timo

In circular motion, it always will. Take the (sin(t),cos(t)) example in above. We hopefully can agree that this is circular motion. Try to find a time for which the acceleration is not perpendicular to the velocity. Try to find a time for which the magnitude of the velocity is not 1. You cannot make a small timestep, say "now my velocity has changed direction", take the old acceleration and say "and it´s not perpendicular to the acceleration". Well you can, but you are comparing v and a for different times/positions, then. And that doens´t make too much sense.

Me neither. And given that the problem is analytically solving the equations of motion (which is solely math and no physics at all), I have serious doubts about it. I don´t understand that. But you can get approximate solutions by simply simulating the system numerically (on a computer).

I have no good explanation for it but you can see it easily from the math. Let a circular motion be described by (x' date='y)(t) = (sin(t), cos(t)). The first derivative (with respect to time t) is the velocity, the 2nd derivative is the acceleration. You will easily see that (a_x, a_y)(t) = -(x,y)(t) It does. Not really. Take it this way: If the acceleration is in direction of the velocity, the speed increases. If the acceleration is in opposite direction of the velocity, the speed decreases. Seen this way it seems only natural that a perpendicular acceleration let´s the speed unchanged, doesn´t it? I don´t get that part. What fact? And what is impossible? Hopefully, that statement becomes superfluous in the light of what I said in above. No good idea how to describe it. But it´s not a prequisite, imho. Circular motion -as most things in physics- is something you get used to by working with it, so don´t worry.

Please keep your erotic fantasies for yourself, there´s some minors in here.

I somehow prefer the explanation by MacSwell.

Three remarks: 1) Is this thread remarkably different from your last ones about the same topic? 2) What time of the year do all planets and the sun lie on one line (as shown in your picture and demanded by your calculation) ? 3) What is the underlying reason to assume the planets orbit around that (incorrectly calculated) center of mass ? EDIT: Forget 2), I found the corresponding passage in your text.

I am not convinced that electrostatics shouldn´t suffice, but either way: Where exactly would you see a problem in post #50? I don´t think you doubt that the field before the vanishing of the charge is ~q/r². So as far as I see there´s only two possibilities left for being errornous: 1) Gauss Law does not apply or does not apply the way I sketched that I want to use it. If you see any error there, please tell me what exactly the problem is. 2) Related to 1) but in my eyes slightly different: The assumption that the charge-free space is rotational symmetric around at least the former position of the charge. Now that would really suprise me if that wasn´t true. My approach in #50 remains the same if you let the charge drop to zero in a finite time interval with any function (linearly, for example), as long as that time interval is sufficiently small (smaller than 8 minutes in this case). So any caclulation footing on a certain q(t) function are very welcome for analyzing what went wrong. True. And it also is a completely different scenario for several reasons, the most important being that my assumptions in #50 don´t hold true there. Neither the use of electrostatics for the q/r² nor the spherical symmetry of the system.

See the beginning of my previous post #50 for an explanation of why I think the change might be instantaneous. In the case of a charge starting to oscillate around there´s two major differences between the scenario I descibed in #50, namely that 1) there is no violation of any basic law of physics and 2) that you cannot apply electrostatics to a moving charge.

That is exactly the point, I think. If you pull the charged sun away rapidly, it would still be there so you couldn´t use the argument for t>T in above as easily (most probably not at all as the electric field should in fact not be zero, then). If I remember correctly the requirement for a Schwarzschild metric (gravitational field of the sun) is spherical symmetry of the energy-momemtum-stress tensor. I assume radiating away the sun at once would still result in a spherical symmetric energy-momentum tensor with the same "effective mass". So possibly there might not be any change at all, then (except for all living on earth dying after 8 minutes because the energy wave reached earth). Well, for me "a force travelling at speed of light" probably means that the basic objects I build up the field upon have no mass and therefore a velocity of c (I have not seriously thought about that before). In that case, iirc the case is quite easy as in the linear approximation, the basic deviations from a flat metric have to obey a wave equation similar to that of photons and especially have a zero mass-term. So if you define the "speed of a force" in the way I just tried to sketch, you get your answer on what the speed of gravity is as soon as you have defined what you were asking for.

They are having a poker game with the continuity equation, I´d suppose. At least I think their absence is related to another. EDIT: Or let me ask the other way round: Except for the heuristic "exchange particle is photon which travels at lightspeed => it takes 8 minutes to note a change"-argument, is there a way to do an explicit calculation that gives me the 8 mins? I get the instant change directly from electrostatics which seems valid due to the charge not moving.

I would suppose instantly ... just like you´d instantly realize the change of an electric field if the sun had charge. (I´m a bit Martin-inspired today so I try to break out of the "give the same answer for the x-th time" routine and rather give a controversial statement)

I´ve always wondered what people mean when they are talking about "speed of gravity". That might depend on what you accept as a proof. I have a flask of water in my hand. If I open my hand, it will fall down and hit the floor afterwards. If the bottle falls down slower than c, the order of the events "I open my hand" and "flask hits the floor" will always be the same. That is very neat considering that relativity -which is where the speedlimit of c comes from- demands that anyone can watch me dropping the bottle and that none of them is more or less correct in what he sees. If the bottle fell down with >c, the order of dropping and hitting the floor would not be unique anymore. Some people would see me dropping the bottle before it hits the floor, some others would see the bottle hit the floor before I even dropped it. That arises a whole lot of problems/questions: How can the bottle hit the floor when I am still holding it in my hand? Who is correct in what he sees? Why do I throw water bottles around at all? In short: The best reason for a speed limit of c that I can think of is that velocities above c cause a real lot of (still unresolved) headaches.

WiSci is a wiki - similar to wikipedia. The advantage in posting "if you decide to study xyz you can later become an abc" there I see is that you have the possibility to keep the list sorted.

I like the idea, too. How about making use if WiSci and create a page /set of pages, there and link from a sticky here. Doing it in the form of a normal thread seems a bit chaotic to me, if everyone writes "...and you can also do thisandthat..." posts without any particular order. Specific questions can still be handeled here (which is a better for of comunication for a conversation).

imho the main reason is that people are usually used to think that the letters we use to write down numbers have a meaning of themselves. That´s what you are used to when you learn to calculate numbers (add them letter by letter, divide them letter-combination by letter-combination, ...). The abstraction that these letters are just a pictorial diagram for some abstract concept (and that two totally different paintings can both show a house, for example) is a way of thinking you usually do not need unless you are doing algebra. Since I almost know this will happen: I doubt that any discussions about whether it is true or are welcome here. We have a very long thread about it (search function should reveal it) which was closed because some mod/admin (I think it was Dave) got fed up with the discussion. EDIT: There´s the old thread in case someone want to read it up: http://www.scienceforums.net/forums/showthread.php?t=3967&highlight=ending+debates

Magnetic boots on an iron floor? Or better: Boots with iron ... errr ... downsides and and intelligent floor that becomes magnetic (electromagnets) when the boot comes near? Doesn´t have to be iron, btw. I´m pretty sure today´s research in material science already offers better-suited materials. About the "like what happens when on earth we get into water": Yes, you´re pretty off the track, there. Besides that the effect is not really related to pressure, the best you could get would be removing all the air which -besides from being a bit uncomfortable- might have an effect in the order of maybe a few gramm. Otherwise you could invent some material which restricts gravitons on the same branes as the other forces, hence effectively strenghtening it. It´s utter crap, of course, but you´re on the same level as many other SF movies, then. Plus, you can probably even justify it with a quote from the holy book (Brian Greene, "The elegant universe" ... what book did you think of?) . Guess I´m not too much of a help for you but at least I have some fun writing this

According to todays physics standards to create gravitational attraction you need mass (energy in a more general form but the resrtiction following will be the same). To create earthlike gravity you need a whole lot of mass - most probably more than you can justify even in a SF novel.

Use the standard method which iirc was also used in 2001 - Odyssee in space: Make the vessel rotate.

I faintly remember that you need the "Auswahlaxiom" which I suppose is called "axiom of choice" in english. Other than that I would not assume that anything physics-specific (the axiom of choice of course is not really physics specific, either) comes in: Sketch of the reasoning I´d try to follow: In QM, operators are linear. => They can be written as a matrix. -> The eigenvectors of a matrix form a base for the space (here comes a small problem as the only people having told me so far are physicists so it might not be true in general - but I think it is).

The people I know at such companies (mostly Infineon) are Physicists, Chemicists and Material Scientists.

I remember that some 5+ years ago some physicists from the applied optics group in Darmstadt showed us around in their lab. They were storing data in some special crystals via interference patterns of lasers (the crystals had the special property to make irreversible structural changes when a sufficiently high electric field was applied). They already could store data in them and told us they will soon be used in industrial applications .... . Well, that was 5+ years ago and I never heard of that technology again. But half a year ago I talked with some solid state physicists who does some magnetic stuff for HDs about that technique and he told me that it´s pretty dead as modern HDs almost get the same capacity they aimed at with their crystals. I cannot judge if he´s correct but he´s likely to be up to date so I guess the idea of storing data in crystals on computers is pretty much cancelled.

The inside of a uniformly charged hollow sphere would come to my mind, first. Admittedly, it might be not what the OP had in mind as the field is constant zero. But strictly speaking it qualifies as constant.

Lets say it this way: What is the transformation matrix between the coordinates (t,x) I see and the coordinates (u,y) the guy on the beam sees ?