a projector," instead think of it as "what can I do to present Chain Rule interactively?" Also, please do avoid powerpoints. One of the other teachers in my building has written a series of powerpoints and just stands at the board flipping pages. Make sure you have kids using the new system and thinking about ways it can help them. For example, being able to enlarge, recolor, print, etc your handwritten notes can be a boon for students with certain special needs.

Some of the other posters in this thread are talking about the larger issue of technology in classrooms. That's fine and all, but I didn't ask for this interactive whiteboard. Now that I have it, I'm trying to make it worthwhile for the kids. Often that's as much control over the larger issues as teachers have.

I'm not "an environmentalist" but I do have increased interest in the environment these days... maybe because of the increased media coverage (undoubtedly so) or maybe my worry over how my kids will live... whatever.

Since you say you do have an increased interest in the environment, I guess you'd be also interested in knowing that there are so many dead zones in the world...the majority along the US coasts - sadly.

This http://www.classzone.com/books/earth_science/terc/ content/investigations/es2206/es2206page04.cfm would be an interesting read.

The core is divided into two parts, the outer core which is liquid, and the inner core which is solid. If you are curious why this is, you need to study the phase diagram (P-T graph) of iron.

How is this known?

S waves do not travel through liquids.

First, I don't think two cars could travel the ribbon at once. Second, a car already at GEO is stationary relative to the earth so it would not provide any force that could be harnessed to power the other car. The force it could provide would depend on how far down the ribbon the car had travelled since below GEO the centrifugal force will be less than its weight. However that force will start from zero at GEO and increase to a maximum at sea level. Think about that. There is no upward force to help lift the upward bound cargo when it needs to get going and the cargo is being propelled violently when it nears the end of its journey at GEO. So I don't think this system would work.

I have concerns about laser assisted solar panels as well. Shining a laser so close to the ribbon could be problematic. A laser beam will travel in a straight line but a straight line is not perfectly straight inside the atmosphere. Some observatories use lasers now to adjust their mirrors reduce the blurring caused by the atmosphere. I don't know whether the effect would be pronounced enough to worry about for this application but I have another reason to worry as well. I expect the ribbon might oscillate like a guitar string for several reasons.

If the ribbon is not anchored directly over the equator there would be a natural tendancy to oscillate since the tug of gravity would not be completely along the length of the ribbon. To understand, imagine if the ribbon were anchored at the pole then think about the pull of gravity and consider the inverse square law and the fact that sealevel is about 4000 miles from the center of the earth while GEO is about 24000.

Moving the anchor to 'avoid space debris' would also "pluck" the string. Atomospheric winds would cause vibration in the ribbon. Imagine the force of a 150 mile per hour jetstream pushing against a 3 foot wide ribbon! And if there are lateral vibrations as in a guitar string then there would also be a circular precession similar to foucault's pendulum.

I can't say if these effects would be negligible or not, but I don't see any discussion of vibration in their FAQ much less an engineering study.

We should be trying to maintain global warming.

temps for last 150,000 yrs (you need flash and ie)