Look: I wanna put this issue to bed and move on. So I'll try to close this topic without being insulting:
You didn't even choose the correct coordinate systems to transform between. Movement within cartesian systems IS trival because it's not fully characterizing the systems under study. Your "transformation" does not express phi equivalently between the two systems.
It is very difficult to decipher what you mean by this attempted criticism. Nonetheless, I have reflected on it very carefully in case I am missing something. Despite the reflection, I have reached the conclusion that my argument is sound.
What I mean is that your transformation must be between polar coordinate systems in order to allow the incorporation of the principle of conservation of angular momentum.
https://en.wikipedia.org/wiki/Polar_coordinate_systemWhile you can easily express position in any instant of time in a cartesian coordinate system, there is no precise way to express angular momentum in a cartesian coordinate system.
The ONLY thing you can possibly be saying is that positionally, you can engage in trivial transformations that express planetary position both in a heliocentric or a geocentric model.
What I'm saying is that you've reduced both models to simple positional reporting, stripping away both the angular components as well as the mass and gravitational components of the models.
You're essentially saying "you can express the position of any body in the solar system w/reference to any other body of the solar system, in a cartesian coordinate system".
Fine. I have no beef with that, because that's almost a useless statement. It's certainly not applicable to astrophysics, it's only applicable to coordnate systems.
It is certainly not a full description of the heliocentric
model nor the geocentric
model.
The emergence of the heliocentric model (and the furor which delivered dire consequences to most men of science involved in the discussion) came about because we (humanity) realized that The Church's geocentric model MUST be wrong because:
- the geocentric model was conceived before, and without reference to, the discovery/characterization of gravity, the gravitational constant, and the principle of the conservation of momentum
- the earth would have to be supermassive, with gravitational field many times larger, to be the center of the solar system
- the sun would have to be super-small, with gravitational field many times smaller,
- observations of how sunlight strikes the moon and the other planets were inconsistent and unexplainable by the geocentric model
- the "mars problem" violates the principle of the conservation of momentum
And yet, men of science were pressured, under threat of death or imprisonment, to renounce their heliocentric observations on the basis of some bizarre, concocted notion having nothing to do with reality, namely the "central importance of man in the universe".
So, to say one model is just a translation of the other, is highly offensive to me. You are excusing that great first battle between the church and science as "a disagreement of convenience, not of substance".
As far as I can tell, your attempted criticism is meant to suggest that (classically speaking) Newton's laws of motion would not work in my new coördinate system because my transform does not preserve the necessary classical invariants compared to the background frame. That is completely correct, but also irrelevant. You just have to derive new laws of motion by using the definition of the transformation.
No. I am not suggesting this. I am going
far beyond and telling you that the geocentric model is a
dead end. There's nothing else to derive because the geocentric model yields incorrect math.
Think about the story of the transition from geocentric to heliocentric: Cathy, the church put Galileo under house arrest. Copernicus' works were considered heretical. There's even a claim that Kepler killed Tyco Brahe to get at his data.
Does this sound to you like a transition from one equivalent model to the other? Not at all. The change from the geocentric model to the heliocentric model birthed the entirely new science of Astrophysics, which was at-once made congruent and "complete" with the cutting edge discoveries of gravity as an inverse-square phenomena, the gravitational constant, mass, density, and the conservation of angular momentum.
What I'm telling you is that the geocentric model doesn't just require "deriving a new law of motion". What I'm telling you is that any new law of motion one COULD derive from it is no law at all, but just a nonsense equation that wold have to change for every other individual planet.
Instead of a universally applicable "law of motion", you would instead have a new "description of motion" that was unique to every planet and every observed rotational phenomena, which would then be different from observed angular momentum on earth.
What I'm saying is that the geocentric model fundamentally contradicts
all of classical Newtonian physics, replacing it with a set of special cases usable only once, rather than being universally usable. (with adjustments for precision)
You can easily transform between coordinate systems to express planetary position. As you have said, yes, that's trivial.
But the geocentric model is a mere observational, positional descriptor. The heliocentric model unifies the separate discoveries of F=ma and the conservation of angular momentum. Your reference to "phi" is unexplained but ϕ is often used to denote angles, so I could also interpret your attempted crticism as suggesting that you think there should be some rotational transformation involved in my argument. This is not necessary for my argument, although you could do it if you wanted. In fact, you could use any kind of crazy coördinate transform that you might dream up. Any one will work, but the laws of motion will have to be written differently depending on which transform is chosen.
I leave it as an exercise to write down the form of the classical laws of motion that would apply under my transform.
It should be clear by now what I mean. If not, I don't plan to clarify further. This is the end of the road for this sub-thread.
...Then, there is the "mars problem" that the geocentric model cannot explain:
http://www.universetoday.com/36487/difference-between-geocentric-and-heliocentric/
This is a problem with the traditional religious geocentrism, but not with the geocentrism described in my posts.
That's not a distinction I care to discuss.
Even more importantly:...
Why would anyone in their right mind do the transforms from a geocentric model to do this work?
Here you have hit upon the real reason that the heliocentric model is classically preferred. Under classical mechanics, the laws of physics take on the same form in all inertial frames of reference but not in a non-inertial frame of reference. In a non-inertial frame, one has to derive different laws of physics.
Thus, it's much simpler to choose our reference frame as an inertial frame because then the laws of physics will be written the same in all other inertial frames. The heliocentric frame is technically not inertial (because the rest of the universe exists, after all), but it's approximately inertial. This means that, under classical mechanics, there really is a sense in which it is "more true" to say that the Earth revolves around the Sun rather than vice versa: namely, choosing the Sun as the centre allows us to deal with planetary physics using the same laws of physics that apply in all inertial reference frames, whereas under my model, you need to use different laws of physics for planetary motion compared to the physics in an inertial frame!
However, this is nothing new. I pointed out in all my posts above that the heliocentric model is simpler and more useful. That was never in dispute.
I should note, however, that this theoretical advantage is unique to classical mechanics, and is not a property of the universe. The point of the Einstein quote I gave is that we could devise a system of physics where the laws are the same in all frames, even ones defined by crazy transforms. The fact that the heliocentric model has conceptual advantages is a consequence of the models we use, rather than a fact of nature.
No no no no, a thousand times no. The geocentric model is inconsistent in any "science" you wish to propose. There is no universally applicable rules (laws) that can be derived on that basis. Here you have hit upon the real reason that the heliocentric model is classically preferred. Under classical mechanics, the laws of physics take on the same form in all inertial frames of reference but not in a non-inertial frame of reference. In a non-inertial frame, one has to derive different laws of physics.
The heliocentric model is preferred because it is always consistent with the Newtonian physics of the time. The geocentric model is discarded because it is never consistent with ANY physics.
You speak of a "preference" for the heliocentric model as-if there's some institute somewhere that has built a strong, consistent astrophysical science based on the geocentric model that does not purely and totally contradict Newtonian physics.
What I'm telling you is that there is nothing that can possibly take the form of a "law of physics" that is derivable from the geocentric model.
Your term "inertial frame of reference" appears to be a self-invented term that I do not want to discuss.
This...language....you have developed is offensive to me. It's as-if you read "Flatland" and believe the solar system can be described in 2D positional coordinate system, ignoring mass, acceleration, density and the gravitational constant.
Galileo point out the initial inconsistencies and problems of the geocentric model. Those problems make the geocentric model not just "non-preferred", they make it contradictory to the wider body of physics.
The discoveries of Newton put the final nail in the coffin of the geocentric model because it became clear for all to understand that the physics governing the movement of planets is the same as the physics governing rotational motion (accounting for friction and losses) on earth itself. All was unified in a clear and complete description that scales beautifully to the planetary level.
At the very least, read the Wikipedia citation, or read the book "Galileo":
https://en.wikipedia.org/wiki/Galileo_GalileiThe Inquisition put Galileo under house arrest for the rest of his life, under the charge of "advocating heresy against the church".
The models are not equivalent and translatable. One is ridiculously inconsistent.