The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Q&A => Topic started by: you guys are funny on December 15, 2012, 07:10:49 PM
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I have a few questions, some are relatively technical, regarding a number of different things that I would like someone who understands FET to answer. Please answer as concisely possible, and don't use any math unless you truly understand (ie, you don't need to put numbers into an equation to be able to understand what it is saying, no matter the level of complexity) it. You shouldn't need to use any math to answer these questions. Conceptual descriptions would be preferable since a lot of people have little to no background in math, but I've found most people are intelligent enough to understand physics anyway.
Each of these four questions are independent of each other, so if you just want to read and answer one at a time, go for it.
First. It is a relatively well known fact (I worked as an engineer, and have seen the calculations for GPS, at a company that was instrumental in the development of the modern GPS systems, but I won't name it here out of professional courtesy) that general relativity (GR) plays a substantial role in the calculation of position for GPS systems. In fact, if GPS systems didn't take GR into account, the accuracy of your receiver would diminish by several meters per day. This fact can be attributed to the person using the GPS being much closer to the earth than the satellites sending the signals. Because the person (driving the car, hiking in the woods, whatever) is closer to the large mass of the earth than the satellite, time (not just how it is measured, but time itself) moves at a different rate than it does for the satellite. A reasonable description can be found on Wikipedia, but it gets to be highly technical and more or less useless for someone with less than 4-5 years of college level physics. How does the FE model account for the discrepancies in the time between the satellite and the GPS user?
Second, another quick question about satellites. Satellites, and all free falling bodies for that matter, follow geometries known as "geodesics" in the space-time continuum. These are seen as parabolas for a baseball tossed across the park (free-fall isn't just when something falls downward, it's when something is moving without any external forces. a baseball moving less than a couple hundred miles per hour is a nice example, an airplane is not), ellipses (circles for ellipses with coincident foci) for satellites, and hyperbolas for light. This is another highly, highly tested fact with enormous daily consequences. How would the FE model account for this?
Third, I've got a question that everyone should be able to relate to: The sky. Why is it blue? In the commonly accepted model of the universe (this applies to all similar bodies and other instances, but let's just assume I mean the Earth), the sky is blue due to a relatively simple effect known as Rayleigh scattering. Because incoming light scatters elastically (it literally bounces off of particles like pool balls would if they had much different masses. The "elastic" part means that there is no energy loss due to the bouncing, and that net momentum remains unchanged) off of the atmosphere, and the likelihood that a specific photon will bounce (before anyone comments on this, no it doesn't matter whether you look at the photon as a wave or a particle because the math works out both ways. It's just a h##l of a lot easier with the particle model and description) off of an atom or molecule in the atmosphere goes up hugely with the energy of the photon (likelihood is proportional to 1/(lambda^4), or energy raised to the 4th power, which is energy*energy*energy*energy). Since the blue end of the spectrum is more energetic than the red (that's how the spectrum is defined), blue light gets scattered more than red, yellow, orange, etc etc. The reason that the sky isn't violet is because we actually see an average of ALL the visible light that is scattered, but the scattering is weighted very heavily to the violet end of the spectrum. That average is blue.
My fourth (and final) question would make sense to anybody who's spent time playing on, or watching someone play on, a merry-go-round. Let's assume something first: The disk-shaped-earth has to be spinning in order to be dynamically stable in space (There is a host of reasons that a disk has to be spinning about the axis that would stand up from the north pole in what I've seen here, so saying it doesn't is just silly). Since it's spinning (and I hope we can agree on that), you will get the same effects as what makes you fall over on a merry-go-round such as the coriolis effect. There are two other effects, but let's not worry about those since they're much less well known. For anyone who is interested in the math here, the wikipedia article on "Lagrangian Mechanics" is actually quite informative and explains it very well in (somewhat) simple terms. How does the FE theory explain why we view the coriolis effect to be maximized at the equator (for argument, let's say "Equador the country") rather than at the poles (north pole or south pole in the RE model, but the north pole and outer edge in the FE model). According to the extremely well understood (they actually use these same calculations when designing the crankshaft in your car, and the forces on a roller coaster among countless other things) principles of classical mechanics, the coriolis effect should be maximized at the outer edge of a spinning disk. You can test this for yourself the next time you're at a park with a merry go round (by the way, if you're going to test this, the coriolis effect is proportional to your walking speed on the merry go round, so you'd have to be walking on it. If you stand still, then the effect goes away). Again, since the question kinda got lost in the text: How does the FE theory explain why the coriolis effect is maximized at the equator, rather than the outer rim (south pole in the common model)
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First. It is a relatively well known fact (I worked as an engineer, and have seen the calculations for GPS, at a company that was instrumental in the development of the modern GPS systems, but I won't name it here out of professional courtesy) that general relativity (GR) plays a substantial role in the calculation of position for GPS systems. In fact, if GPS systems didn't take GR into account, the accuracy of your receiver would diminish by several meters per day. This fact can be attributed to the person using the GPS being much closer to the earth than the satellites sending the signals. Because the person (driving the car, hiking in the woods, whatever) is closer to the large mass of the earth than the satellite, time (not just how it is measured, but time itself) moves at a different rate than it does for the satellite. A reasonable description can be found on Wikipedia, but it gets to be highly technical and more or less useless for someone with less than 4-5 years of college level physics. How does the FE model account for the discrepancies in the time between the satellite and the GPS user?
You'll find many different opinions here as to whether actual satellites exist, as opposed to pseudolites and stratolites, but in general (heh, punny) FE'ers accept GR to be mostly accurate - except that what Einstein took for gravity on earth is actually acceleration. An easy mistake to make, as they're identical. GPS is typically understood to work via a system of towers, pseudolites, and stratolites, but in the case of the latter (or an actual satellite), eddies in the aether caused by the celestial bodies above us act against the effects of Universal Acceleration (aka Earth's "surface gravity") creating lessening gravitation, and thus relativistic time dilation in the upper atmosphere and space above the Earth. In short - pretty much the same as a spherical earth, except many of us don't believe in satellites, and we substitute acceleration for gravity.
Second, another quick question about satellites. Satellites, and all free falling bodies for that matter, follow geometries known as "geodesics" in the space-time continuum. These are seen as parabolas for a baseball tossed across the park (free-fall isn't just when something falls downward, it's when something is moving without any external forces. a baseball moving less than a couple hundred miles per hour is a nice example, an airplane is not), ellipses (circles for ellipses with coincident foci) for satellites, and hyperbolas for light. This is another highly, highly tested fact with enormous daily consequences. How would the FE model account for this?
In most models, sustained spaceflight isn't possible (though I'm willing to consider that it is and I'm working on a model that allows for it), so most of us will tell you that these so-called satellites don't exist. See many threads and the FAQ on the "Conspiracy" of spaceflight - I don't like to talk about it because I'm not a conspiracy theorist, I'm a flat earth theorist.
Third, I've got a question that everyone should be able to relate to: The sky. Why is it blue? In the commonly accepted model of the universe (this applies to all similar bodies and other instances, but let's just assume I mean the Earth), the sky is blue due to a relatively simple effect known as Rayleigh scattering. Because incoming light scatters elastically (it literally bounces off of particles like pool balls would if they had much different masses. The "elastic" part means that there is no energy loss due to the bouncing, and that net momentum remains unchanged) off of the atmosphere, and the likelihood that a specific photon will bounce (before anyone comments on this, no it doesn't matter whether you look at the photon as a wave or a particle because the math works out both ways. It's just a h##l of a lot easier with the particle model and description) off of an atom or molecule in the atmosphere goes up hugely with the energy of the photon (likelihood is proportional to 1/(lambda^4), or energy raised to the 4th power, which is energy*energy*energy*energy). Since the blue end of the spectrum is more energetic than the red (that's how the spectrum is defined), blue light gets scattered more than red, yellow, orange, etc etc. The reason that the sky isn't violet is because we actually see an average of ALL the visible light that is scattered, but the scattering is weighted very heavily to the violet end of the spectrum. That average is blue.
I just wanted to thank you for explaining why the sky isn't Violet. :D
The sky is blue on a flat earth for the same reason as it is on a spherical one. Rayleigh scattering is well understood (excepting that whole "shortest wavelength" fallacy that causes so many neophytes to encounter the question of violet and get stumped) and I'm not sure why the shape of the earth should matter :)
Hopefully this was helpful to you.
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You'll find many different opinions here as to whether actual satellites exist, as opposed to pseudolites and stratolites, but in general (heh, punny) FE'ers accept GR to be mostly accurate - except that what Einstein took for gravity on earth is actually acceleration. An easy mistake to make, as they're identical. GPS is typically understood to work via a system of towers, pseudolites, and stratolites, but in the case of the latter (or an actual satellite), eddies in the aether caused by the celestial bodies above us act against the effects of Universal Acceleration (aka Earth's "surface gravity") creating lessening gravitation, and thus relativistic time dilation in the upper atmosphere and space above the Earth. In short - pretty much the same as a spherical earth, except many of us don't believe in satellites, and we substitute acceleration for gravity.
Einstein's thought experiment from which Special Relativity was derived actually stated that in is impossible to tell a body force (such as gravity) from acceleration in many circumstances. This is a point that I would have to go outside the bounds of my original comment to argue, so I won't. I will, however, point out some other flaws in your logic. For starters, the Universal Acceleration you speak of: what causes it? Also, the aether theory was disproved in the late 1800s by careful measurements of the homogeneity of space (Michaelson and Morley if my memory serves correctly), noting that the luminiferous aether does not change the speed of light in different directions as it would if it were real and the earth were accelerating (or, more simply, moving) through it. Also, if there were "eddies" in the aether above (assuming the axis of rotation of the "disk" to be parallel or anti-parallel, it doesn't really matter since I know which direction you take to be positive) that cause the time dilation effects (I cringe simply in writing this sentence because...) they would cause enormous local anisotropy of space as well as inhomogeneities that would render calculations we depend on daily (I know this works because I got to the restaurant last Friday night...) to be nearly, if not completely, impossible since we would then have variances in "aether" densities, accelerations (keep in mind circular motion in an eddy is actually acceleration about a centralized point), velocities, etc, and also likely have gravitational effects between these "aether eddies" themselves. Perhaps this would be an exciting problem for the chaos theorists (mathematical theory of non-repeating systems, not the doomsday believers), but I find it atrocious as a satellite engineer with a physics background.
In most models, sustained spaceflight isn't possible (though I'm willing to consider that it is and I'm working on a model that allows for it), so most of us will tell you that these so-called satellites don't exist. See many threads and the FAQ on the "Conspiracy" of spaceflight - I don't like to talk about it because I'm not a conspiracy theorist, I'm a flat earth theorist.
Well, if you're not a conspiracy theorist, then you'll believe me when I say I've (or, at the very least, that someone, somewhere has... It doesn't matter to me at all whether you believe some random person on an internet forum who claims this, let's just not argue over whether it's possible because it's sheer silliness to think it isn't, especially if you have an iPhone or Droid) worked on the designs of satellites, physically held their hardware in my hands, and seen them launched. There is no question in my mind whether satellites are real. With that said, why would sustained spaceflight in any model be impossible? If the earth is accelerating due to some force, and has no gravitational attraction of its own, why can't you just send a satellite a little do the left (right, whatever direction you want) of the earth and just let it accelerate past, thereby leaving perpetual spaceflight with no orbital maintenance required? In fact, if that's the case, perpetual spaceflight should really just be a matter of standing on the edge of the earth and throwing something off... it should continue with it's initial horizontal (parallel to the plane of the disk) motion, with only air drag to slow it, until very soon it is behind the earth and left in freefall about the sun.
In fact, what, exactly, is it that creates the force that accelerates the earth, and where does it get its energy? it should be immensely hot (because of the infinite, or nearly infinite, energy it would have to posses in order to smoothly and perpetually accelerate the earth) and therefore radiating. With that, we should be able to see scattering from the atmosphere at the edge of the disk...
I just wanted to thank you for explaining why the sky isn't Violet. :D
The sky is blue on a flat earth for the same reason as it is on a spherical one. Rayleigh scattering is well understood (excepting that whole "shortest wavelength" fallacy that causes so many neophytes to encounter the question of violet and get stumped) and I'm not sure why the shape of the earth should matter :)
Hopefully this was helpful to you.
I brought up the Rayleigh scattering because the only logical way to describe a red sunset is that as the incident angle of radiation from the sun changes, the amount of atmosphere it must go through changes, and therefore the amount of filtration of the higher energies in the light changes. If the earth were flat and the sun were simply some light emitting disk that moves in a circular (again, accelerated) path through the sky, then the only rational explanation for the path it takes, combined with the incident angles (which we can now both agree on measuring due to the Rayleigh scattering you acknowledged) of the radiation is that it must travel, at the very least, below the edge of the disk at some point (otherwise you wouldn't be able to account for the reddening of the sun as it sets and rises, it would have to go red to yellow, to red, to yellow, etc).
Also, what's accelerating the sun, then? If nothing's accelerating it, then the only place it could be would be over the north pole. If that were the case, someone standing at the north pole would have a perpetual noon. How does one explain the several months of darkness known to anyone who lives above the arctic circle?
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You'll find many different opinions here as to whether actual satellites exist, as opposed to pseudolites and stratolites, but in general (heh, punny) FE'ers accept GR to be mostly accurate - except that what Einstein took for gravity on earth is actually acceleration. An easy mistake to make, as they're identical. GPS is typically understood to work via a system of towers, pseudolites, and stratolites, but in the case of the latter (or an actual satellite), eddies in the aether caused by the celestial bodies above us act against the effects of Universal Acceleration (aka Earth's "surface gravity") creating lessening gravitation, and thus relativistic time dilation in the upper atmosphere and space above the Earth. In short - pretty much the same as a spherical earth, except many of us don't believe in satellites, and we substitute acceleration for gravity.
Einstein's thought experiment from which Special Relativity was derived actually stated that in is impossible to tell a body force (such as gravity) from acceleration in many circumstances. This is a point that I would have to go outside the bounds of my original comment to argue, so I won't. I will, however, point out some other flaws in your logic. For starters, the Universal Acceleration you speak of: what causes it? Also, the aether theory was disproved in the late 1800s by careful measurements of the homogeneity of space (Michaelson and Morley if my memory serves correctly), noting that the luminiferous aether does not change the speed of light in different directions as it would if it were real and the earth were accelerating (or, more simply, moving) through it. Also, if there were "eddies" in the aether above (assuming the axis of rotation of the "disk" to be parallel or anti-parallel, it doesn't really matter since I know which direction you take to be positive) that cause the time dilation effects (I cringe simply in writing this sentence because...) they would cause enormous local anisotropy of space as well as inhomogeneities that would render calculations we depend on daily (I know this works because I got to the restaurant last Friday night...) to be nearly, if not completely, impossible since we would then have variances in "aether" densities, accelerations (keep in mind circular motion in an eddy is actually acceleration about a centralized point), velocities, etc, and also likely have gravitational effects between these "aether eddies" themselves. Perhaps this would be an exciting problem for the chaos theorists (mathematical theory of non-repeating systems, not the doomsday believers), but I find it atrocious as a satellite engineer with a physics background.
In most models, sustained spaceflight isn't possible (though I'm willing to consider that it is and I'm working on a model that allows for it), so most of us will tell you that these so-called satellites don't exist. See many threads and the FAQ on the "Conspiracy" of spaceflight - I don't like to talk about it because I'm not a conspiracy theorist, I'm a flat earth theorist.
Well, if you're not a conspiracy theorist, then you'll believe me when I say I've (or, at the very least, that someone, somewhere has... It doesn't matter to me at all whether you believe some random person on an internet forum who claims this, let's just not argue over whether it's possible because it's sheer silliness to think it isn't, especially if you have an iPhone or Droid) worked on the designs of satellites, physically held their hardware in my hands, and seen them launched. There is no question in my mind whether satellites are real. With that said, why would sustained spaceflight in any model be impossible? If the earth is accelerating due to some force, and has no gravitational attraction of its own, why can't you just send a satellite a little do the left (right, whatever direction you want) of the earth and just let it accelerate past, thereby leaving perpetual spaceflight with no orbital maintenance required? In fact, if that's the case, perpetual spaceflight should really just be a matter of standing on the edge of the earth and throwing something off... it should continue with it's initial horizontal (parallel to the plane of the disk) motion, with only air drag to slow it, until very soon it is behind the earth and left in freefall about the sun.
In fact, what, exactly, is it that creates the force that accelerates the earth, and where does it get its energy? it should be immensely hot (because of the infinite, or nearly infinite, energy it would have to posses in order to smoothly and perpetually accelerate the earth) and therefore radiating. With that, we should be able to see scattering from the atmosphere at the edge of the disk...
I just wanted to thank you for explaining why the sky isn't Violet. :D
The sky is blue on a flat earth for the same reason as it is on a spherical one. Rayleigh scattering is well understood (excepting that whole "shortest wavelength" fallacy that causes so many neophytes to encounter the question of violet and get stumped) and I'm not sure why the shape of the earth should matter :)
Hopefully this was helpful to you.
I brought up the Rayleigh scattering because the only logical way to describe a red sunset is that as the incident angle of radiation from the sun changes, the amount of atmosphere it must go through changes, and therefore the amount of filtration of the higher energies in the light changes. If the earth were flat and the sun were simply some light emitting disk that moves in a circular (again, accelerated) path through the sky, then the only rational explanation for the path it takes, combined with the incident angles (which we can now both agree on measuring due to the Rayleigh scattering you acknowledged) of the radiation is that it must travel, at the very least, below the edge of the disk at some point (otherwise you wouldn't be able to account for the reddening of the sun as it sets and rises, it would have to go red to yellow, to red, to yellow, etc).
Also, what's accelerating the sun, then? If nothing's accelerating it, then the only place it could be would be over the north pole. If that were the case, someone standing at the north pole would have a perpetual noon. How does one explain the several months of darkness known to anyone who lives above the arctic circle?
Most of your questions seem to be in regards to what is causing the accelation, and the simple answer is that we don't know, but the fact that universal acceleration is occuring isn't just something we made up. http://en.wikipedia.org/wiki/Accelerating_universe (http://en.wikipedia.org/wiki/Accelerating_universe)
As an aside, here's a quote regarding what accepted science believes is causing this acceleration:
Models attempting to explain accelerating expansion include some form of dark energy, dark fluid or phantom energy. The most important property of dark energy is that it has negative pressure which is distributed relatively homogeneously in space. The simplest explanation for dark energy is that it is a cosmological constant or vacuum energy.
Most of us believe that dark energy is causing the acceleration. Some of us substitute the term "aetheric wind" because refraction due to aether helps explain certain visible phenomena on a flat earth, such as sunsets and the southern celestial pole.
The disc of earth isn't rotating - the cosmos rather rotates around us, on several concentric axes (I'm working on a model of this, based upon Ptolemy's work with retrograde orbits). There are differing theories here as to whether the earth is a finite disc or an infinite plane, and indeed some of the infinite plane models nix the UA in favor of more traditional gravity, so there is still room for us to improve and solidify our model. Our method is based upon personal observation, and thus is highly subjective, but we generally welcome alternative interpretations.
The sun (and moon) rotate in a circle above the earth. The sun's orbit widens and narrows throughout the year - on the solstice this month it will make its smallest circle above the north pole, and then begin widening again.
Once again, thanks for well reasoned and civil discourse, it's always refreshing here :)
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[Quote from: Tintagel on December 15, 2012, 09:52:00 PM]
Most of your questions seem to be in regards to what is causing the accelation, and the simple answer is that we don't know, but the fact that universal acceleration is occuring isn't just something we made up. http://en.wikipedia.org/wiki/Accelerating_universe (http://en.wikipedia.org/wiki/Accelerating_universe)
As an aside, here's a quote regarding what accepted science believes is causing this acceleration:
Quote
Models attempting to explain accelerating expansion include some form of dark energy, dark fluid or phantom energy. The most important property of dark energy is that it has negative pressure which is distributed relatively homogeneously in space. The simplest explanation for dark energy is that it is a cosmological constant or vacuum energy.
Most of us believe that dark energy is causing the acceleration. Some of us substitute the term "aetheric wind" because refraction due to aether helps explain certain visible phenomena on a flat earth, such as sunsets and the southern celestial pole.
The disc of earth isn't rotating - the cosmos rather rotates around us, on several concentric axes (I'm working on a model of this, based upon Ptolemy's work with retrograde orbits). There are differing theories here as to whether the earth is a finite disc or an infinite plane, and indeed some of the infinite plane models nix the UA in favor of more traditional gravity, so there is still room for us to improve and solidify our model. Our method is based upon personal observation, and thus is highly subjective, but we generally welcome alternative interpretations.
The sun (and moon) rotate in a circle above the earth. The sun's orbit widens and narrows throughout the year - on the solstice this month it will make its smallest circle above the north pole, and then begin widening again.
Once again, thanks for well reasoned and civil discourse, it's always refreshing here [/quote]
What bothers me most is that you insinuate ENORMOUS complexities that you simply attribute to "dark energy". It really seems that people who follow this FET are adding one complexity at a time to try to account for each new piece of anecdotal evidence to the contrary. Your theory(ies?) has (have?) already reached a point where there are absolutely gaping inconsistencies with reality. Assuming "dark energy" is causing the acceleration of the "disk" (I will flat out tell you that I don't believe you, but am playing along for the sake of argument), the "disk" is hugely unstable, and simply the radiation pressure from the sun (or whatever you substitute for it) would be enough to knock it off of its stable position (assuming the "dark energy acceleration" was in equilibrium to start with) where everything is nice and flat, causing it to tumble chaotically. This would of course lead to many horrible things, just use your imagination on a randomly tumbling flat earth disk and what it would entail for us... I know this is true through a rigorous study of classical mechanics. (and forewarning, don't even try to use advanced cosmological concepts such as the Hubble expansion if you choose to discredit their foundations in classical mechanics and General Relativity)
Again, assuming for the sake of argument that the earth is being accelerated by something (in a dynamically stable configuration, which is physically impossible as anyone who has spent time playing at gyroscopes, footballs, firearms... the list goes on... can tell you) at a constant rate of 9.8m/s^2, then even one year's worth of this (I've lived for 20-something years on this planet, so I know that 1 year is at least a reasonable assumption for the longevity of life on earth) would lead to 31556900 (seconds in a year) * 9.8m/s^2 = 309257620 which is 3.092*10^8. You seem to have accepted that relativity holds true, which depends on the fact that nothing can move faster than the speed of light. However, one year's worth of linear acceleration (a geocentric model would really have to have linear acceleration otherwise it wouldn't be geocentric) would mean that the earth is already moving faster than the speed of light! What about the other several billion years that this planet has been around?
With respect to the planets, stars, galaxies, galaxy clusters, galaxy super clusters, cosmological filaments, etc, etc, etc, all rotating about us, the energy that would be necessary for that to be true is enormous (truly universally enormous, not just enormous for someone like you or me to comprehend) and it is impossibly unlikely that the axis would be even parallel, let alone coincident. When faced by the absolutely incalculable odds (exponential with the number of atoms in the universe) that things just happen to line up the way they do and don't follow a set of very simple (General relativity is actually incredibly simple, it's just that our math system is set up in a way that makes computation rather annoyingly difficult) rules, why is it so hard to accept that the simplest answer is very often the truth.
So, as I see it, your description of the universe is becoming more and more complex (and you've been cherry picking from accepted physics, taking into account convenient cosmological theories, but disregarding the fundamental truths upon which they are based), and looks like it will continue to increase in complexity without bound. Perhaps you will someday find a model that works in local space, but I can promise you that it will not hold true universally, certainly not as well as mainstream physics does.
Why not simply accept that if it looks like a duck, swims like a duck, and quacks like a duck, it probably is a duck? There's no need for all of these inanely complex and grandiose theories that you guys are perpetuating when there already exists one that has been, can be, and will be enormously tested and utilized. The classical world that we live in is actually quite pleasantly simple and only takes a few years (more like 5, but still a small commitment in the grand scheme of things) of dedicated study to thoroughly understand.
One last thought: I've read several people say that the earth must be flat because it looks flat. Let's say your standing on the edge of the disk (I understand that your model of gravity doesn't allow this, but lets say that due to some feat of engineering, you could stand directly off the edge of the disk, such that a line from your head to your feet would lay flat against the earth's surface).
From your position on the edge of the disk, would you be able to perceive its curvature? According to elementary geometry, there would be no way for a person to stand and look at the edge of the disk and know it is not a square plate because the curvature would be so small (1/radius of the earth "disk") that no one could tell the difference between the visible segment of the circle and the straight edge of a square plate.
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What bothers me most is that you insinuate ENORMOUS complexities that you simply attribute to "dark energy". It really seems that people who follow this FET are adding one complexity at a time to try to account for each new piece of anecdotal evidence to the contrary.
I'm with you here, actually. A lot of this complexity comes from the fact that if you read the FAQ, the Wiki, and any given 10 posts from theorists here, you'll get ten differing opinions on what's 'actually' going on.
Again, assuming for the sake of argument that the earth is being accelerated by something (in a dynamically stable configuration, which is physically impossible as anyone who has spent time playing at gyroscopes, footballs, firearms... the list goes on... can tell you) at a constant rate of 9.8m/s^2, then even one year's worth of this (I've lived for 20-something years on this planet, so I know that 1 year is at least a reasonable assumption for the longevity of life on earth) would lead to 31556900 (seconds in a year) * 9.8m/s^2 = 309257620 which is 3.092*10^8. You seem to have accepted that relativity holds true, which depends on the fact that nothing can move faster than the speed of light. However, one year's worth of linear acceleration (a geocentric model would really have to have linear acceleration otherwise it wouldn't be geocentric) would mean that the earth is already moving faster than the speed of light! What about the other several billion years that this planet has been around?
Actually, according to GR, we'll never actually reach the speed of light. The relevant formula is v/c = tanh (at/c). Since tanh (at/c) is always less than 1, then no, we will never reach the speed of light. Even the round-earth scientists here concede this point (though there are plenty of other places they find fault with our ideas).
So, as I see it, your description of the universe is becoming more and more complex (and you've been cherry picking from accepted physics, taking into account convenient cosmological theories, but disregarding the fundamental truths upon which they are based), and looks like it will continue to increase in complexity without bound. Perhaps you will someday find a model that works in local space, but I can promise you that it will not hold true universally, certainly not as well as mainstream physics does.
I apologize if it seems like I'm cherry-picking - I'm admittedly not a physicist, I'm a math girl who's done a bit of reading.
From your position on the edge of the disk, would you be able to perceive its curvature? According to elementary geometry, there would be no way for a person to stand and look at the edge of the disk and know it is not a square plate because the curvature would be so small (1/radius of the earth "disk") that no one could tell the difference between the visible segment of the circle and the straight edge of a square plate.
This is an interesting thought experiment. The radius of the "known" earth-disc for those who subscribe to that version is twice the radius of the sphere-earth, so 6,378.1*2 = 12,756.4. Since I just did this math for another thread, I know that 63 kilometers around the equator (planar or flat - they're both the same distance from the center) yields a curve of about a half a degree... here, that distance would be doubled and I daresay it'd look pretty flat, and may actually be flat enough so that the opacity of the air may even obscure objects that should otherwise be visible, but we're talking about an object that is twice as wide as the earth, so on a spherical earth the curve would be more apparent. I would work out exactly how far the disc-edge would "drop" in a given distance but it's Sunday evening and I've opened a bottle of wine and I can't be bothered to do math right now. :D There are other threads featuring that very figure, for an object with a spherical earth-radius, one would only have to plug in the larger r value to calculate it, but right now this glass of wine is more interesting. :)
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With regards to the constant acceleration of the earth exceeding the speed of light within a year, I do actually understand that this is impossible (physics was one of my majors at university), and used this to point out the fact that the earth can't constantly accelerate at a rate of 9.8m/s^2 ad infinitum. This would be "doable" until you start to get to relativistic speeds (typically relativity is factored in as a large percentage of the effects at velocities somewhere between 0.1c and 0.5c. Because it's a continuous transition from the newtonian to relativistic models, it's up to the user to determine when each model fits his or her needs). Since the local acceleration is held to be continuous (otherwise we would feel ourselves getting heavier or lighter with the changes in gravity), the change in momentum of the system (acceleration being the first temporal derivative of momentum, divided by mass... a = (1/m)*dp/dt), also known as force (F = ma = dp/dt) must be constant. However, according to relativity, the energy needed to cause acceleration increases with the speed of object (this gets into a little big of calculus so I won't put it here, but you said you like math, so you should understand what I'm getting at anyway), and approaches an asymptote at "c". This means that the linear acceleration of 9.8m/s^2 would only be possible for a couple of months under a constant force (faster objects have more mass according to relativity, which is why photons have momentum) Essentially what I'm saying is that it is impossible for our constant acceleration toward the earth to be due to a uniform acceleration of the entire earth against us because (although they ARE indistinguishable for a short time) this system is not something you could maintain indefinitely, or even for more than a few months (assuming, of course, that all of the right factors, such as passive dynamic stability of a non-spinning disk (impossible...), aether flows, dark energy, etc etc etc lined up to make this work.)
If you understand, or at least aren't intimidated by, math, then you should watch this lecture series on classical mechanics. Leonard Susskind is one of the foremost physicists in the world and, even more rare, a fantastic teacher. If you decide to look into it, you'll probably learn a bit about dynamics and see why physicists see the world as they do (and are able to accomplish some pretty fantastic feats regardless of whether people "believe" in them).
Classical Mechanics | Lecture 1 (http://#ws)
He has several other pretty fantastic series on topics ranging from special and general relativity, quantum mechanics (proven to be true because you're reading this on a computer screen that requires QM to work in its transistors...) and statistical mechanics (fascinating topic, but one of the hardest classes i took at my university, so don't anticipate being an expert any time soon, I'm sure not). I will warn you, though, that Susskind shows pretty much the full formulation for all of these theories and techniques, so the math is very intensive, but well explained.
The universe is a really fascinating place, and in no small part due to its fantastic simplicity. Give physics a shot, I think (since you've followed a pretty logical argument process here) that you'll probably find it's more right than you know...