Annoying nitpicking: has the geocentric view of the solar system been refuted?

[I don't know]

Seeing as motion always has to be defined relative to something. And seeing that relative to, say, the sun, the Earth spins around it's own axis...

Doesn't that mean that, relative to Earth, everything moves around it?

It's not elegant neither mathematically nor logically, but isn't it technically true, though?

 

[mathman]

Logically you are correct. However to do any useful physics, the center of the solar system is placed at the center of mass, which, for practical purposes, is at the center of the sun.

 

[Astronuc]

I believe celestial mechanics and planetary motions indicate that the solar system is heliocentric. The Earth is in a periodic motion, as one can witness from the position of stars on an annual basis, but the sun position does not change as such.

 

[turbo]

As Astronuc has explained, the visible stars change slowly over the course of the year, as the the dark side of the Earth (night sky) points to in slightly different direction every day, eventually coming back around over the course of a year.

There is another more subtle effect called parallax. As the Earth moves from one extreme of its orbit to the other, closer stars that are perpendicular to these extrema appear to change positions with respect to more distant background stars. These changes in position can help us judge the actual distance to these nearer stars, and they can help researchers differentiate between quasars and faint brown dwarf stars as they identify candidates for follow-up spectrography. You can see from this that the heliocentric model is not only the preferred model - it also provides a valuable tool that can be used to improve our observations of extra-galactic objects like AGN/quasars.

 

[DaveC426913]

Seeing as motion always has to be defined relative to something. And seeing that relative to, say, the sun, the Earth spins around it's own axis...

Doesn't that mean that, relative to Earth, everything moves around it?

It's not elegant neither mathematically nor logically, but isn't it technically true, though?

It is technically possible to create a system of laws and forces wherein the universe revolves around the Earth. The trouble is, the giant list of laws and forces that control the various complex motions rapidly grows with each new observation of the gyrations of the moons, planets and stars until the whole theory collapses under its own weight.

For example, it's very difficult to develop a mechanism to cause the naked eye planets such as Mars to temporarily move retrograde across the sky for a portion of their orbits. And that's just the mechanism; you still don't have a theory to explain why they would behave this way.

 

[NerfMonkey]

The Earth is in a periodic motion, as one can witness from the position of stars on an annual basis, but the sun position does not change as such.

Doesn't the sun orbit the center of the galaxy very slowly (I've heard ~60mph, by my calculations less than a thousandth of Earth's velocity)? Or are those effects too small to be of any importance?

 

[DaveC426913]

Doesn't the sun orbit the center of the galaxy very slowly (I've heard ~60mph, by my calculations less than a thousandth of Earth's velocity)? Or are those effects too small to be of any importance?

Yes, it makes one revolution every 260 million years.

But there's no reason why you couldn't devise a model to show the galaxy orbiting the Earth system rather than the other way 'round; it would just be ridiculously complex.

BTW, physicists, as a rule, don't tend to believe in "effects too small to be of any importance"

 

[Gokul43201]

I'm no cosmologist, but I'd imagine that a frame attached to the Sun would be a much closer approximation to an inertial frame than one attached to the Earth (at least for the purpose of studying dynamics within the solar system), and inertial frames are extremely useful things.

 

[D H]

Doesn't the sun orbit the center of the galaxy very slowly (I've heard ~60mph, by my calculations less than a thousandth of Earth's velocity)? Or are those effects too small to be of any importance?

The Sun's (and hence the Earth's) orbital velocity about the galaxy is an order of magnitude greater than the Earth's orbital velocity about the Sun. The solar system is about 26,000 light years from the center of the galaxy. With an orbital period of about 2.25 million years, that corresponds to over 200 kilometers/second. The Earth's orbital velocity is about 30 kilometers/second.

We are able to ignore the gravitational acceleration toward the center of the galaxy because at 26,000 light years, the galactic gravity gradient across the entire span of the solar system is negligible. We are similarly able to ignore the gravitational acceleration toward the sun for nearby events on the surface of the Earth because the solar gravity gradient is very small at typical terrestrial distances. A geocentric POV is perfectly valid for addressing Earth-based physics.

In fact, a geocentric POV is perfectly valid for computing the orbit of another planet about the Sun or even one of Uranus' moons about Uranus. The Sun's (or Uranus') gravity of course cannot be ignored. All one has to do is to treat the geocentric frame as an accelerating reference frame. There's nothing wrong with doing physics in an accelerating reference frame. Just ask a meteorologist about the Coriolis effect.

 

[Gokul43201]

The Sun's (and hence the Earth's) orbital velocity about the galaxy is an order of magnitude greater than the Earth's orbital velocity about the Sun. The solar system is about 26,000 light years from the center of the galaxy. With an orbital period of about 2.25 million years, that corresponds to over 200 kilometers/second. The Earth's orbital velocity is about 30 kilometers/second.

This makes the Earth's acceleration about 10⁶ times bigger than the Sun's (w.r. to Galactic center). I imagine that the primary reason we see heliocentric depictions more often than geocentric ones is that the former is closer to an inertial frame. I'm not disputing the usefulness of non-inertial frames - I don't know about celestial mechanics - but I expect calculations in an inertial frame are more often easier than not.

 

[I don't know]

It is technically possible to create a system of laws and forces wherein the universe revolves around the Earth. The trouble is, the giant list of laws and forces that control the various complex motions rapidly grows with each new observation of the gyrations of the moons, planets and stars until the whole theory collapses under its own weight.

For example, it's very difficult to develop a mechanism to cause the naked eye planets such as Mars to temporarily move retrograde across the sky for a portion of their orbits. And that's just the mechanism; you still don't have a theory to explain why they would behave this way.

- I realized that a geocentric view would be insanely complex, but I didn't really appreciate the scale of the awkwardness before I saw this post :)

As for a theory - I guess the standard model will do okay?

 

[I don't know]

I'm no cosmologist, but I'd imagine that a frame attached to the Sun would be a much closer approximation to an inertial frame than one attached to the Earth (at least for the purpose of studying dynamics within the solar system), and inertial frames are extremely useful things.

- Looked at the wikipedia article on "inertial frame" and I think I get it (if I do, the second sentence in the first paragraph is kind of wrong and confusing: http://en.wikipedia.org/wiki/Inertial_frame) I guess that would be true about the gravitational center of whatever system you're talking about then?

What is a frame anyway, could it be defined as "a point we define as not moving" or should I be thinking of something more three dimensional? :)

 

[D H]

What is a frame anyway, could it be defined as "a point we define as not moving" or should I be thinking of something more three dimensional? :)

I am going to limit this discussion to Cartesian coordinates. A one dimensional reference frame gives us a way to assign a single coordinate to a point on a line. A two dimensional reference frame gives us a way to assign a pair of coordinates to a point on a plane. We live in a three dimensional world. A three dimensional reference frame gives us a way to assign a set of three coordinates to a point in space. To do this, we need a reference point (the origin of the frame) and a set of orthogonal, directed lines (the axes of the frame).

Suppose we have some reference frame. Shifting the origin or rotating the axes gives a different reference frame. Now suppose we have some object such as a planet or a spaceship. We can describe the position and orientation of the object relative to one of our reference frames. We can also establish a new reference frame based on that object itself. For example, the origin is the center of the object and the axes are some set of axes defined by the object. For example, the Earth can serve as a reference frame. The origin of this geocentric frame is the center of the Earth. If we define the axes to be fixed with respect to the Earth we get what is called a rotating reference frame. We can also define a reference frame based on a car moving along the Earth's surface. The center of the front fender is a well-defined point and can thus serve as the origin. Forward (i.e., along the centerline of the car), rightward, and down are well-defined orthogonal directions: our automotive axes. The car accelerates and turns. This is an accelerating (and rotating) reference frame.

Newton's laws do not hold in accelerating or rotating reference frames. Contrary to Newton's first law, objects that are not subject to any external forces do not have a constant velocity in an such "non-inertial" reference frame.

I guess that has to be it for now; my wife wants the computer to pay the bills.

 

[I don't know]

Thanks, I'm pretty sure I get it - it reminds me of some things in 2D and 3D graphics programs. Off topic, but I'm curious: why does it make a difference if the reference frame is rotating?

 

[Rainbow Child]

Thanks, I'm pretty sure I get it - it reminds me of some things in 2D and 3D graphics programs. Off topic, but I'm curious: why does it make a difference if the reference frame is rotating?

Imagine that the Earth isn't rotating. When you throw a stone vertically upwards then it will return at the same point from where it was initially.

But the Earth is rotating. So when you throw the stone it will hit the ground not at the initial point, because the Earth (and you) had moved during the stone's movement.

Thus in a rotating reference frame you have to consider additional forces to explain the motion of the stone. That' s the difference!

 

[Gokul43201]

So when you throw the stone it will hit the ground not at the initial point, because the Earth (and you) had moved during the stone's movement.

It's not just that the Earth has moved but that it has accelerated.

 

[Rainbow Child]

I was trying to keep it simple! After all since it is rotating, it is accerelating!
But you are right, I should be precise!

 

[dotman]

Getting back to the subject, I agree with astronuc and others in that a geocentric view of the solar system has been sucessfully refuted for some time.

I mean, I can do physics from the reference frame of the goose flying around the pond outside, but that doesn't make the Earth goose-centric. Because the sun is the dominant actor on the solar system stage, I think a heliocentric view is the only appropriate stance to take.