$ 1000 offered for proving Earth revolves around the sun

[tharkûn]

From the guy whose been avoiding a request for evidence from the first post I've made in this thread.

Evidence of WHAT? That in an Martian frame of reference Earth's trajectory goes around Mars? That all frames of reference are equivalent? You first post was this vague BS:


This justification I have got to hear. Einstien must be hitting 70,000RPM at the concept of someone twisting 'Well, it doesn't matter what point is 0,0,0 for charting movement' and 'No matter where you are, gravity is universal and cee is constant' into 'Mars goes around Earth! Earth goes around Mars! WHEEEEE!'

Pick a frame of reference - let's go with a Martian one. Okay what happens with Earth's trajectory? It follows a continious curve that completely circumnavigates the origin. What, in colloquial English would we say that trajectory means? That Earth goes around Mars.

Are you seriously so stupid you do see how the trajectory of Earth in a Martian frame goes around Mars?

State your goalpost of what would prove my statement to you or quit making a bigger ass of yourself.

It also fits the the English word "orbit", one of whose definitions is regions of influence. While it would be fairly simple to mathematically describe your orbit around me when I twirl on my swivel chair (wheee!), the phrase "tharkun orbits Michael Wong" generally implies influence, not just incidental translation for that reason.

Generally, not universally. You and I use different definitions, though in everyday practice I suspect you and I use the same description of orbits - you go for influence most of the time - I go for simplicity of math most of the time.

[SirNitram]

From the guy whose been avoiding a request for evidence from the first post I've made in this thread.

Evidence of WHAT? That in an Martian frame of reference Earth's trajectory goes around Mars? That all frames of reference are equivalent?

That Earth orbits Mars and Mars orbits Earth, the two claims I challenged at the beginning. You can throw your little bitchfit about how it might have been 'vague', but your inability to back up your own bullshit is not my fault, you insipid little troll. Shit, you defeated your own argumen here:

No Einstein would predict that Mars orbits around two foci, as has been known since the 17th century. Those two foci can occur next to exactly NOTHING, as seen in most binary star systems. The reason Sol appears to be one of those foci is that they are determined by the center of mass, which Sol greatly exceeds.

That pretty clearly shows you're bullshitting, tharks. You proved yourself wrong. Thanks for the show.

[Illuminatus Primus]

He's completely right, Martin. His definition of orbit is not wrong, and within pure science the choice is arbitrary.

[SirNitram]

He's completely right, Martin. His definition of orbit is not wrong, and within pure science the choice is arbitrary.

Picking a definition of orbit which is useless for science(Stop and use that brain I know you have, Primus: If you do assume that Mars orbits Earth or Earth orbits Mars, can you predict a damn thing about their movements? No, because their movements are dictated by their interaction with the barycenter of this system) and pretending it's the only definition is the definition of semantics whoring. Sorry if I'm not impressed by this like you are.

[Illuminatus Primus]

He's completely right, Martin. His definition of orbit is not wrong, and within pure science the choice is arbitrary.

Picking a definition of orbit which is useless for science(Stop and use that brain I know you have, Primus: If you do assume that Mars orbits Earth or Earth orbits Mars, can you predict a damn thing about their movements? No, because their movements are dictated by their interaction with the barycenter of this system) and pretending it's the only definition is the definition of semantics whoring. Sorry if I'm not impressed by this like you are.

I'd really love to see your physics credentials. The links I posted above had tharkun give several utilities for considering the math from different frames of reference within the solar system. And quite frankly, since tharkun does give specific examples within equations and math for how this all works out, and you reply with pure rhetoric, I am going to take him more seriously. From this post it just looks like some moderately-read amateur trying to bluff his way through physics beyond his education.

[SirNitram]

I'd really love to see your physics credentials. The links I posted above had tharkun give several utilities for considering the math from different frames of reference within the solar system. And quite frankly, since tharkun does give specific examples within equations and math for how this all works out, and you reply with pure rhetoric, I am going to take him more seriously. From this post it just looks like some moderately-read amateur trying to bluff his way through physics beyond his education.

For the love of fuck. You whine about credentials instead of addressing this primitively simple concept:

Mars goes around Earth: Useful predictions from this: Zip, zero, zilch. Evidence for? Semantics whoring of the word Orbit, with no regard for what's causing and influencing the movement.

Mars goes around the barycentre caused by Sol's gravity: Useful predictions for this: Well, what Mars' orbit will be like, and how it will change should some effect alter where the barycentre is. Evidence for? That big gravitational field we know influences Mars' movement.

For pure science, only one generates useful predictions, and is thus useful. This is the most simple basics, Primus.

[tharkûn]

That Earth orbits Mars and Mars orbits Earth, the two claims I challenged at the beginning

Oh please now you are blatantly lying SN before any of this semantic whoring about the word orbits this is exactly what you challenged.


Mars goes around Earth. Earth goes around Mars. It is just a matter of perspective and how difficult you want the math to be. A trajectory calculated in a Sol static frame is identical to one calculated in an Earth centered frame after the requisite transformation.

A modified Tychonian model would accurately send the probes to Mars.


This justification I have got to hear. Einstien must be hitting 70,000RPM at the concept of someone twisting 'Well, it doesn't matter what point is 0,0,0 for charting movement' and 'No matter where you are, gravity is universal and cee is constant' into 'Mars goes around Earth! Earth goes around Mars! WHEEEEE!

Notice neither I nor you use the word orbit. In my susbsequent attempts to understand what the hell your objection is to a valid observation I begin using the word orbit which you then have proceeded to semantic whore to death.

Does Mars go around Earth in an Earth centered frame of reference? Yes. Where is your bloody problem do you doubt that the trajectory of Earth doesn't circumnavigate Mars in such a frame?

You proved yourself wrong.

Right saying what Einstein himself using the conventions he was known to use somehow shows I'm BS'ing. Get over it. SN it is a perfectly valid observation to say Earth goes around Mars in a Martian frame of reference.

If you do assume that Mars orbits Earth or Earth orbits Mars, can you predict a damn thing about their movements?

Yes because the trajectories would have been derived from numeric methods, a task similar to that done by Kepler centuries ago. It would tell you nothing about why the orbit was that shape, but it would accurately predict velocity and position for an indefinate amount of time.

No, because their movements are dictated by their interaction with the barycenter of this system

No their motions are determined by the some of all forces acting upon them. For instance the galatic center exerts a stupendous force on their movements, likewise light pressure and solar wind influence the trajectories of orbiting bodies. Further the center of mass acting upon Mars is not the same one acting upon Earth, this becomes readily apparant in trinary star systems. Technicly Earth and Mars don't have a common center of mass as the mass of Earth is excluded from the center of mass acting on Earth and the mass of Mars is excluded from the center of mass acting on Mars.

pretending it's the only definition is the definition of semantics whoring.

I'm not saying it is the only definition. I've said it was the one I was using.

So according to you I use the wrong definition of "orbit"? What in bloody hell does that have to do with the original point that some vague something is wrong with saying Earth goes around Mars and Mars goes around Earth?

[SirNitram]

That Earth orbits Mars and Mars orbits Earth, the two claims I challenged at the beginning

Oh please now you are blatantly lying SN before any of this semantic whoring about the word orbits this is exactly what you challenged.

You have a bizarre idea of what 'Lying' is, Tharkun.

This justification I have got to hear. Einstien must be hitting 70,000RPM at the concept of someone twisting 'Well, it doesn't matter what point is 0,0,0 for charting movement' and 'No matter where you are, gravity is universal and cee is constant' into 'Mars goes around Earth! Earth goes around Mars! WHEEEEE!'

Oh look. Mars orbits Earth, Earth Orbits Mars, that appears to be exactly what you said, and exactly what I challenged. And you, even now, aren't substantiating it. What a fucking surprise.

Keep trying to dance, kiddo.

Mars goes around Earth. Earth goes around Mars. It is just a matter of perspective and how difficult you want the math to be. A trajectory calculated in a Sol static frame is identical to one calculated in an Earth centered frame after the requisite transformation.

A modified Tychonian model would accurately send the probes to Mars.


This justification I have got to hear. Einstien must be hitting 70,000RPM at the concept of someone twisting 'Well, it doesn't matter what point is 0,0,0 for charting movement' and 'No matter where you are, gravity is universal and cee is constant' into 'Mars goes around Earth! Earth goes around Mars! WHEEEEE!

Notice neither I nor you use the word orbit. In my susbsequent attempts to understand what the hell your objection is to a valid observation I begin using the word orbit which you then have proceeded to semantic whore to death.

Ah, you're going to whine and cry about me saying 'Goes around' instead of 'orbit'. This late in the game you're trying this bullshit to get around meeting the burden of proof? Worthless troll, you identify yourself once again.

Does Mars go around Earth in an Earth centered frame of reference? Yes. Where is your bloody problem do you doubt that the trajectory of Earth doesn't circumnavigate Mars in such a frame?

My problem is you claiming it's fine to say it orbits Earth, you puss-filled sack of shit. And also saying Earth goes around Mars. Which is an amusing thing, since it'll never get to the far side of Mars. But you just sweep that one under the table in your endless quest to never concede even the smallest bit of your bullshit.

You proved yourself wrong.

Right saying what Einstein himself using the conventions he was known to use somehow shows I'm BS'ing. Get over it. SN it is a perfectly valid observation to say Earth goes around Mars in a Martian frame of reference.

Not really. Never gets to the far side of Mars, IE, the section aimed at Jupiter and Saturn and such. You're just full of lies and misdirection.

If you do assume that Mars orbits Earth or Earth orbits Mars, can you predict a damn thing about their movements?

Yes because the trajectories would have been derived from numeric methods, a task similar to that done by Kepler centuries ago. It would tell you nothing about why the orbit was that shape, but it would accurately predict velocity and position for an indefinate amount of time.

No it wouldn't, as it wouldn't take into account that orbits are slipping; the years are getting slowly shorter. It also wouldn't offer any useful predictive capabilities on changes with the real source of that movement, the barycenter. Oops! Totally worthless theory.

No, because their movements are dictated by their interaction with the barycenter of this system

No their motions are determined by the some of all forces acting upon them. For instance the galatic center exerts a stupendous force on their movements, likewise light pressure and solar wind influence the trajectories of orbiting bodies. Further the center of mass acting upon Mars is not the same one acting upon Earth, this becomes readily apparant in trinary star systems. Technicly Earth and Mars don't have a common center of mass as the mass of Earth is excluded from the center of mass acting on Earth and the mass of Mars is excluded from the center of mass acting on Mars.

At what point did I claim the center of mass for both is identical? Hrm, I didn't. You're full of shit, again. There will be tiny variations with each, but as anyone who is actually educated will tell you, the main source is the centre of mass. You just bring up the smallest variables in an attempt to deflect the fact you're fucking full of it.

pretending it's the only definition is the definition of semantics whoring.

I'm not saying it is the only definition. I've said it was the one I was using.

So according to you I use the wrong definition of "orbit"? What in bloody hell does that have to do with the original point that some vague something is wrong with saying Earth goes around Mars and Mars goes around Earth?

'Some vague something'. Gods, you're a laugh a minute.

And just for the fans at home: Yet another Tharkun post without evidence! What a surprise!

[tharkûn]

You have a bizarre idea of what 'Lying' is, Tharkun.

Changing the actual text of what was posted so you can semantic whore, exactly how would that not be lying? Oh wait you were kidding, jerking my chain, or some other specious BS that disguises the fact you deliberately changed the initial statement so you could harp about definitions of the word "orbit".

Ah, you're going to whine and cry about me saying 'Goes around' instead of 'orbit'.

The obersvation is valid. Sketch the trajectories and they will "go around" the origin in respective frames of reference.

Never gets to the far side of Mars, IE, the section aimed at Jupiter and Saturn and such.

The far side of Mars in an Earth centered frame of reference behaves just like the far side of Earth in a Sol centered frame of reference i.e. the section of Earth aimed at Jupitor and such will revolve and bring itself into view.

At what point did I claim the center of mass for both is identical? Hrm, I didn't.

No, because their movements are dictated by their interaction with the barycenter of this system -note the complete lack of an 's' on the end of "barycenter" SN not only hasn't a clue about physics he doesn't know that refering to multiple barycenters requires the plural form

You state both planets' movements are dictated by interaction with a singular entity. That is still technicly wrong.

No it wouldn't, as it wouldn't take into account that orbits are slipping; the years are getting slowly shorter.

Kepler did it without having even Newtonian mechanics to work with. Numerical methods work given a long enough baseline and good enough data. A geocentric frame is terribly ugly calculations, but nothing a good computer can't handle.

It also wouldn't offer any useful predictive capabilities on changes with the real source of that movement, the barycenter.

Of course light pressure, solar wind, and external gravitation can all be ignored even though they have all demonstrated significant changes in certain systems

Here's another clue it's called the Einstein Field Equation because you are working with a tensor field. There is no single point that determines motion, it is a continious effect. The barycenter model is an approximation which is useful for certain problems, but not in and of itself wholly correct. For instance the barycenter model predicts certain 3-dimensional symmetries about the field which are not necessarily true, such as with trinary stars.

If you are talking about what is "real", which apparantly you have your own private meaning for, the motion is determined by a tensor field not a point effect, even the barycenter.

There will be tiny variations with each, but as anyone who is actually educated will tell you, the main source is the centre of mass.

The main source is the tensor field, but that is a bitch to work with so for many applications the barycenter appoximation is close enough no one gives a damn. However you seem to have a major hang up about what is "real" and the barycenter determinging motion isn't it.

'Some vague something'. Gods, you're a laugh a minute.

What is invalid about saying in an Earth centered frame of reference Mars goes around, circumnavigates, does an ugly looking rotation about - whatever phrase you won't semantics whore - Earth?

[SirNitram]

You have a bizarre idea of what 'Lying' is, Tharkun.

Changing the actual text of what was posted so you can semantic whore, exactly how would that not be lying? Oh wait you were kidding, jerking my chain, or some other specious BS that disguises the fact you deliberately changed the initial statement so you could harp about definitions of the word "orbit".

Whatever, Tharkun. The quotes I've been making was a direct C&P. You're just making a last minute, desperate wail of a defeated bitch.

Eh, not like I give a shit. You're just going to continue blubbering like a retard. You've shown you won't do anything but that clearly enough.

But you want the real crux of it? How I know you've been full of shit from the beginning? Because page two starts with a million dollar offer from a reliable, verifiable group if you can prove these specious claims and ones like that. If you actually could prove a speck of this, you wouldn't be debating a name over a gif of a beloved Squaresoft character. No, you'd be out earning your cool million.

But you're here, trying to pick up cool points for the equivalent of 0=1. No one's impressed.

[Zero]

Nitram, he isn't trying to prove that Earth is the center of the solar system/universe/whatever, he's trying to explain that all points of reference are equal, and that there's exceptions to the heliocentric model as well, such as our own moon, which does orbit the earth. The sun is revolving around something itself, so it isn't really a center of anything either. There is no center. All reference points can be made to make sense if you're willing to put up with the fucked up math for different models. We use the heliocentric model because it's simplest for practical purposes, but that doesn't mean that it's any more or less correct then a geocentric model. The math's just easier.

[SirNitram]

Nitram, he isn't trying to prove that Earth is the center of the solar system/universe/whatever, he's trying to explain that all points of reference are equal, and that there's exceptions to the heliocentric model as well, such as our own moon, which does orbit the earth. The sun is revolving around something itself, so it isn't really a center of anything either. There is no center. All reference points can be made to make sense if you're willing to put up with the fucked up math for different models. We use the heliocentric model because it's simplest for practical purposes, but that doesn't mean that it's any more or less correct then a geocentric model. The math's just easier.

Gaaah. Another person who don't get it.

Of course there's no centre. I never fucking said there was. My statements have simply been that the only sensible use of orbit in regards to science and space puts Mars and Earth orbiting the sun, or at least the centre of gravity of the system.

Adding difficulty? Claiming they move in their way because of another reason? Just adding bullshit. Which, you know, falls under Parsimony.

But it's not like anyone here seems to understand science, as Primus showed when he babbled about 'Pure Science' and how we should support the theory which offers no usable predictions..

Maybe it's a temporary bug. Like 24hours of insanity.

[Kuroneko]

Part of the definition of orbits is that object A should significantly influence object B's movement. If you magically remove the Earth from the solar system, Mars would continue to orbit around the Sun. If you magically remove the Sun, Mars would fly away.

Part of the problem is that a universally accepted definition of 'orbit' does not seem to exist. It is fairly frequent among relativistic books to adopt the mathematical definition, which is by far more loose--in terms of dynamical systems, 'trajectory' and 'orbit' are synonymous [1]. In this kind of sense, 'orbit around' is really nothing more than 'goes around'. The hypothetical-object-removal approach may be reasonable (albeit incompatible with common usage), but there needs to be a precise definition of 'object' consistent with relativity. If 'object' means something along the lines of 'collection of mass-energy', then it would be impossible for there to be orbits around isolated black holes, since they are vacuum solutions: there is neither mass nor energy anywhere in spacetime. I don't know how to fix this, or even if it is possible to fix while remaining purely in relativity.

If you magicly remove the Sun Mars would continue to orbit the old center of mass until the gravity wave reached Mars.

No. If the Sun magically disappears, then general relativity would simply be broken (unlike Newtonian gravity, which is compatible with violations of conservation laws), but if one insists on applying relativity anyway, then there would still be no gravity wave. If the mass-energy tensor magically vanishes, the Ricci curvature would also vanish, and assuming there is no Weyl curvature to compensate (i.e., the Sun did not spontaneously form a black hole, but actually disappeared), then the surrounding spacetime would (magically) turn flat. Immediately.

This is what I specifically said in the last post. You don't need an absolute frame of reference to notice that Earth and Mars orbit the barycenter. It can be determined from anywhere, just by analyzing what's acting on the two bodies.

The question of what is acting on what and in what manner is a very loaded one. In general relativity, 'gravitational force' is just as fictitious as the centrifugal and Coriolis forces of Newtonian mechanics. Additionally, gravity is non-linear in relativity; a general situation cannot be decomposed into 'influence of X + influence of Y + influence of Z + ...', etc. The only way to make your approach sensible is then ask how the system would behave with some object removed, which is exactly Mr. Wong's idea. Unfortunately, it is either flawed or incomplete. Something more precise is necessary.

[1] Randomly poking around on my shelf, O'Neill's Semi-Riemannian Geometry (good book) is an example. Frequently, even basic relativity books, which are typically less concerned with mathematical formalism, adopt this definition as well (e.g., d'Inverno's Introducing Einstein's Relativity).

[tharkûn]

The quotes I've been making was a direct C&P. You're just making a last minute, desperate wail of a defeated bitch.

I'm still waiting for you to state specificly what is wrong with saying Earth goes around Mars in a Martian frame of reference. All of the BS where you show your ignorance about orbital mechanics doesn't change the fact the irregardless of what causes Earth's relative motion it still goes around Mars in a Martian frame of reference.

Because page two starts with a million dollar offer from a reliable, verifiable group if you can prove these specious claims and ones like that. If you actually could prove a speck of this, you wouldn't be debating a name over a gif of a beloved Squaresoft character. No, you'd be out earning your cool million.

What part of equivalent don't you understand? If it is impossible to conclusively prove one frame wouldn't it then follow that it would be impossible to conclusively prove an equivalent frame? Why yes, dumbass, it would. Either system generates a valid set of physical observations and the ONLY difference is the simplicity of the mathematics.

But you're here, trying to pick up cool points for the equivalent of 0=1. No one's impressed.

-1 = -1
-1/1 = 1/-1
i/1 = 1/i
i*i = 1
-1 = 1
0 = 2
0 = 1


What anyone who comprehends modern physics, which pointedly excludes you, understands is that if you could definitively prove either challenge then relativity must be false. For many problems a heliocentric model is simpler (the most notable exception being problems centered on the Earth/Luna system), but that is all. Somehow I doubt or Catholic friends are going to accept that reasoning.

My statements have simply been that the only sensible use of orbit in regards to science and space puts Mars and Earth orbiting the sun, or at least the centre of gravity of the system.

Not the galatic center

It is the most sensible to set things up that way, but it is by no means the only valid one. For instance if you have a set of problems working with Mars, Earth, Luna, and the Lunar liberation points it would most likely be simplest to work them in a frame of reference where Mars goes around Earth. The 'orbit' of Mars under such a frame would be ugly but the Luna and L point orbits could be expressed simpler.

In real physics you pick whichever frame is most convenient and if you observe screwy things in that frame of reference, well you observe screwy things but they are nevertheless valid.

[tharkûn]

No. If the Sun magically disappears, then general relativity would simply be broken (unlike Newtonian gravity, which is compatible with violations of conservation laws), but if one insists on applying relativity anyway, then there would still be no gravity wave. If the mass-energy tensor magically vanishes, the Ricci curvature would also vanish, and assuming there is no Weyl curvature to compensate (i.e., the Sun did not spontaneously form a black hole, but actually disappeared), then the surrounding spacetime would (magically) turn flat. Immediately.

Correct me if I'm wrong, but I thought that changes in spacetime curvature propogated at c, rather than instaneously. What relativity I took is years behind me and rusty but I recall something like that.

[Darth Wong]

Tharkun, the fact is that "orbit" can be taken to include the "influence" portion of the English word definition, or not. But if you choose to ignore the "influence" portion of the definition, then the question of which object orbits around which other object becomes totally meaningless, since any object in the whole solar system can be said to orbit anything else. Merely by asking the question in the first place, one is automatically implying a more restrictive definition of "orbit" than the one you are using.

As Kuroneko says, there is no "official" scientific definition of the word "orbit", which is not surprising since science is not primarily concerned with semantics. But as I said, the nature of the question automatically implies a definition other than the one you're using.

[Kuroneko]

Correct me if I'm wrong, but I thought that changes in spacetime curvature propogated at c, rather than instaneously. What relativity I took is years behind me and rusty but I recall something like that.

That depends on what precisely is meant by that statement. There is certainly no limit to speed of spacetime itself, as demonstrated by universe solutions with positive cosmological constants (there can be points in space that undergo superluminal separation in those cases). So, if there is nothing to gravitate in an asymptotically flat spacetime, and the object did not turn into a black hole, then it would make sense for spacetime to turn itself flat. On the other hand, if by 'changes in spacetime', what is meant is that there is pertubation (e.g., mass ejection), then yes, the new gravitational arrangement will be felt only at some delay, propagating at the speed of light. This is enforced by Einstein's field equation. However, in the case of a magical disappearance of the Sun, Einstein's field equation is broken quite explicitly, since the relativistic conservation law is a consequence of the field equation. On further consideration, I think both views are wrong--attempting to apply relativity to an event that explicitly breaks relativity is simply nonsensical. So, probably the best answer to "what happens if the Sun disappears under relativity?" is "the theory doesn't cover that."

[The Silence and I]

What I am confused about is the length of the argument so far...

tharkûn stated that from the points of views of the Earth and Mars the one goes around (circumnavigates/describes a complete path about/whatever the hell you want to call it) the other and that mathematically speaking this is as good as saying they go around the Sun.

So my question to Nitram is this:

Can it be said the Earth goes around* Mars and vice versa? Yes or no?

_________________________________


*To ensure absolute, precise, clarity:
Forget the word "orbit;" within the context of the statement it does not exist and has no relevance. So what if you don't want to abandon the sun centered model as the "reality" of the situation; wether or not the Earth and Mars orbit the sun and only the sun is a side issue, and should never have come up.

P.S. I realize this post has a small chance of convincing anyone intended of anything I want it to, but I feel I should try.

[SirNitram]

What I am confused about is the length of the argument so far...

tharkûn stated that from the points of views of the Earth and Mars the one goes around (circumnavigates/describes a complete path about/whatever the hell you want to call it) the other and that mathematically speaking this is as good as saying they go around the Sun.

So my question to Nitram is this:

Can it be said the Earth goes around* Mars and vice versa? Yes or no?

Only if one completely and utterly tosses aside the fact that, you know, we know planets rotate. Because as long as planets rotate, we can know that Earth will never be on the 'other' side of Mars(IE, the side where the asteroid field is). You can, if you want to be a semantic-whoring bullshitter, get away with the reverse, since Earth's orbit is entirely encased by Mars', but it's still a stupid, misleading statement.

[tharkûn]

Mike:

but if you choose to ignore the "influence" portion of the definition, then the question of which object orbits around which other object becomes totally meaningless, since any object in the whole solar system can be said to orbit anything else.

I was taught that you defined what orbited what in whichever manner is most convenient to the problem at hand. For some problems I define Luna to orbit Earth and for others I'd define Luna to orbit Sol on an epicycle.

Yes this implies that any body orbits any arbitrary point when you pick the "correct" frame of reference. However if you first define your frame of reference then there are limits. In a heliocentric frame the statement Earth orbits Jupitor would be false, in a Jupitor centered frame it would be true. Likewise you only get on free orbit by definition, if you deal with more there is no garuntee they will all be orbiting the same arbitrary point.

Only if one completely and utterly tosses aside the fact that, you know, we know planets rotate. Because as long as planets rotate, we can know that Earth will never be on the 'other' side of Mars(IE, the side where the asteroid field is). You can, if you want to be a semantic-whoring bullshitter, get away with the reverse, since Earth's orbit is entirely encased by Mars', but it's still a stupid, misleading statement.

In a Mars centered frame the asteroid field rotates as well. There are an infinite number of points in a heliocentric frame which will never line up, such as the gravitational saddlepoint at L3. Likewise Sol, Jupitor and the Trojan asteroids will never be colinear in a heliocentric frame - so what?

[Kuroneko]

Tharkun, the fact is that "orbit" can be taken to include the "influence" portion of the English word definition, or not. But if you choose to ignore the "influence" portion of the definition, then the question of which object orbits around which other object becomes totally meaningless, since any object in the whole solar system can be said to orbit anything else. Merely by asking the question in the first place, one is automatically implying a more restrictive definition of "orbit" than the one you are using.

That's really the crux of the matter. My only concern is more philosophical--specifically, the defining 'orbit' in the proper sense doesn't seem to be possible within strict relativity (the black hole orbit example in particular; it is not a physical object in GTR, so the otherwise sensible object-removal test fails). However, that's not really central here (it is an interesting thing to think about, but not much more), as there is no reason for a working scientist to be constrained to a minimalist GTR. One such way would be to include black holes as metaphysical objects, thus restroring the object-removal test of influence directly; a more straightforward way could be simply to jettison generality and assume asymptotically flat spacetime (this would allow some nice properties, including sensible definition of energy as a scalar and a center of mass). The exact details simply don't matter.

Mr. Tharkûn's problem is not so much as he makes statements that are factually incorrect (they are perfectly valid), but that he ignores the context of the issue, which is simple: either way, it is a lose-lose proposition for the geocentrist. As stressed before (in this thread and some previous, as quoted by Mr. Primus), a geocentrist has only two choices: accept a criterion that makes sense of his or her claims, and subsequently judges them incorrect, or insist on a criterion that renders such claims meaningless. The geocentrist cannot afford to go the latter route.

Still, it would be interesting to see if it is possible to have a purely relativistic definition of 'orbit around' that is applicable in even exotic cases and is as consistent with the Newtonian barycenter view.

[SirNitram]

Only if one completely and utterly tosses aside the fact that, you know, we know planets rotate. Because as long as planets rotate, we can know that Earth will never be on the 'other' side of Mars(IE, the side where the asteroid field is). You can, if you want to be a semantic-whoring bullshitter, get away with the reverse, since Earth's orbit is entirely encased by Mars', but it's still a stupid, misleading statement.

In a Mars centered frame the asteroid field rotates as well. There are an infinite number of points in a heliocentric frame which will never line up, such as the gravitational saddlepoint at L3. Likewise Sol, Jupitor and the Trojan asteroids will never be colinear in a heliocentric frame - so what?

Of course the bloody field rotates. It even rotates if you toss out this sophist bullshit and go back to the land of science where we define orbits by what's making them move, instead of vague, semantical bullshit. That doesn't change the fact it verifiably stays on the far side of Mars' path from Earth.

[SirNitram]

Still, it would be interesting to see if it is possible to have a purely relativistic definition of 'orbit around' that is applicable in even exotic cases and is as consistent with the Newtonian barycenter view.

Assuming I understand this correctly(IE, that you mean we can really use any frame of reference equally while determining orbits), nothing stops us from doing that now. We just have to understand that even 0,0,0, whatever we're using for that today, is in motion too. Once you come to terms with that, we can find what we're moving around.

[Kuroneko]

Assuming I understand this correctly(IE, that you mean we can really use any frame of reference equally while determining orbits), nothing stops us from doing that now. We just have to understand that even 0,0,0, whatever we're using for that today, is in motion too. Once you come to terms with that, we can find what we're moving around.

What I mean is to be able to determine in an arbitrary scenerio without invoking a metaphysical view of what consitutes an object (why? because such things should be minimized). There are some situations in GTR in which things like global energy or center of mass are not even definable, which really makes a mess of things if one wishes to transplant the Newtonian barycentric view. Again, that's really an aside to the whole geocentrism/heliocentrism issue; even the most sympathetic interpretation of relativity destroys geocentrism--all that's changed is whether geocentrism is just plain wrong or "not even wrong."

[pskouson]

I have read this thread with great interest. I notice no one has, at least on this thread, proven that the Earth revolves around the Sun. I know it does, so does everyone else I know. But none of you have yet proven it. I certainly don't have the expertise to prove it, and yet I am sure the Earth orbits the Sun. All my observations seem to point to it, but I don't think I can prove it.

I hope you will forgive any perceived 'preachy' or 'fundie' tone in this post. I assure you none is intended.

You seem to have deviated a bit from the OP, but you still seem to be making the Catholics' points for them:

1) You will NEVER be able to convince someone of something they refuse to believe. You are all extremely intelligent, yet can't convince each other. Pride often trumps brains.
2) You can't always prove what you know.

Now, I grant you that these are not ALL the points they are trying to make, but doesn't it weaken the position of those who disbelieve God's existence due to lack of proof or credible evidence?