The continued irony constantly being told that Newton's equations produce good enough results and are worth teaching, by people who are actually denying Newton's results is not lost on me.
https://en.wikipedia.org/wiki/Three-body_problem
Because Newton depends on picking random accelerating reference frames you can make it look like anything you want. Pick the centre of the galaxy as your reference frame and everything in the solar system is following an ellipse far more perfectly than a thrown object follows your beloved parabola.
Einstein just said that if it's not being accelerated it follows a straight line at constant velocity. If you look through what I've said, you'll find me saying that, you won't find me saying that a 3 body problem solves to an ellipse.
I thought I was a rude prick... clearly I have a lot to learn.
I realise now that when you were talking about a parabola, and said "It is an ellipse only if there is a single other point source of gravitational attraction, which isn't even as practical an approximation for orbital mechanics." you'd changed the subject to 3 body systems. And you complain about Catina posting hard to understand missives.... (Wait, was that you who complains about that or Greg... Sorry may have got that arse-about).
You can also look through what I've said and see where I said that I'd given a complete explaination of all the different ways one can apply Newtonian physics in the real world. You won't find that either.
You will find somewhere where I say that people who's job it is to actually guide spacecraft don't use dimly remembered high school lessons... Which if you think for even one second, implies that no high school lesson is adequate to apply this stuff in the real world anyway. You'll also find where I say that the actual role of high school is to give students some understanding of the world around them. ie not for practical use, so your straw man that Newtonian physics is not of practical use is... well a straw man.
Further examination of what I said will reveal that I said the right thing to do when teaching was to apply broad brush strokes, and then fill in the details. The easily grasped broad brush stroke of Newtonian motion is 2 body, and then fill in the details with N body. Understanding N body doesn't required that you realise that 2 body was wrong, it's just applying the same equations in a more complex situation. That's in stark contrast to teaching parabolas, (which is wrong, because it uses the wrong equation to describe what's going on. I had thought indisputably wrong but apparently it is disputable...) and then teaching 2 body, which for understanding, depends on you realising that what you had been taught about parabolas was actually wrong. Something that's apparently near impossible.
Of course I'd rather that schools didn't just stop teaching 12th century physics and then applying some sort of weird correction to bring it up to 17th century. I'd rather that they started off by teaching modern physics. Not least because it's much easier to understand.
]]>Glad to hear that...
]]>Well in this case. I googled for books containing the exact phrase "an orbit followed by electrons around an atom's nucleus"
I got 205 books. Text books that someone pays through the nose to buy, that contain that exact word order. I only checked the first 30 or so but they all had the same phrase embedded in the same paragraph, with the same punctuation.
Oh... even more interesting. I just refreshed and now google refuses to search books on that phrase. However it will return results if I google a slightly different part of the paragraph: "An electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the '1 shell' (also called 'K shell'), followed by the '2 shell' (or 'L shell'), then the '3 shell' (or 'M shell')"
Searching on "an electron shell may be thought" gets me 198 books. Google's AI is doing something very interesting that I don't understand.
Titles seemed to be mostly biology in some variation or another, but some are the solar system, earth sciences, various forms of chemistry, anatomy, medicine, physics and QM. The anatomy ones diverge slightly from they physics and chemistry ones but all the anatomy ones contain the same spelling mistake. I think you might be able to create a DNA like tree of life out of them, which would be amazing.
Could it be that the reason schools teach 12th century physics is that for the last 900 years "writing a text book" meant "copying someone else's text book". Surely not... I mean, at the university where my Mum was head of school if she caught her science students plagiarizing she would politely suggest that they could either withdraw or be expelled. No second chance. Surely no academic would take such a risk. Must be just co-incidence.
Really, could schools be any worse? I struggle to think how.
]]>The reason for the last is that the 'true' model is often essentially unusable, in addition to being completely unteachable except to good mathematicians. Atomic structure is extreme, in that doing chemistry or surface physics using first principles calculations is both extremely tricky and needs a MASSIVE amount of computing power. It is quite impossible by hand. Even today, the state of the art is inadequate for using it for even simple biochemistry, and so a variety of empirical approximations are used.
]]>Once you've managed to get your space ship into orbit you clearly see that it's in an elliptical orbit that you can play with (for instance extend it or try to make as closely to a circle as possible).
And when you de-orbit you see the ellipse shrinking until it crosses the ground, but it's clearly still an ellipse that closes on itself inside the planet (or whatever body you're orbiting).
It's immediately obvious that—when it makes ground contact—the ellipse doesn't somehow magically turn into a parabola, but simply becomes partially embedded in the planet, while remaining an ellipse.
And even when you reach escape velocity and your path appears to become a straight line at first glance, the only thing you need to do is to zoom out in the map view, and you immediately see that you're not on a straight line (or parabola, or any other path), but still in an ellipse, now orbiting the sun instead of the planet. And by extension it's easy to understand that even if you could escape the orbit around the sun (I don't know whether that's in the scope of the current version of KSP) you wouldn't be "free", but would be in an elliptical orbit around the next bigger structure.
So there's really no need to talk about parabolas if you visualise it this way. Which means that I tend to agree with gasdive.
]]>I don't think I've seen that specific behaviour before (probably because I don't allow Google to set cookies or run javascript), but it does definitely look to me like a further manifestation of a class of behaviour of which Google is all too fond, to wit, deliberately being a pain in the arse to try and make sure you see what they want you to see instead of what you want to see.
Boogle Gooks is particularly bad in that respect. Far as I'm concerned when I click on a link to a document I expect to retrieve the entire document, complete and unabridged. I find it both unacceptable and thoroughly infuriating to be presented with some arbitrary and small subsection of it, and worse, to then encounter deliberate obstacles trying to prevent me retrieving the missing bits. When on top of that the web page itself is deliberately written in such a way as to make it slow, unresponsive, awkward, dysfunctional and generally a thorough arseache to use, that's just too much. So not only do I never bother to even click on a Boogle Gooks link, I gain another reason to eschew the search engine as well and use Bing instead - Bing, as a rule, does not throw up multiple pages of useless Boogle Gooks results and bugger all else.
]]>(Taking an opportunity to bash Google is a different matter :))
]]>The trajectory of a projectile in vacuum is of course an ellipse. However, given that the semi-major axis is 6400km or thereabouts and the width of the ellipse at the relevant point is at most 120km (the Paris Gun mentioned below) a parabola is a reasonable approximation.
Why? Because other sources of inaccuracy are vastly more important, given that the idea of artillery is to hit a target. Such things as minor variations in particle size and composition of the propellant, thermal expansion and drooping of the barrel, wear on the barrel (all of these three are taken into account in tank gunnery) and, much more important, distortions of the trajectory caused by the projectile passing through air instead of a vacuum. Not just air resistance, but probably also forces caused by the spin of the projectile.
Probably also the Coriolis effect as well, at the longer ranges.
Incidentally, the ellipticity of the orbit is itself an approximation because the Earth is not a perfect sphere and is not of uniform density. This only matters at really long ranges, however, but it does matter; for example, ICBM targeting needs a detailed gravity map for accuracy to be obtained.
I rather doubt that orbital perturbations caused by other Solar System bodies are significant, but maybe the perturbations caused by the Moon might be. Not being a missile targeting expert, I wouldn't know.
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