Making Earth the Center of the Solar System

[K^2]

Yes, but frame-invariance was introduced with Special Relativity precisely to salvage the heliocentric model after the Michelson-Morley experiment detected no relative movement of the Earth.

Let me just stop you right there. Are you aware of the fact that General Relativity is absolutely essential for operation of GPS satellites? I know you aren't. Or you wouldn't be saying such nonsense. Please, read up on the subject before you embarrass yourself further.

Oh, and Brotoro nailed it on the matter of dark matter.

[lodestar]

Dark matter has nothing to do with interpreting Hubble shifts as velocity shifts. Our Galaxy (and other galaxies) simply does not have enough visible matter to rotate as it does without flying apart. Similarly, the way galaxies in galaxy clusters can hold together with their observed velocities indicates that those clusters contain more matter than we can see.

Really? And how do you calculate galaxies distances without interpreting redshifts as velocity shifts and plugging in the numbers for a 13.75 billion years old universe?

[N_las]

Really? And how do you calculate galaxies distances without interpreting redshifts as velocity shifts and plugging in the numbers for a 13.75 billion years old universe?

I am pretty sure you are confusing dark matter with dark energy. Those are different things.

[lodestar]

lodestar: So how exactly are you explaining that the Michelson-Morley experiment gives the same result if you strap it on a car/plane(and, but as far as I know, untested, a satellite)¿ If the earth stands still, then that vehicle obviously doesn't.

Not even speaking about tons of other effects not taken care of by pre-relativity stuff (mercury or atomic clocks, anyone¿).

In the same way that I could hear your voice unchanged if we were talking inside a supersonic jet, the result is relative to the medium. If you get the same result in a vaccum, then we might have something, but as far as I know, no repeat of the Michelson-Morley experiment ever did that.

[ZetaX]

Build one yourself if someone hasn't already (not even meant as a joke, should be possible). Your statement simply contradicts too many other things like mercury's behaviour, time dilation, etc. to be believable without more than "I think it sounds too complicated".

[lodestar]

Let me just stop you right there. Are you aware of the fact that General Relativity is absolutely essential for operation of GPS satellites? I know you aren't. Or you wouldn't be saying such nonsense. Please, read up on the subject before you embarrass yourself further.

Oh, and Brotoro nailed it on the matter of dark matter.

Yes, I am aware. That's called Sagnac Effect and was discovered by Georges Sagnac in 1913, three years before Einstein published his General Relativity. General Relativity is not "absolutely essential" for GPS satellites, since the Sagnac Effect appears in either a relative or absolute model, as the one proposed by Sagnac, which was completely antithetical to GRT. It's particularly amusing that you patronize me with that, and direct me to read on the subject, while it's obvious you're not aware that GPS satellites use the Sagnac effect theory for corrections, assuming an absolute space, and not General Relativity. You're just confusing observed reality with chosen model. The Sagnac effect is observed, and George Sagnac explained it in an absolute model. You can explain it within General Relativity and many other models too, but this is no confirmation for either one.

Buddy... being wrong, if that was the case, would be no embarrassment to me, because I'd learn something. On the other hand, the contrast between the ignorance of your remarks and the arrogant attempt to patronize would definitely embarrass me if I did something like that. You don't even know me, why the need to be so aggressive?

Edited February 1, 2014 by lodestar

[lodestar]

Build one yourself if someone hasn't already (not even meant as a joke, should be possible). Your statement simply contradicts too many other things like mercury's behaviour, time dilation, etc. to be believable without more than "I think it sounds too complicated".

First of all, I have no interest in doing that. Second, even if I had, I doubt funding and publication bias would allow me to do it. Third, it's not my statement, nothing I said is original research, it's just the current state of astrophysics and cosmology that any dedicated student should be aware of. You think my statement contradicts something because you're obviously trying to fit it into another model, while either model is reasonably consistent within itself and in the end of day it's just a matter of personal belief. I can quote a dozen physicists right now acknowledging the issue if you need.

[ZetaX]

So how does your model explain the things I mentioned then¿

Any quote, or even better, any explaination, by a real physicist saying that a geocentric system solves such problems is also welcome; one that dark energy/metter/whatever other unsolves problem exists is not a prove, not even evidence, towards what you said. Nothing you said is "current state" (that would at least include agreement by a relevant part of the scientific community), instead it is utter nonsense (I bet that both K^2 and me had heard more lectures and read more books on physics than you).

And no, it is you who is ignorant: you cherry pick facts, make up a "theory" and then ignore any counterevidence that should throw out your version before it was even written down in a forum, yet published; that says nothing about the current models being true, just how bad yours is.

[lodestar]

I am pretty sure you are confusing dark matter with dark energy. Those are different things.

They are the exact same thing: a fudge factor to make the observations fit in the math and assumed constants. When you need mass to make the math fit, you add make-believe matter and call it Dark Matter, when you need energy to propel that mass you add make-believe energy and call it Dark Energy. Problem solved.

[TheDarkStar]

They are the exact same thing: a fudge factor to make the observations fit in the math and assumed constants. When you need mass to make the math fit, you add make-believe matter and call it Dark Matter, when you need energy to propel that mass you add make-believe energy and call it Dark Energy. Problem solved.

That's not quite right. We can see the effect of dark matter's mass but not any electromagnetic interactions ( = does not interact with light). As for dark energy, that's something entirely different. We can see the universe expanding faster and faster (and I don't think it matters where the earth is for that), which is the opposite of what you'd expect based on gravity. Hence, something must be there causing this expansion to speed up. They are in no way imaginary - unless you count anywhere that you can't literally see as imaginary (like across town or anywhere out of your field of vision).

I expect K^2 to point out some things that aren't correct, so you might want to wait for confirmation by him (he's studying theoretical physics in college right now).

[N_las]

If I understand your idea of geocentricity correctly, the sun orbits the earth. The other planets orbit the sun, hence they just indirectly orbit the earth. What keeps them from directly orbiting the earth? Why does the sun orbit the earth directly, but the other planets doesn't?

Because it is a matter of faith either way? Some belive that the earth is special, and others belive that the earth is not special?

Ultimately, it all rests in faith. If you want to believe Earth has a privileged location in the universe, or if you want to believe the distribution of matter in the universe is uniform and Earth is in some random corner.

Well, I hope you realize, that there is a difference between 'believing the earth is not special', and 'not believing the earth is special'.

If you rest your understanding of the universe at the believe the earth is privileged, you make an assumption. This assumption could be wrong and obstruct the truth. If one doesn't believe the earth is privileged, there is no assumption.

The funny thing is: Every argument for geocentrism also works for lunacentrism, neptun-centrism and ISS-centrism.

[lodestar]

So how does your model explain the things I mentioned then¿

First of all, it's not my model. This is not an original theory that I'm presenting to you here at the KSP forum for review. This is common knowledge among physicists. I haven't said a single word that isn't accepted widespread knowledge.

The only thing you mentioned so far is asking me how the Michelson-Morley experiment would behave in a moving vehicle, and I answered that properly, I believe, since you presented no counter-argument other than asking why I don't do the experiment myself. Is there anything else I missed?

Any quote, or even better, any explaination, by a real physicist saying that a geocentric system solves such problems is also welcome;

This is something anyone with an education on the subject should know, and if you're asking me for it as if I'm saying something original, it simply means you don't really know much about the subject. I can answer any questions if you know what to ask, but I can't educate you on the subject from the scratch here. As I said, I can quote dozens of classic textbooks, peer-reviewed articles and even popular science books acknowledging the issue. I don't have my notes with references right now, but these are a few I could remember and Google for you:

Edwin Hubble, on his Observational Approach to Cosmology, on not interpreting redshifts as velocity-shifts:

"The assumption of uniformity has much to be said in its favour. If the distribution were not uniform, it would either increase with distance, or decrease. But we would not expect to find a distribution in which the density increases with distance, symmetrically in all directions. Such a condition would imply that we occupy a unique position in the universe, analogous, in a sense, to the ancient conception of a central earth. The hypothesis cannot be disproved but it is unwelcome and would be accepted only as a last resort in order to save the phenomena. Therefore, we disregard this possibility and consider the alternative, namely, a distribution which thins out with distance."

Fred Hoyle, on Astronomy and Cosmology:

“We know that the difference between a heliocentric theory and a geocentric theory is one of relative motion only, and that such a difference has no physical significance. But such an understanding had to await Einstein’s theory of gravitation in order to be fully clarifiedâ€Â

Let it be understood at the outset that it makes no difference, from the point of view of describing planetary motion, whether we take the Earth or the Sun as

the center of the solar system. Since the issue is one of relative motion only, there are infinitely many exactly equivalent descriptions referred to different centers – in principle any point will do

Stephen Hawking, on his A Brief History of Time, that you probably read:

Now at first sight, all this evidence that the universe looks the same whichever direction we look in might seem to suggest there is something special about our place in the universe. In particular, it might seem that if we observe all other galaxies to be moving away from us, then we must be at the center of the universe. There is, however, an alternate explanation: the universe might look the same in every direction as seen from any other galaxy too. This, as we have seen, was Friedmann’s second assumption. We have no scientific evidence for, or against, this assumption. We believe it only on grounds of modesty: it would be most remarkable if the universe looked the same in every direction around us, but not around other points in the universe

Robert H. Dicke, Gravitation and the Universe:

"Particularly significant in the distribution of galaxies about us is uniformity and isotropy. The galaxies appear to be uniformly distributed about us. Not only is the distribution uniform but the above described motions with respect to us represent a uniform dilation. How is this to be interpreted? We might be tempted to conclude that man occupies some special central point in the Universe, that galaxies move away from us. An alternative interpretation is that the Universe is uniform in structure and that all points are similar. Thus the Universe might appear isotropic from any particular galaxy in which man happened to be living…The mathematical transformation is easily carried out and leads to the conclusion that in the average the Universe would appear the same when seen from other galaxies."

George Ellis, in an interview in Scientific American, vol. 245, which is remarkable in the context of this discussion, since you seem to believe I'm saying something new, against the mainstream science:

People need to be aware that there is a range of models that could explain the observations. For instance, I can construct for you a spherically symmetrical

universe with Earth at its center, and you cannot disprove it based on observations. You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that.

one that dark energy/metter/whatever other unsolves problem exists is not a prove, not even evidence, towards what you said.

Yes, it is. Current cosmology astrophysics is basically a choice between Dark Matter and geocentrism, and while everyone in the field is aware of this, very few are willing to choose geocentrism. There are a few who do. Robert Sungenis two volume book, Galileo Was Wrong is probably the most gentle introduction you'll find.

Nothing you said is "current state" (that would at least include agreement by a relevant part of the scientific community),

As I said, it does include agreement by the most relevant part of the scientific community. You probably just don't know the scientific community as much as you think you do.

instead it is utter nonsense

Talk is cheap. If something I said here is nonsense, show it and present a counter-argument. So far you presented neither. Claiming something is nonsense without any argument is nonsense.

(I bet that both K^2 and me had heard more lectures and read more books on physics than you).

That remark is incredibly childish. It's not a matter of how many lectures or books you read, but which books and how much you understand it. If read only one short book very carefully, Hubble's Observational Approach to Cosmology, you'd be very aware of what I'm talking about.

And no, it is you who is ignorant: you cherry pick facts, make up a "theory" and then ignore any counterevidence that should throw out your version before it was even written down in a forum, yet published; that says nothing about the current models being true, just how bad yours is.

First of all, no need for insults or being aggressive. I assume we're all adults here, despite being in a videogame forum. Second, if I'm cherry-picking something and you know it or you can present a counter-argument, just do it. So far I've seen nothing. That kind of talk doesn't take us very far. Third, as I said above, this is not "my" theory or anything new at all. Basically, if you know the history of the special and general relativity theory and big bang theory, you'd know what I'm talking about very well. Buddy, any physics student should be aware of this. This is junior year physics. Most of the classic textbooks mention the issue. Any physics graduate is perfectly aware how most of the 20th century astrophysics and cosmology revolves around this issue and the crisis of the chosen path is the current state. If you are not aware of this, you're probably just an enthusiast who reads a lot of recreational science books and magazines, watch youtube videos, but has no formal education on the subject. If that's the case, no surprise, it's very common. Usually, I see aggressive reactions like yours in this kind of people, while graduates or students are often aware of what I'm talking about and we usually have productive talks.

[ZetaX]

You still did not go into any detail about why time dilation occurs and why mercurys perhilon precesses the way we observe. And all other in http://en.wikipedia.org/wiki/Tests_of_general_relativity .

Nice remark on you knowing more about "physics" than us. I bet you can explain to me such a simple concept like a topological space; or its cohomology; or what a flat connection is; or any math above "I can add numbers".

And please stop "quoting" physicists in such a way; they have human rights.

Edited February 1, 2014 by ZetaX

[Brotoro]

Really? And how do you calculate galaxies distances without interpreting redshifts as velocity shifts and plugging in the numbers for a 13.75 billion years old universe?

We find the distances to galaxies by a number of unrelated methods. For galaxies close enough to see individual giant stars, we can easily spot Cepheid variable stars. Cepheids have a correlation between their pulsation periods and their luminosities, so from how bright they look we can tell how far away they are. Similarly, we can use other 'standard candles' of known luminosity (with distance-luminosity relationships calibrated using methods that work in our own Galaxy and nearby galaxies) such as novae, star clusters, supernovae (especially Type Ia), and the Tully-Fisher relationship between the infrared luminosity and the width of the rotation curves of spiral galaxies.

We measure the Hubble expansion FROM all these different methods. Also, objects that are very distant (such as quasars) not only have large redshifts, their spectra can also show absorption lines of from gas clouds of lower redshift, and gravitational lensing, caused by closer galaxies, which are separate indications that they are further away.

Edited February 1, 2014 by Brotoro

[lodestar]

That's not quite right. We can see the effect of dark matter's mass but not any electromagnetic interactions ( = does not interact with light). As for dark energy, that's something entirely different. We can see the universe expanding faster and faster (and I don't think it matters where the earth is for that), which is the opposite of what you'd expect based on gravity. Hence, something must be there causing this expansion to speed up. They are in no way imaginary - unless you count anywhere that you can't literally see as imaginary (like across town or anywhere out of your field of vision).

I expect K^2 to point out some things that aren't correct, so you might want to wait for confirmation by him (he's studying theoretical physics in college right now).

You're making the same confusion someone else here did, getting into a petitio principii by taking the interpretation that depends on the assumption in discussion as evidence for the assumption itself.

We don't observe the effects of dark matters mass. We model it and make it fit the observations. There are models with no Dark Matter that will also fit the observations. Dark Matter is simply the preferred theory at the moment because we don't have to get rid of anything important, read waive ideological assumptions like the cosmological principle, although you have the simple problem of actually finding it.

We don't see the universe expanding faster and faster. What we see is homogeneous redshifts everywhere around us and we decide to interpret that as an expanding universe, but it's not the only interpretation and not even the simpler one. It totally matters where Earth is for that, because if the universe is expanding, you'd see homogeneity from anywhere else, pretty much like the distance between dots on a baloon's surface grows equally as you fill it. IF the universe is not expanding, the only place where you'd see that homogeneity is in the center. Since putting the Earth in the center would violate the cosmological principle, we instead chose to interpret that as an expanding universe.

As I mentioned before, this is not my theory, this is Edwin Hubble's theory in his Observational Approach to Cosmology, p. 63, a basic textbook in physics. I'm not saying anything revolutionary or new here. This is basic. If K^2 is a physics student and don't know what I'm talking about, he's probably playing KSP too much.

[N_las]

Iodestar:

Imagine the earth would become uninhabitable, but a few people would manage to escape to mars and somehow would make mars habitable. After several thousand generations the descendants would't remember that transition, and would think there natrual home Planet is mars. If they observe the solar system and the rest of the universe, they will basically make the exact same observations than we do now.

If they make on mars the exact same observations, as their ancesters (we) on earth, and the observations permits that the earth is the center of the universe, than the observation will also permit the conclusion that mars is the center of the universe.

If anyone is intellectualy honest, one has to say there would be no way to tell, if earth or mars is the actual center. The same would be true for all planets in the solar system, from all points the observation will make it possible to interpret that point as the center of the universe.

So even if all obersavtion would be consisten with an geocentric universe, there has to be another reason to conclude that it is.

If you don't agree that one would observe basically the same from mars as from earth, please explain your reasoning.

Edited February 1, 2014 by N_las

[lodestar]

If I understand your idea of geocentricity correctly, the sun orbits the earth. The other planets orbit the sun, hence they just indirectly orbit the earth. What keeps them from directly orbiting the earth? Why does the sun orbit the earth directly, but the other planets doesn't?

First, this is not my idea, this is one of the many equivalent models available, and any physicist will tell you that no observations made from the Earth can favor one over another.

Second, to answer your question, all bodies within a system orbit the center of mass of that system, so if the center of mass of the whole universe is very near or inside the center of the Earth, it would be immobile, while the center of mass of the local system itself, inside the sun, would be revolving around it, carrying the whole system with it. Frankly, where it bears on the issue of relative movement, there's no physical relevance in assuming the validity of one over any other. You can take any point in the universe and assume that's the center of gravity and the math will work just fine.

Now ask me about parallax...

Well, I hope you realize, that there is a difference between 'believing the earth is not special', and 'not believing the earth is special'.

If you rest your understanding of the universe at the believe the earth is privileged, you make an assumption. This assumption could be wrong and obstruct the truth. If one doesn't believe the earth is privileged, there is no assumption.

Actually, that's wrong. Both could be assumptions, but the real problem is that Earth being in a privileged position is an observable phenomena. The assumption, named Cosmological Principle, is precisely that Earth isn't in a privileged, position, therefore, most of 20th century astrophysics and cosmology theories are about finding a way to make the observations that show Earth in a privileged position fit in a model where Earth isn't in a privileged position, in order to preserve that assumption. This is a philosophical decision, not a scientific one. If scientists accept Earth in a privileged position, it automatically asks the questions, why and who did it? You'll have to deal with final causes, and science can't deal with final causes.

The funny thing is: Every argument for geocentrism also works for lunacentrism, neptun-centrism and ISS-centrism.

Not quite. Yes, from the problem of relative movement, you can choose any frame of reference and the math for any centrism works, but that's precisely because assuming there's no absolute frame or reference is the solution to the problem of a central Earth conflicting with the Cosmological principle. So, not every argument works, hence, there are still some dilemmas in the current model that are still looking for a solution other than geocentrism, the redshift of quasars, for instance.

[lodestar]

You still did not go into any detail about why time dilation occurs and why mercurys perhilon precesses the way we observe. And all other in http://en.wikipedia.org/wiki/Tests_of_general_relativity .

Nice remark on you knowing more about "physics" than us. I bet you can explain to me such a simple concept like a topological space; or its cohomology; or what a flat connection is; or any math above "I can add numbers".

And please stop "quoting" physicists in such a way; they have human rights.

I expected you to act as an adult. If you can't and will insist on condescension and sarcasm, I guess our conversation is over.

[K^2]

Yes, I am aware. That's called Sagnac Effect

Sagnac Effect only covers frequency shift. Not the fact that the clock rate on GPS satellite doesn't match clock rate on Earth, which is critical for GPS operation. In fact, GPS clock is affected both by Lorentz and Gravitational time dilation, making General Relativity absolutely essential to operation of GPS.

Again, actually learn something about the subject before embarrassing yourself.

[lodestar]

We find the distances to galaxies by a number of unrelated methods.

Indeed, but all of them, besides parallax and its derivatives, depend on other assumptions that gets us back to square one on the matter of choosing a model over another. The point is not if the current model is internally consistent. It is, most of the time. The point is that if there aren't other models equally valid and consistent, or even more.

For galaxies close enough to see individual giant stars, we can easily spot Cepheid variable stars. Cepheids have a correlation between their pulsation periods and their luminosities, so from how bright they look we can tell how far away they are. Similarly, we can use other 'standard candles' of known luminosity (with distance-luminosity relationships calibrated using methods that work in our own Galaxy and nearby galaxies) such as novae, star clusters, supernovae (especially Type Ia), and the Tully-Fisher relationship between the infrared luminosity and the width of the rotation curves of spiral galaxies. We measure the Hubble expansion FROM all these different methods.

Assuming that we're not in a privileged position and the statistical data we get from near bodies is also valid for distant bodies.

Also, objects that are very distant (such as quasars) not only have large redshifts, their spectra can also show absorption lines of from gas clouds of lower redshift, and gravitational lensing, caused by closer galaxies, which are separate indications that they are further away.

Right, but even if the distance measurement for quasars is correct, how do you account for the distribution of all known quasars in groupings of concentric spheres around the Earth, without scraping the Cosmological Principle?

[N_las]

Second, to answer your question, all bodies within a system orbit the center of mass of that system, so if the center of mass of the whole universe is very near or inside the center of the Earth, it would be immobile, while the center of mass of the local system itself, inside the sun, would be revolving around it, carrying the whole system with it. Frankly, where it bears on the issue of relative movement, there's no physical relevance in assuming the validity of one over any other. You can take any point in the universe and assume that's the center of gravity and the math will work just fine.

If we assume the center of mass of the whole unverse is the earth. If we now enter the sun into the system, it will orbit around the center of mass, hence around the earth. If we now enter neptun into the system, it should also orbit around the center of mass, hence around the earth. Why is it, that neptune instead chooses to revolve around the sun. There is no significant difference between neptun and the sun. Yes, the sun is much heavier, but it would't matter in comparison to the center of mass of the whole universe, would it? To make that argument work, not only the earth should be in the center, but the sun has to be truly special.

But let us assume the the issue of movement isn't relevant in this discussion, as you said. Than one can't use this argument to promote geocentrism either, just counter some conter-arguments. So there has to be another reason to assume the earth is the center.

Observations of the universe outside our solar system could theoretically point to the conclusion, that the earth is the center. But since the stars are so distant, one would make nearly the same observations about redshift, parallax, etc. from any other planet of the solar system. So that oberservations can not be used to argue for geocentrism either, it could just narrow the center of the universe down to a point in our system.

Since that covers ALL oberservations from the sky, there is nothing there to support the claim of geocentrism. But you claim that there are such observations:

...but the real problem is that Earth being in a privileged position is an observable phenomena.

So you can only refer to 'introspective' observations, like the Michelson-Morley-experiment. Would you agree with me, thats the only kind of observation that could possibly point to a earth centerd universe? If not, please ellaborate why . If yes, than we all know that we don't have to discuss cosmical observations anymore, but can concentrate on such 'introspective' observations.

Edited February 2, 2014 by N_las

[lodestar]

Sagnac Effect only covers frequency shift. Not the fact that the clock rate on GPS satellite doesn't match clock rate on Earth, which is critical for GPS operation.

I think you don't understand the scope of the discussion. We're not discussing the validity of GR within the current model. We're discussing if both models are equally valid and it's not a scientific decision to choose one over the other, but as the OP suggests, a philosophical or ideological decision which ultimately rests on if our existence has a final cause or not.

Yes, in both models the Sagnac Effect covers the frequency shift, in a frame-independent model the change in clock rate is ascribed to a change in the flow of time itself, and in a geocentric frame, it's a result of the variations in ether density due to not using an absolute frame and the relative motion through it.

In fact, GPS clock is affected both by Lorentz and Gravitational time dilation, making General Relativity absolutely essential to operation of GPS.

Not at all, because the observed gravitational time dilation is the same in both models, with a rotating Earth or a rotating universe. In the ECI in a geocentric model, speed doesn't affect time itself, but will affect the ticking rate of clocks relative to the ECI. General Relativity is not essential to anything when you put Earth in the center of an absolute space. Simple as that. For GPS operation, General Relativity not only isn't essential, but it would make it a lot more complicated if it were actually used for synchronization in orbit, instead of synchronizing all satellites before launch with respect to an isotropic light-speed frame as it does. That isn't even consistent with Special Relativity, but it is consistent with the MLET and a geocentric model.

Again, actually learn something about the subject before embarrassing yourself.

Again, I don't feel embarrassed when I'm wrong, because I'm not trying to pretend superiority like you seem to be.

Edited February 2, 2014 by lodestar

[ZetaX]

I expected you to act as an adult. If you can't and will insist on condescension and sarcasm, I guess our conversation is over.

You expect me to be "adult" after you obviously and on full purpose ignored my request to explain how your claims account for those effects at _least_ four times¿ Also, I only added a bit of sarcasm after you fully claimed that some here, e.g. K^2, are too stupid or uneducted to know your "theory", which you claim is true by misquoting physicists (apart from them never saying such things, this would at best be argument from authority). You insult me and others, and then claim you don't need to account for holes in your theory because sarcasm; really¿

[K^2]

You've claimed that dark matter is not necessary, because General Relativity is wrong. Now you are back to claiming that GR is correct, it's just not the only correct model. If an alternative model is equivalent to General Relativity in your chosen frame, then it will make all the same predictions, including dark matter.

And yeah, you can pick Earth as the center of your coordinate system, then warp things about with "density" variations until time flow is consistent with General Relativity. Guess what? You've just went and constructed a special case of the manifold which is generally described from perspective of relativity. You haven't solved any problems. Just created a bunch of new ones. And even then, you still end up with galaxies having way more mass than they should based on luminous matter.

Now, if you don't feel embarrassed about saying dumb stuff like that, that's unfortunate, but it's your right. But please, do it somewhere else. This is a science section, and we have certain standards around here.

[Brotoro]

I can write a system of equations and physical laws based upon the assumption that my head is the center of the universe. This simply makes sense, of course, because all of the observations I have of the universe are based on what comes into my head. My head always stays perfectly still. As my mighty legs move, the Earth rolls underneath my stationary body. When I want to look off to the side, my head, of course, stays stationary while you and the rest of the objects in the universe rapidly zip through 90-degree arcs. Sure, I can do that.

And if K^2 feels upset about this because it makes him feel less special, he too can write a system of equations and laws that describes the universe with HIS head at the center (probably with fewer math errors than I'd make). If fact, just so nobody feels left out, we can ALL write systems of equations and physical laws for our own personal egocentric universes that are all equally valid.

But why would we want to? What do we gain? I certainly don't want to have some engineer building bridges (that are going to slide under my stationary head) having to use such a cocked-up set of equations (too easy for him to make mistakes that could result in the bridge failing and causing the very massive Earth to suddenly rush up and smack my head). Rather than argue over which of our 7 billion heads is REALLY the center of the universe (because, really, what are the chances that it's mine or yours, right?), it is more useful to understand that the universe doesn't really care who thinks his head is in the center (and all the equations are simpler, and we get safer bridges, and the scientists have an easier time figuring out the rules of the universe so that the engineers can then go on to build us cooler toys).

I could write a fudged up set of equations and laws based on the assumption that our Sun is the center of the universe, with all the wackiness that that would entail. It might be embarrassing to try to explain why the two hundred billion stars in our galaxy all seem to have a different opinion of where the center of things is (all being distributed around some center point 8.33 kiloparsecs away from me in the direction of Sagittarius), but I can continue to feel superior in seeing that they all go pirroetting around us in an obviously subservient fashion as the Sun rotates.

But why would I do that? Why would I want to to argue with the hundreds of billions of equivalent opinions of who's in the center when there is a simpler, easier system to use? Unless I was just dead set on ME being in the center as a starting assumption for some personal reason.

And let's not even discuss the arguments between all of the billions of galaxies that think THEY are in the center of the universe…because some of them are really obstinate and won't give up their opinion on being special no matter how long you talk to them.