studiot

You said it yourself. By pressing her button. Transponders of one sort or another have been around for decades. They were certainly small enough by the mid 1970s to meet your description.

Well so far I've got as far as printing the pdf out and having a swift butchers. It's really good that you have declared (hopefully all) your variables at outset. +1 It's also interesting to see a chemical engineer using the ideal gas equation rather than z or w factors. Anyway I'm not sure which 2 equations you want to solve for, presumably the characteristic equations at the end 5.06 and 5.05 or 5.07 ?

fair comment +1

So what is a line spectrum from Sol and Sirius if it is not a comparison to two clocks in different widely separated gravity wells ?

What about the gravity well conditions I offered you ?

Please read more carefully the quote you made from my post. I did not suggest that DM can form atoms, or any other particles. I said explicitly we don't know if.......

I don't have this book to hand at the moment and I can't rememember if he covers wheels explicitly, but Steven Vogel does an excellent job investigating the reasons how and why nature and man achieve identical mechanical goals in the sifferent ways they do. Fo example no muscle can generate a push force by itself.

I really don't understand what's special about this proposed experiment Since the early days, it has been a tenet of astrospectroscopy that the pattern of spectral lines (including shifts thereto) and aberations are determined by phenomena described by GR. So light arising in galaxies (and therefore gravity wells) far far away mr skywalker, are calibrated using GR.

I still think your question is rather limited for no obvious reason. Here is a Wikipedia discussion on the wider subject. https://simple.wikipedia.org/wiki/Rolling_and_wheels_in_the_natural_world

I don't follow the significance of limiting this to organs? What about the tortoise ? What even do you mean by a wheel ? Here is an image of the famous falkirk wheel.

Obviously not in respect of whatever conditions are being applied. That is true of all models. We don't expect elastic analysis to match reality beyond the 'elastic limit'.

Actually nature uses rotation in some suprising ways. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=rotating+microbes&iflsig=AJiK0e8AAAAAY7g0_8kobF67VuYcPl8mgs7idJ3VWaj_&gbv=2&oq=rotating+microbes&gs_l=heirloom-hp.3..0i546l2.11096.32186.0.32384.19.16.1.2.2.0.176.2198.0j16.16.0....0...1ac.1.34.heirloom-hp..0.19.2308.MRvTaHdMUtY https://en.wikipedia.org/wiki/Gömböc good point +1

Of course not. All you have to do is out dt = 0 @t=0 into the equations to see that there must still be an apparent atttraction felt between massive bodies. It must still give measurably verifiable results in the case of static situations.

I would recommend against using the letter [math]v[/math] for clarity since not only does it come out different in the standard font used on this site but it also can represent velocity, as can [math]u[/math], and so can easily be confused with 'parameters'. Addition of velocities is decidedly non linear in SR.

To put it mathematically If LT represents a Lorentz transformation is represents a transformation of something. That something is one of the four coordinates, x,y,z,t. It is easy to show that aLT (x) = LT (ax) ; where a is some coefficient. and the same for the other three coordinates. As joigus noted, LT does not act directly on v, the relative velocity. which is a condition that forms part of the definition of linear in mathematics.

I was rather hoping you might read my post and say to yourself: "That's interesting I wonder why he said that and made the distinction between the formula and the transformation. Perhaps there is something I can learn here." And then ask what a professional mathematician meant when he said For instance the sine function is nonlinear, but the fourier series and transform is a linear application of it. This is a linear polynomial [math]a{x^5} + b{x^4} + c{x^3} + d{x^2} + ex[/math] although only the last term is specified by a linear formula.

The transformations are linear. The formulae involved are not. Edit since composing this I see a non productive exchange of red points.

You are stating british custom. I asked about french custom. My point is that there is no intrinsic correctness or right of this. It is a matter of custom and practice.

Answering the actual question When 1mol of calcium carbonate decomposes into 1mol of calcium oxide and 1mol of carbon dioxide, 177.8kJ of heat is absorbed.

The intent was to bring out that Nature favours spirals at the very large - galactic - and very small - micro crystals in rocks scales. And yes as your link shows that it also applies at normal human scales.

Yup.

Here is a maths free resource for those looking for Maths Tutorials, from the Centre for Innovation in Maths Learning. The two links give the centre's home page, a topic list. https://www.cimt.org.uk/ https://www.cimt.org.uk/projects/mepres/alevel/ These are first class resources available for download in pdf.

Well a telescope is used to make the image of very large objects small enough to fit on the page in normal operation. If you turn it round you get another sort of instrument. The spiral is formed by microscopic grains of quartz in a much larger garnet crystal in schist rock.

The problem, as I see it, is that we don't know anywhere near enough. These guys know heaps more than I do, yet they readily note that they are still guessing. https://starchild.gsfc.nasa.gov/docs/StarChild/questions/question59.html We postulate 'particles', we don't know if DM has particles or if these particles can form DM atoms, or what those DM atoms might look like. So we don't know if there are such reactions as DM nuclear reactions.

Citation please, from someone who has actually measured DM 'particle' velocities.