From what frame of reference does the Earth orbit the sun?

[mitcho]

I have been doing some study on the theory of relativity and it has got me thinking. We say that the Earth revolves around the Sun but from what reference frame? From the reference frame of Earch, we are stationery and the Sun simply spins. Why is any reference frame more accurate than another? Why can't we say that the Earth is stationery and the Sun simply rotates? I also ask this in regards to the Earth and Moon.
Any help would be appreciated.
Thanks.

 

[Vanadium 50]

Why can't we say that the Earth is stationery and the Sun simply rotates?

Revolves.

We can. But it is difficult to use such a coordinate system. For example, there is an enormous fictitious force whirling the sun around the earth. It is far better to pick a coordinate system where the motion looks simple, and the sun-centered one is that system.

 

[mitcho]

For example, there is an enormous fictitious force whirling the sun around the earth

I don't see why we need to adopt some enormous fictitious force, we should be able to use true forces since einstein said that the laws of physics will remain constant from all reference frames.

 

[harrylin]

Revolves.

We can. But it is difficult to use such a coordinate system. For example, there is an enormous fictitious force whirling the sun around the earth. It is far better to pick a coordinate system where the motion looks simple, and the sun-centered one is that system.

Yes, it is a question of classical mechanics. Newton's mechanics is approximately valid for inertial reference systems, wrt which motion makes sense physically (no assumption of fictitious forces). As a bonus the equations are simpler as well.

Special relativity relates to those reference systems of classical mechanics, see the intro of:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[Mueiz]

In space-time there is no motion ... there are only static worldines .

 

[russ_watters]

I don't see why we need to adopt some enormous fictitious force, we should be able to use true forces since einstein said that the laws of physics will remain constant from all reference frames.

Yes, he did - but one of those laws is f=ma and so since the "m" of the sun is much larger than the "m" of the earth, it takes a much bigger "f" to give it the same "a" to make it travel in a circle around the earth. So you have to give it an extra force for which there is no cause - a fictitious force.

 

[John232]

Acceleration can be thought of as a known velocity. It is not like an object traveling at a constant speed where it can say it is at rest or traveling at a constant speed at the same time. When under acceleration the person accelerating can prove that they are the one that is actually accelerating, so then it being in motion takes priority over it not being in motion. Still, I think it is strange that we don't feel any forces of acceleration while sitting on Earth. So, if you said that an object under acceleration was actually at rest then there would be a fictitious force that acted on all objects that are at "rest".

 

[Dale]

Acceleration can be thought of as a known velocity.

No, the units are different.

When under acceleration the person accelerating can prove that they are the one that is actually accelerating

Yes.

Still, I think it is strange that we don't feel any forces of acceleration while sitting on Earth.

We do feel forces of acceleration while sitting on Earth. Take an accelerometer and you will see that we feel an upwards acceleration of magnitude g.

So, if you said that an object under acceleration was actually at rest then there would be a fictitious force that acted on all objects that are at "rest".

Yes, that fictitious force is gravity.

 

[D H]

I don't see why we need to adopt some enormous fictitious force, we should be able to use true forces since einstein said that the laws of physics will remain constant from all reference frames.

The laws of physics dictate that the equations of motion will take a relatively simple form in some reference frames but a rather ungainly form in other frames. Those extra terms in the ungainly form are fictitious forces. (Or fictitious accelerations. There is no need to multiply by mass to yield a force because the very next step is to divide by mass to yield acceleration.)

While one could describe the behavior of the solar system from the perspective of an Earth-centered frame, you hit the nail on the head in the original post when you asked "Why is any reference frame more accurate than another?" The "best" (read: most accurate) frame of reference for computing the orbit of a satellite orbiting the Earth is an Earth-centered frame. You'll still get fictitious forces, but nonetheless the propagated orbit will be more accurate when computed in an Earth-centered versus a solar system barycenter frame.

Suppose instead the vehicle is transiting from Earth to Jupiter, and once at Jupiter, goes into orbit about Jupiter. To obtain the greatest accuracy you need to be quite adept with your frames of reference, switching integration frames along the way. The key to this switching is the gravitational sphere of influence.