General Relativity- the Sun revolves around the Earth?

[Dertulm01]

Someone I know recently stated according to General Relativity, the following statements are both correct:

1. The Sun rotates around the Earth.

2. The Earth rotates around the Sun.

Is this true?

 

[CompuChip]

I think this is even according to classical mechanics. Only the sun is so large and heavy that the center and radius of rotation of the sun lie within the sun. So if you can already see it it's more like a little wobble around its center of mass.

 

[Dertulm01]

I understand that the way it seems can vary depending on where one is experiencing the moving objects, but both statements can't actually be true, can they? The physical reality is that the Earth is revolving around the Sun...right?

 

[CompuChip]

Without involving GR, AFAIK the physical reality is that they are both revolving around a common center of mass, that lies somewhere inside the sun.

 

[Dertulm01]

Without involving GR, AFAIK the physical reality is that they are both revolving around a common center of mass, that lies somewhere inside the sun.

Which means that it's not actually possible for the Sun to be revolving around the Earth. But the Earth does revolve around the Sun.

 

[D H]

Without involving GR, AFAIK the physical reality is that they are both revolving around a common center of mass, that lies somewhere inside the sun.

That is how things look from the viewpoint of an inertial reference frame. In Newtonian mechanics, inertial reference frames are viewed as being somehow better / closer to truth than non-inertial frames.

There is nothing wrong with looking at things from the perspective of a non-inertial frame. It is sometimes much easier to look at things from such a perspective. For example, modeling the Earth's atmosphere from the perspective of an inertial frame would be insane.

From the perspective of an Earth-centered reference frame, the Sun does indeed orbit around the Earth. In GR, all reference frames are equally valid. There is nothing particularly special about inertial reference frames in GR.

 

[Dertulm01]

From the perspective of an Earth-centered reference frame, the Sun does indeed orbit around the Earth. In GR, all reference frames are equally valid.

Reference frames may all be equally valid, but nothing about GR infers that the Sun is actually revolving around the Earth, right?

 

[D H]

In saying "actually" you are implying the existence of some vaunted reference frame that is somehow more truthful than other reference frames of lesser validity. That is not the case. All reference frames in general relativity are equally valid. Some are just a bit harder to work with than others.

 

[Dertulm01]

In saying "actually" you are implying the existence of some vaunted reference frame that is somehow more truthful than other reference frames of lesser validity.

I'm doing no such thing! I'm not talking about reference frames at all. I'm asking if according to GR, both statements that I posted in the OP are true. As in actually true, not whether or not is can seem like either reality is equally valid.

The Earth is in an elliptical orbit around our Sun. I'm not talking about reference points here, I'm talking about what's actually happening. The Earth is orbiting the Sun because of its velocity. This is what happens in reality. I'm not talking about reference points. The Sun does not actually revolve around the Earth, and GR does not change that, correct?

 

[Crosson]

Someone I know recently stated according to General Relativity, the following statements are both correct:

1. The Sun rotates around the Earth.

2. The Earth rotates around the Sun.

Is this true?

Those statements are sloppy, they become true if we amend them as follows:

1. For an observer who is at rest on the surface of the earth, the Sun rotates around the Earth.

2. For an observer who is at rest on the surface of the sun, the Earth rotates around the Sun.

Hopefully both of those sentences make sense to you, and you realize they are true.

 

[Crosson]

I'm not talking about reference points here, I'm talking about what's actually happening. The Earth is orbiting the Sun because of its velocity. This is what happens in reality. I'm not talking about reference points. The Sun does not actually revolve around the Earth, and GR does not change that, correct?

No, what you don't understand is that all motion involves a reference point. It doesn't make sense to ask 'what is happening in reality', we can only describe what various observers would see from their various points of reference.

 

[pallidin]

That's a good point: "All motion involves a reference point"

 

[Dertulm01]

No, what you don't understand is that all motion involves a reference point. It doesn't make sense to ask 'what is happening in reality', we can only describe what various observers would see from their various points of reference.

Why doesn't it make sense to ask what is happening in reality? Let's say I shoot off a model rocket. For an outside observer, it may seem like either the rocket is moving away from the Earth or the Earth is moving away from the rocket (depending on if the observer is moving in relation to the Earth or rocket). But in reality, the rocket is being propelled away from the Earth. The Earth's velocity has not changed and is it's not moving away from the rocket.

 

[Dertulm01]

From this thread.

One of the problems with the geocentric model is that the trajectories of the heavenly bodies don't get any prettier. If it were only the sun it wouldn't be that bad. Seen from us its trajectory is nearly circular. But the trajectories of the other planets are very complicated. All of this can be resolved by assuming the planets revolve in nearly circular (elliptic) orbits around the sun. Then the trajectories (wrt the sun!) become very easy. It was this thought that scientist like Galileo and Kepler had a few centuries ago, and didn't make them any more popular by the church.

Even without relativistic concepts, some observational things cannot be replicated without resorting to a seasonal variation in Earth's motion - in particular stellar parallax, for example, cannot be explained with a 'stationary' earth. The seasonal motion of Earth about the sun is easily accounted for by appealing to the seasonal variation in stellar parallax.

Creator

It seems there is evidence that there is more to the reality of motion than a viewer's reference point.

 

[D H]

From this thread.

That thread is flawed from the onset because it is talking about special relativity, which relied on the concept of an inertial frame. The concept of an inertial frame has significantly reduced value in general relativity.

It seems there is evidence that there is more to the reality of motion than a viewer's reference point.

Yes, it is a bit harder to explain stellar parallax from the perspective of an Earth-fixed reference frame than from the perspective of a solar system barycentric reference frame.
On the other hand, it is extremely difficult to explain a cyclone from the perspective of a solar system barycentric reference frame. No meteorologist would even think of using anything other than an Earth-fixed reference frame to model the weather.

BTW, it's not all that hard to explain stellar parallax from the perspective of an Earth-centered frame. The motion of the stars can be explained in terms of the "third body effect". People who model the behavior of satellites in Earth orbit vastly prefer to use an "Earth-centered inertial" reference frame (a non-rotating reference frame with origin at the center of the Earth) than a barycentric frame. From the perspective of such a reference frame, the Sun and Moon (and the planets) make the satellite's orbit not quite Keplerian. The perturbation is explained by a pseudo-force called the third body effect. An article: http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/763654" .

The choice of reference frame can make it easy or hard to describe some behavior. One could, for example, describe the motion of a satellite in orbit around the Moon from the perspective of a Neptune-centered inertial frame. It is silly to do so, but nonetheless it can be done. (I know it can be done because I have done exactly that. This is one of the verification tests for the simulation tools that I help build for NASA.)

We use mathematical descriptions of the way things work as a map. These maps are very useful. However, it is important to remember that "the map is not the territory" (Alfred Korzybski, General Semantics). Our maps are a description of reality. They are not reality in and of themselves.

 

[dst]

Why doesn't it make sense to ask what is happening in reality? Let's say I shoot off a model rocket. For an outside observer, it may seem like either the rocket is moving away from the Earth or the Earth is moving away from the rocket (depending on if the observer is moving in relation to the Earth or rocket). But in reality, the rocket is being propelled away from the Earth. The Earth's velocity has not changed and is it's not moving away from the rocket.

If you have not even managed to grasp Newton's relativity then is there really any point talking about general relativity?

There is no such thing as "The Earth's velocity", there is only "the Earth's velocity relative to a reference point". Also, the Earth's velocity does change which is easy to see from application of f=ma to both sides. So if our rocket has 1000 Newtons of thrust force and has mass 100kg, then a = 10 m/s^2. Apply the same case to the Earth, since the rocket also exerts 1000N on the Earth, with a mass of the Earth approx. 6x10^24kg. Then acceleration (i.e. CHANGE IN VELOCITY) = 1000/(6x10^24) m/s^2. While it is negligible, it is definitely there.

This change in velocity exists regardless of reference point.

 

[Dale]

It seems there is evidence that there is more to the reality of motion than a viewer's reference point.

The point of relativity (Galilean, special, and general) is that the results of any physical experiment are independent of the reference frame. In other words, as long as you do the math right and apply all appropriate physical laws you will get the same answer in any coordinate system. This includes standard coordinate systems where the Earth and sun revolve around a common barycenter as well as unusual coordinate systems where the sun revolves around the earth, etc.

 

[W.RonG]

Why doesn't it make sense to ask what is happening in reality? Let's say I shoot off a model rocket. For an outside observer, it may seem like either the rocket is moving away from the Earth or the Earth is moving away from the rocket (depending on if the observer is moving in relation to the Earth or rocket). But in reality, the rocket is being propelled away from the Earth. The Earth's velocity has not changed and is it's not moving away from the rocket.

au contraire. when you shoot a rocket up from the surface of the earth, the Earth actually moves away from the rocket too (an acceleration). a very small amount but real nonetheless.
rg

 

[maverick_starstrider]

Actually if you launch a rocket from the Earth conservation of momentum is conserved so mass of the rocket * velocity of rocket = mass of Earth * added velocity of earth. So if you were to somehow stay at the exact point (relative to some distant object like the sun or some such) then both the rocket AND the Earth would be seen to move away from each other. The REALITY is that all references frames are equally valid and this understanding is FUNDAMENTAL and the basis of the theories of special and general relativity. As for your discussion of the Earth around the sun vs sun around the Earth the most 'elegant' or mathematically simplistic frame of motion to do calculations with is neither. It's the easiest to consider the motion of the two from the barycenter (the center of mass of the two body system) which, as someone mentioned previously, is still in the interior of the sun (but NOT at its center)

 

[Gabe911]

so let me get this straight, for me to say the sun revolves around the earth, there is nothing wrong with this from a scientific perspective because of the theory of general relativity?

 

[K^2]

Well, mostly. I mean, it really doesn't matter, but you have to account for centrifugal force. If you say that Earth rotates around its axis, then centrifugal force takes care of itself. If you say that Earth stands still and the Sun rotates around the Earth, you have to invent some hobgoblins that are pulling the Earth in different directions. There is nothing really wrong with the later approach, but the former is more general.

From the point of General Relativity, yes, I can write down a correct metric for Space-Time around Earth such that Earth would be the center of the universe and be still, and all heavenly bodies would revolve around it. This has added benefit of not involving hobgoblins, but it's just as specific. It would describe this Earth and nothing other than this Earth.

 

[pallidin]

Let's not retro astronomical dynamics, please.
It is abundantly clear without question that the Earth revolves around the sun.

 

[disregardthat]

It is abundantly clear without question that the Earth revolves around the sun.

The point is that the fact that the Earth revolves around the sun is not as opposed to that the sun revolves around the earth. Not in GR, SR or classical mechanics.

 

[sophiecentaur]

The words "really" and "reality" have been used too frequently in this thread.
Many of these posts are assuming that, underneath it all, there is an system of xyzt (cartesian) coordinates, describing space and that the observers are, somehow, just seeing this grid from their own point of view.
There is no ultimate xyzt frame of reference. It's ALL relative and many, many experiments show this.
Poor old Galileo had this problem, where Copernicus didn't. Galileo fought the Church because he said "this is the way it really is". Copernicus said "you can look at it this way and it gives the right answers". The Church would never have felt the need to threaten Copernicus with torture - even if they'd been able to get hold of him.

 

[Gabe911]

so i could say that this time lapse is not simply an appearance, in GR, but a reality(sorry for for overusing the word)? that the sun is moving around us as we see it is just a valid explanation as the Earth is spinning on its axis giving the appearance of the sun's movement around us? do i understand it correctly?

 

[Cleonis]

Someone I know recently stated according to General Relativity, the following statements are both correct:

1. The Sun rotates around the Earth.
2. The Earth rotates around the Sun.

Is this true?

(I started reading existing replies, but I ran out of patience, so I just reply to the original post.)

The short answer is: No
Size matters - therefore only the statement: 'the Earth rotates around the Sun' is correct.



Let me state what classical mechanics (CM) and GR have in common.
The Sun is more massive than the Earth. In terms of CM the Sun exerts a way stronger gravitational force than the Earth.

For the sake of simplicity I will refer to a 'gravitational field' as described by GR. (Actually the gravitational field as described by GR does not exist in the same form in Classical Mechanics. But there is no alternative for the word 'field'. So the expression 'gravitational field' will have to do.)

In terms of GR the gravitational field of the Sun is way stronger than the gravitational field of the Earth. The point is: the Sun being more massive than the Earth is independent from choice of frame of reference. It's just more massive.

For the case of the Moon and the Earth and the Sun: The common center of mass of the Earth-Moon system is orbiting the Sun. The Earth is so much more massive than the Moon that the common center of mass of the Earth-Moon system is beneath the Earth's surface. Again, this is independent of choice of reference frame. Regardless of how you represent the physics taking place, the physical description locates the common center of mass some distance beneath the Earth's surface. Size matters.

You get a hierarchy of larger and larger systems. The common center of mass of the Solar system is orbiting the center of gravity of our galaxy. Our galaxy is gravitationally affected by the surrounding galaxies. In terms of GR this hierarchy is just as relevant as in Classical Mechanics.

Compared to classical mechanics GR presents a fundamental rethinking of gravitation and motion, but some things do carry over from classical mechanics, in particular the hierarchy of larger and larger gravitational systems as described above.

I hope you will stick with the subject, and that in the future you will be in a position to study GR, and go through the experience of fundamentally changing your thinking about motion and gravitation. It's worth the effort.



I sometimes encounter the following faulty syllogism:
"Special relativity asserts relativity of inertial motion."
"General relativity is more general than special relativity."
Ergo:
"GR asserts that all motion is relative."

While GR is a more profound theory than SR, thus replacing SR, it's not about extending relativity beyond relativity of inertial motion.


I sometimes see the following reasoning presented:
"In GR we can always adjust the description in such a way that any particular point we assign is treated as stationary point, and with sufficient ingenuity we can solve the equations for that representation. This proves that GR extends relativity of motion."

The thing is: in classical mechanics we have just the same freedom! It's mathematically more complicated, but we can assign any point to be treated as stationary point. Having that freedom in GR is of no particular significance.

GR is a most profound theory, but it's not about extending relativity of motion.

 

[K^2]

Cleonis, you did not understand a thing about General Relativity if you think that Sun being heavier has anything to do with which revolves around which.

I can write down the correct metric for Sun-Earth system with Earth as the center of the system and Sun revolving around the Earth. That metric will be a solution to Einstein Field Equation, and will therefore be completely kosher with GR.

 

[Cleonis]

[...]
Many of these posts are assuming that, underneath it all, there is an system of xyzt (cartesian) coordinates, describing space and that the observers are, somehow, just seeing this grid from their own point of view.
There is no ultimate xyzt frame of reference.
[...]

I agree of course that we should stay away from any hypothetical 'underneath system'. Descriptions of motion should be based only on making comparisons.

It's safe, I think, to assume that such a thing as mass exists, and that different objects can have different masses.

The Earth has more mass than the Moon.
It's fine to assert that without reservation.
In terms of classical mechanics the Earth has more mass.
In terms of GR the Earth has more mass.
And whatever theory replaces GR in the future, we expect that in that theory the Earth has more mass than the Moon.

 

[Cleonis]

I can write down the correct metric for Sun-Earth system with Earth as the center of the system and Sun revolving around the Earth. That metric will be a solution to Einstein Field Equation, and will therefore be completely kosher with GR.

Of course you can; of course that will be a solution.
You seem to be discussing a different subject than I was discussing.

I think you are discussing the capabilities of the mathematical formalism. My focus is not the mathematical formalism.
Some examples:
There have been setups where sufficiently precise atomic clocks were positioned in a valley and atop the nearest mountain. Over time the clocks go out of sync, which we attribute to gravitational time dilation.

As we know, the GPS satellites carry atomic clocks, and those clocks count more time than Earth based clocks, which we attribute to gravitational time dilation.

No such precise atomic clocks are onboard ISS in its low Earth orbit, but we can calculate that ISS clocks will count less proper time than Earth based clocks.
The interpretation is that while ISS is at a higher gravitational potential, it also has more velocity than the Earth, because ISS is orbiting the Earth.

I agree of course that it's possible to set up a representation in which ISS has no velocity. And that if you carry through the computations for that representation the final outcome will be the same time dilation between the Earth based clocks and the ISS clocks. All that thanks to the versatility and the power of the mathematical formalism

But I argue that independent of the details of the mathematical representation, the physical interpretation has a significance of its own.

I submit that being way up high or being way down low in a gravitational potential is significant in itself.

 

[K^2]

In that case, show me an experiment that would confirm that Earth is indeed moving around the Sun, and not the other way around. That would prove that one physical interpretation is correct and the other is not. Anything else is hand-waving.

Just because I don't want you to waste too much of your own time, keep in mind that such an experiment would violate General Relativity.

 

[1MileCrash]

I understand that the way it seems can vary depending on where one is experiencing the moving objects, but both statements can't actually be true, can they? The physical reality is that the Earth is revolving around the Sun...right?

Well, not to veer off from the topic, but to answer this question in a general sense, yes, both statements can be true, and no, there is no "physical reality."

Lets have an example. Say you're traveling extremely fast, toward and relative to someone holding a plank of wood to where you would pass next to them, at a constant speed. You are facing perpendicular to them.

They drop the plank of wood straight down to their feet as you begin to pass them, so that both ends hit at the same time from their frame of reference.

However, from your frame of reference, the end of the board closer to you hits the ground first, and the other end hits second.

Which one is true? Which is the physical reality? Both, and neither. Relative to you you're still, they are moving extremely fast towards you, and they drop the board one end at a time. Relative to them, they are still, you are moving extremely fast towards them, and they drop the board both ends at the same time.

You can't say who's "right" because you can't say who's "absolutely" moving. So even some of the things that seem like they have a physical reality are still just relative.

I could be wrong, but I would say that there is no "absolute" way to show that the Earth revolves around the sun and not vice-versa. My guess for why we say "the Earth revolves around the sun" is because if we established Earth as a frame of reference, the sun orbits the earth, BUT every other planet in the solar system orbits the Earth while orbiting the sun. If we establish the sun as the frame of reference, all planets are revolving around it.

 

[DaveC426913]

This thread is all over the map.

The discussion can't even settle on what the OP means. It has, at times, answered with reference to:
- the barycenter of the Earth-Sun system (sun revolves around Earth - check),
- relativity (all frames of reference are relative - check)
- relativity of simultaneity (two events are observed to occur at differnt times depending on FoR - check)

Perhaps we should (re)start by clearly defining what the OP was asking (two years ago).

 

[Cleonis]

That would prove that one physical interpretation is correct and the other is not.

Your disagreement is not with me. The point of view you are arguing against isn't mine.


It goes without saying that as physicists we're not claiming to know absolute truths.

Still, we are confident that knowledge is possible. For instance, we rely on the principle of relativity of inertial motion. As physicists we work with a range of degrees of certainty. Some theories are tentative, some are regarded as beyond reasonable doubt.

Part of our set of physical interpretations is that such a thing as gravitational potential exists, and that there are gravitational time dilation effects.

As physicists we're not in the business of delivering absolute proofs, as those don't exist. As physicists our measures to go by are weight of evidence, and reasonable doubt.

 

[K^2]

Cleonis, you seem to also be confused on the purpose of the theory.

Is Heliocentric system more convenient, and therefore, more useful? Absolutely. Does it give you any predictions you could not acquire in Geocentric system? Absolutely not.

And when I map coordinates on Earth, is it more convenient to keep inertial frame of reference, or one that is fixed to rotating Earth. The later, of course. But does that mean that the Earth suddenly stopped rotating? No.

Convenience of one model over the other does not imply any sort of physical truth. It's just that, a convenience. In order for one thing to be true and for another to be false, the two models must provide disagreement in predictions.

Are there any disagreements in predictions? No. Then it is no more wrong to say that Earth is the center of the universe around which all else rotates, than it is to say that Earth rotates around the Sun.

 

[1MileCrash]

Right, right, I agree with you K^2.

However, please help me out with the mental picture.

From Earth's frame of reference, it's completely still, and therefore the sun orbits around it once per year. However, the Earth is also rotating. If we also "transfer" that movement as to be earth-relative, the sun is also orbiting around the Earth once per 24 hours.

I'm just having trouble picturing it. Or is the Earth still rotating from it's own reference frame?

What exactly is the sun doing from Earth's frame of reference, taking into account both orbit and rotation?