# The Sun revolves around the Earth?

1. Jan 27, 2005

### eNathan

Hi everyone, I am fairly new to PF.

So I start off with a rather strange idea, derived from SR.

According to the first postulate of Special Relativity, it would be more accurate to say that the sun revolves around the earth, because we are stationary relevant to the earth, right? Correct me if I am wrong, but I am sure I am right.

Wait until I tell me Astronomy Teacher :rofl:

Last edited: Jan 27, 2005
2. Jan 27, 2005

### da_willem

What are the restrictions of the postulates of SR? Something about inertial frames rings a bell?

3. Jan 27, 2005

### eNathan

No, it does not ring a bell :uhh: . I would appreciate it if you could explain it to me. I have never taken a class on SR or GR, in fact, I have never taken a physics class at all. I do all my studies on the internet. But yes, I have heard of the internal reference frames, I never got it down tho.

4. Jan 27, 2005

### da_willem

Well, to some extent you are right in saying the sun is revolving around the earth, this is how it looks from the earth! That's one of the reasons the geocentric model (stationary earth, all other things revolving around us) of the universe was the standard one for such a long time (the other being, that they thought the earth must take a very special place amongst all other things). 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.

The reason you can't use special relativity in this case is that special relativity only applies to 'inertial frames', that's what makes the theory special wrt general relativity. An inertial frame is a 'frame of reference' where Newtons laws apply. Examples of noninertial frames are accelerating frames, (in special relativity acceleration is not relative!) or frames in the presence of a gravitational field. To make things easy in some cases being both accelerating and in a gravitational field makes them inertial again, this is nearly the case in free fall for example. The earth is ot an inertial frame, it is spinning, revolving around the sun, in the gravitatinal field of the sun, planets, moon , distant stars... So that's why you should be careful using SR.

So it's a little more difficult than saying: all motion is relative so there's no difference between we revolve around the sun or the sun revolves around us.

5. Jan 27, 2005

### jcsd

Speial relativty applies to non-inertial frames too, the postulates of special relativty don't apply directly to non-inertial frames (for example it don't expect the speed of light to be constant or the laws of physics to be the same).

Some say that GR says that the Sun orbiting the Earth is valid viewpoint as the general rleativstic laws of physics are still the same whethr you choose an Earth-centred or Sun-centred frame. To me asking wheeehr the Earth goes round the Sun or vice versa is a question of ontology rather than physics.

6. Jan 27, 2005

### Phobos

Staff Emeritus
Welcome to Physics Forums, eNathan.

(kind of repeating here...)

Special Relativity (SR) applies to inertial reference frames (non-accelerating). In any inertial reference frame, the speed of light is measured to be constant and the laws of physics are the same. Because the Earth is going around the sun, it's in a state of acceleration relative to the sun (an orbit is the result of a balance between tangential velocity & inward acceleration). So, you don't apply SR in that case...or if you do, things get tricky, like jcsd said.

7. Jan 27, 2005

### da_willem

If you are accelerating wrt a lightsource do you measure a different speed than c? Hmm, in the light of general relativity where there is an equivalence between accelerating and a homogeneous gravitational field I guess you do measure a different speed! Wow, never realised that.

8. Jan 28, 2005

### eNathan

When you say
, I get a little confused. In fact, I have in general, been confused with the difference of Velocity and Acceleration. As far as I know, acceleration is a frame of reference that is continually speeding up. And velocity stays the same. So, by saying that SR only applies to Accelerating frames of reference, does that mean that it does not apply to a frame of reference that is not accelerating, but has a constant velocity. The lorenz transformation is $sqr (1- \frac {v^2} {c^2})$ NOtice that the variable which determines the relativity is "v", not "a". I think I have something wrong tho, can someone please explain it to me?

9. Jan 28, 2005

### Creator

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

10. Jan 28, 2005

### da_willem

I get a little confused here too. Acceleration is a frame of reference? Acceleration is the rate of change of velocity in time, so an object with constant velocity is not accelerating. In special relativity velocity is always relative to something, acceleration is absolute.

SR only applies to non-accelerating frames of reference! These are called inertial frames; in contrast to accelerating frames wich are non-inertial.

The Lorentz transformations say how your coordinates change when you switch from one inertial frame (a=0) to another with a different speed v. So it is perfectly natural these transformations depend on v. The acceleration only enters the story as a restriction on the range of applicability of the transformations. The frames your transforming between must be inertial, nonaccelerating, a=0.

11. Jan 28, 2005

### eNathan

So what if I was accelerating, is there any dilation in time, or contraction in length, or mass increase relavent to a stationary observer? And what Exaacly is the definition of an internal frame of reference?

12. Jan 28, 2005

### da_willem

It is velocity that is associated with these phenomena you name, not acceleration. And an inertial reference frame is (as I stated earier) a frame of reference in wich Newtons laws appy.

13. Jan 28, 2005

### ohwilleke

You don't need SR for the sun to revolve around the Earth. The same result can be achieved in Cartesian coordinates and Newtonian gravity and mechanics.

Either way, from the perspective of a coordinate system centered on Earth, the Sun revolves around the Earth. The trouble with using that coordinate system is that the planets start doing loop da loops in the sky and the entire galaxy has to jiggle a little every year. This is very hard math and very hard conceptually.

But, most people find the math and the conceptual understanding easier to achieve with the Sun as the center of the coordinate system. It is a stylistic preference, but one that make eminent sense and is unique in reducing the degree to which understanding of the system is complicated.

In fact, really the Earth follows a path around the Sun that is a bifocal ellipse, perturbed by the other bodies in the solar system (and universe) most notably the Moon and Jupiter, it is not simply a sphere with the Sun as its center point. They really orbit their combined center of gravity.

Last edited: Jan 28, 2005