# General Relativity- the Sun revolves around the Earth?

1. Jul 16, 2008

### 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?

2. Jul 16, 2008

### 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.

3. Jul 16, 2008

### 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?

4. Jul 16, 2008

### 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.

5. Jul 16, 2008

### Dertulm01

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.

6. Jul 16, 2008

### D H

Staff Emeritus
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.

7. Jul 16, 2008

### Dertulm01

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

8. Jul 16, 2008

### D H

Staff Emeritus
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.

9. Jul 16, 2008

### Dertulm01

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?

10. Jul 16, 2008

### Crosson

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.

11. Jul 16, 2008

### Crosson

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.

12. Jul 16, 2008

### pallidin

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

13. Jul 16, 2008

### Dertulm01

Why doesn't it make sense to ask what is happening in reality? Lets 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.

14. Jul 16, 2008

### Dertulm01

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

15. Jul 16, 2008

### D H

Staff Emeritus
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.

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" [Broken].

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.

Last edited by a moderator: May 3, 2017
16. Jul 16, 2008

### dst

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.

17. Jul 16, 2008

### Staff: Mentor

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.

18. Jul 17, 2008

### W.RonG

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

19. Jul 18, 2008

### 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)

20. Dec 7, 2010

### 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?