Einstein says objects do not fall to the Earth?

[Nick O]

Ah, I guess I had no idea what kind of output an accelerometer produces. I thought that 0 would also be the "rest" value, resulting in no net change when falling.

 

[harrylin]

According to this video, a bowling ball and a feather fall at the same rate because according to Einstein, they aren't falling:
[..]
The video actually said that Einstein's view was that no force was acting on the feather or on the ball.

I never saw Einstein make such a claim about gravitational fields. To the contrary, according to Einstein he was "struck by the fact that the force of gravitation possesses a fundamental property, which distinguishes it from electro-magnetic forces. [..] All bodies fall in a gravitational field with the same acceleration"
- https://en.wikisource.org/wiki/A_Brief_Outline_of_the_Development_of_the_Theory_of_Relativity

However, it is possible to describe the same observation in a different way, as others explained.

 

[rajeshmarndi]

Suppose two balls were "dropped" at the same time on opposite sides of the Earth. Which way would the Earth fall?

The answer given by

Let's assume for simplicity that the two balls have the same mass.

Using Newton's model, the forces between each ball and the Earth would be of equal magnitude and opposite direction, so the Earth would experience no net force and the balls would be drawn towards the Earth according to Newton's $F=ma$ by the forces acting on the balls.

Using Einstein's model, the geodesic paths of the two balls and the Earth would intersect. The curvature of spacetime bends the paths of the two balls towards the path of the earth. Eventually they collide.

I didn't get the above answer, when we say it is the Earth that moves towards the ball, the answer given above, is that the balls followed their curved path towards the earth.

 

[Nugatory]

I didn't get the above answer, when we say it is the Earth that moves towards the ball, the answer given above, is that the balls followed their curved path towards the earth.

You're right, I didn't word that very well. The two balls travel along geodesics in curved spacetime; the curvature of spacetime means that these straight lines will eventually intersect the equally straight line followed by the center of the earth.

 

[stevendaryl]

Suppose two balls were "dropped" at the same time on opposite sides of the Earth. Which way would the Earth fall?

There is a sense in which it is correct to say that the surface of the Earth is accelerating upward: there is an upward force on the surface of the Earth, and this force causes the surface to accelerate upward relative to a freefall path (or geodesic). All parts of the Earth are accelerating upward, in this sense (I wouldn't call it "falling" upward, falling means traveling in the absence of any forces holding you up, and that is not the case with the surface of the Earth; the surface of the Earth is held up by contact forces from the rocks below). This notion of acceleration, relative to a geodesic, or freefall path, is local, so different spots on the Earth are accelerating in different directions.

How is it possible for opposite sides of the Earth to be accelerating in different directions, without the Earth expanding? I think it's helpful to think of a lower-dimensional analog. Think of spacetime as the surface of a globe, and think of the time axis as being measured North-South, while spatial distances are measured East-West. Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

 

[LitleBang]

Interesting how people can be experts about gravity without being able to tell us the mechanism of gravity.

 

[LitleBang]

In my opinion when he said they were not falling he meant that in their frame of reference the Earth was moving toward them.

 

[stevendaryl]

Interesting how people can be experts about gravity without being able to tell us the mechanism of gravity.

Well, you have to think about what it means to understand the "mechanism" behind some physical phenomenon. It usually (if not always) means to explain the phenomenon in terms of more basic phenomena. So we explain chemical reactions in terms of interactions of molecules, and explain molecules in terms of interactions of atoms, and explain atoms in terms of interactions of electrons, protons and neutrons, and explain protons and neutrons in terms of interactions of quarks. But at some point, you've gotten down to as basic a level as you know. At that point, giving "mechanisms" has to stop.

General Relativity views curved spacetime as the most basic level of describing gravity. There is no mechanism more basic, at least not until we develop a quantum theory of gravity.

 

[inertiaforce]

In my opinion when he said they were not falling he meant that in their frame of reference the Earth was moving toward them.

Agreed. My understanding of GR is that since there is no absolute state of rest or absolute state of motion, it is therefore just as valid to say that the Earth is moving toward an object as it is to say that an object is moving toward the earth. Both frames of reference are equally valid. Motion and rest are relative. There is no absolute state of motion or absolute state of rest. Therefore, it is apparently just as valid to say that the Earth is moving toward the ball and feather as it is to say that the ball and feather are moving toward the earth. Therefore, if it is just as valid to say that the Earth is moving toward the ball and feather, then that means that the Earth would run into the ball and feather at the same time, which is what we saw in the experiment when the ball and feather hit the ground at the same time. The whole point of relative motion is that you can't tell who's moving. That's why relativity says that everything is "relative" to the observer. There is no absolute frame of reference to tell who's moving and who's at rest. You can't distinguish between rest and motion.

 

[LitleBang]

General Relativity views curved spacetime as the most

So if a quantum theory of gravity doesn't happen should we look for some other method or just throw up our hands?

 

[stevendaryl]

So if a quantum theory of gravity doesn't happen should we look for some other method or just throw up our hands?

Some other method of doing what? General Relativity provides a description of gravity as curved spacetime. There is no need for a "mechanism" beyond that, except to take into account phenomena that are not described by General Relativity.

"Discovering a mechanism" amounts to explaining one theory in terms of a second theory. There's no point in doing that, unless the second theory is more complete than the first--describes more phenomena, and is more general.

 

[A.T.]

I didn't get the above answer, when we say it is the Earth that moves towards the ball, the answer given above, is that the balls followed their curved path towards the earth.

1) Movement is relative. The Earth's surface moves in the frame of the ball.

2) Proper acceleration is absolute. But proper acceleration away from the center doesn't imply movement away from the center. See the green apple hanging on the branch at 0:40 in the below animation. It must accelerate upwards just to stay at constant height, like the Earth's surface.

How is it possible for opposite sides of the Earth to be accelerating in different directions, without the Earth expanding? I think it's helpful to think of a lower-dimensional analog. Think of spacetime as the surface of a globe, and think of the time axis as being measured North-South, while spatial distances are measured East-West. Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

That is a good analogy. Here is a visualization for both sides of the planet and the inside:
http://www.adamtoons.de/physics/gravitation.swf

 

[inertiaforce]

Guys, watch this video from 12:00 to 12:46. Now imagine this explanation from the frame of reference of the ball and feather. From the ball and feather's point of view, could it be said that there is a gravitational field causing the Earth to be accelerated in their direction?

Here is the video:

 

[A.T.]

Guys, watch this video from 12:00 to 12:46.

This video shows the effect of acceleration in flat space time, far from gravity sources. What they call "gravity" is a inertial force in an accelerated frame.

Now imagine this explanation from the frame of reference of the ball and feather. From the ball and feather's point of view, could it be said that there is a gravitational field causing the Earth to be accelerated in their direction?

No. That is an inertial frame, so there is no inertial force there. The Earth surface accelerates in their direction, because of the EM-repulsion from below, which is a real force, that causes proper acceleration.

But in the non-inertial frame of the surface, there is an inertial force that accelerates the ball and feather down. Inertial forces and curve-linear coordinates like in the video in post #47 are two different way to describe non-inertial frames.

 

[stevendaryl]

Guys, watch this video from 12:00 to 12:46. Now imagine this explanation from the frame of reference of the ball and feather. From the ball and feather's point of view, could it be said that there is a gravitational field causing the Earth to be accelerated in their direction?

No. In the frame in which the ball and feather are at rest, it is true that the ground is rushing upward, but it's not rushing upward because of gravity.

Think of the ball and feather falling toward a platform, and this platform is hovering above the ground by using rockets. Then from the frame in which the ball and feather are at rest, the platform is rushing upward using rocket power.

If the platform is resting on the ground, then the platform is being held up by contact forces. Gravity isn't holding it up.

 

[inertiaforce]

Ok thanks. My mistake lol.

 

[rajeshmarndi]

Now I understand, If I'm right ,that opposites ball when released hit the Earth surface at the same time because the curve path of the balls and that of the Earth collide at the same time, as time move on.

How is it possible for opposite sides of the Earth to be accelerating in different directions, without the Earth expanding?

Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

I didn't understand "It requires a force to keep the two objects 10 meters apart as they move North." How does this correspondence to acceleration of Earth surface in different direction.

What is the source of Earth acceleration in all direction. I can think as Earth revolves around sun at constant velocity experience acceleration as it changes direction continuously. Also the Earth rotation on its axis.

 

[stevendaryl]

I didn't understand "It requires a force to keep the two objects 10 meters apart as they move North." How does this correspondence to acceleration of Earth surface in different direction.

Once again, picture two objects both moving straight north, starting at the equator. Do you see that the distance between them shrinks as they move North? To keep the distance between them from shrinking, you have to have a force pushing them apart. That force pushes one object to the west, and it pushes the other object to the east.

An analogous thing is happening to two points on the opposite sides of the Earth. It requires a force to keep those two points from getting closer together. The force has to keep the two points apart.

What is the source of Earth acceleration in all direction.

Pressure. The material that the Earth is made out of is under pressure, and that pressure exerts an outward force on all points on the surface of the Earth.

 

[Nugatory]

Interesting how people can be experts about gravity without being able to tell us the mechanism of gravity.

That's true about just about all of science; the same criticism can be levied at just about all of classical mechanics: We know that like charges repel and unlike charges attract, and we can describe the forces using Coulomb's law $F=Cq_1q_2/r^2$ but that's a description not an explanation of mechanism.

 

[rajeshmarndi]

Pressure. The material that the Earth is made out of is under pressure, and that pressure exerts an outward force on all points on the surface of the Earth.

What is the term referred to the above phenomenon.

So, the pressure of the material, which actually causes experiences of the weight?
But we studied, we feel weight because of Earth gravity. It seems gravity and weight are two different thing.

I understand due to gravity or due to curvature of space, as each points on Earth follow this curved path, they build internal pressure, which exert on our body and we feel it as weight.

But as commonly understand, our body is pulled to the Earth surface and it exert pressure on the surface, in return the surface exert equal opposite force on us.

 

[georgir]

Weight is still the same thing as in the classical explanation - the force which an object exerts on its support, equal and opposite to the "normal force". But you are right that in GR the "normal" comes first, as a result of the support's "pressure" or more generally just its tendency to keep a fixed distance from the Earth's center (or from the definition of "fixed support"), and that weight is then just its equal and opposite counter force.

Edit:
As to "What is the term referred to the above phenomenon.", can you say which phenomenon that is? Do you mean why the earth, or anybody for that matter, does not collapse under its own gravity? I guess the term would be "rigidity", until we move to the surface of a gas giant ;)

 

[rajeshmarndi]

As to "What is the term referred to the above phenomenon.", can you say which phenomenon that is?

stevendaryl said: ↑
"Pressure. The material that the Earth is made out of is under pressure, and that pressure exerts an outward force on all points on the surface of the Earth."

The above statement, where it says, "...The material that the Earth is made out of is under pressure..."

 

[stevendaryl]

What is the term referred to the above phenomenon.

So, the pressure of the material, which actually causes experiences of the weight?

Yes, you don't actually feel gravity when you stand on the ground. You feel the force of the ground pushing up against your feet.

But we studied, we feel weight because of Earth gravity. It seems gravity and weight are two different thing.

You can't feel gravity. If you were falling, you wouldn't feel any different than if you were floating in space (well, except for the air rushing past you). The only time you feel weight is when you are being prevented from falling, by the ground (or whatever is holding you up). As I said, what you feel as weight is an upward force preventing you from falling.

I understand due to gravity or due to curvature of space, as each points on Earth follow this curved path, they build internal pressure, which exert on our body and we feel it as weight.

But as commonly understand, our body is pulled to the Earth surface and it exert pressure on the surface, in return the surface exert equal opposite force on us.

Yes, that's the way that Newton viewed gravity.

 

[Wes Tausend]

According to this video, a bowling ball and a feather fall at the same rate because according to Einstein, they aren't falling:

https://testtube.com/dnews/which-falls-faster-a-feather-or-a-bowling-ball/?utm_source=FB&utm_medium=DNews&utm_campaign=DNewsSocial

What does this mean exactly? The Earth comes up to the ball and the feather?

Suppose two balls were "dropped" at the same time on opposite sides of the Earth. Which way would the Earth fall?

Since Newton came up short, gravity never attracts and nothing accelerates in a fall anymore. It just looks like it does. It's all because of Einsteins wonderful Equivalence principle, of which he used to look at gravity from a different perspective in a unique coordinate system.

Many years ago I developed a thought experiment that allows me to see how a rendition of the Equivalence principle works. Perhaps it will help others. A good thought experiment is even better than youtube, and is all we had back then anyway.

The trick is to temporarily imagine Earth expanding as stevendaryl briefly mentioned earlier. In this imaginary case, the surface of an enlarging model Earth rises to meet the surfaces of the bowling ball and feather "simultaneously".

The easiest way to visualize this comprehensive thought experiment is to imagine we have a large, sealed bell jar that we may began to evacuate of air. The internal experiment must also take place in a gravity-free area of space, or free-fall (the same thing).

In this bell jar we place several soap bubbles. For PeroK's 2-ball thought experiment, somewhat towards the center, we place a large soap bubble we will call earth. Above(?) it we place a smaller bubble we call ball 1. Below "earth" we place another similar sized small bubble we call ball 2. Now we began to evacuate the chamber by opening a valve that is hose-connected to an indefinitely large tank that already contains a near vacuum. We have a well equipped lab. When the air leaves the chamber, the Earth body and two smaller balls will all began to enlarge, or swell, because the air pressure on the outside of the bubbles reduces. If we keep opening the valve further all the time, the bubble expansion will accelerate. If we open the valve slightly, then leave the setting, the expansion will only represent an undetectable steady inertial movement. We will choose the former for our acceleration experiment.

Now imagine the bubbles want to maintain their center-to-center distances, i.e. remain at rest. In this case the surface of the large Earth bubble will expand into the space that the surfaces of the smaller bubbles also wish to expand and occupy. The surface of model Earth will rise to hit the balls at the same time the swelling balls have a small "enlargement gravity" of their own. This is classic Equivalence principle. There is a catch, but I won't say for now and chance breaking this Lawrence Welk spell.

For inertiaforce's thought experiment, one can carry the thought experiment a bit further and imagine that beside one of the other normal balls (ball 1) there is a tiny bubble. This delicate little guy can be the feather. If the surfaces of the feather and ball 1 are equally distant from the surface of earth, they will strike Earth simultaneously (or Earth will strike them). Now it is important that both small bubble surfaces, not the centers, be equi-distant from the surface of earth. Otherwise one can imagine that the larger "heavy" ball has a head start to make contact. The ball and the feather also do one other thing that is remarkably like gravity. They both seem to "fall" towards Earth's center and towards one another at the same time. If the ball and feather are in close proximity compared to their relative distance from earth, they may even make "swelling" contact before contacting the surface of our model earth. Besides "falling" towards the center of model earth, they also seem to move closer together on their own, which is in keeping with properties of all material objects, which of course have a small amount of gravity of their own. Ignoring ball 2, these three bodies seek not the center of earth, but a common center.

One other Equivalence thought coincidence, that is remarkable, results when we place a special small bubble on the surface of our Earth bubble. This precious bubble can be our human observer. This flat-footed human bubble must enlarge in our vacuum chamber also. So the relative comparative size of this "human" and that of model Earth never change, ala Poincaré. We could even grant him/her a bubble for a yardstick, but our oblivious human observer still has no way to measure that he/she is part of a slow bang process. But yet the human bubble experiences a mysterious acceleration that he/she interprets as gravity. As we, the real humans, safely watch the chamber from our assigned privilaged rest outside our little bell-jar universe model, we will see that as the model Earth bubble expands, the small human bubble actually squashes a bit as he/she rides the accelerating surface of the Earth bubble. This equivalent compression is so true in our real world, over many years I have permanently become nearly an inch shorter from the perpetual stress of standing, and I, like all of us, am always longer when I lie down.

And that is my shortest condensed rendition of the Equivalence principle. I think Poincaré would have particularily liked it.

P.S.
Earlier I mentioned a catch to this ancient thought experiment though. If we really evacuated a chamber, the air between the bubbles would expand also. That means the bubbles would be drawn apart in expanding space and perhaps never make contact. It seemed a story spoiler to openly mention this too soon. I'm sorry if it nagged at some of you throughout.

Wes
...

 

[A.T.]

The trick is to temporarily imagine Earth expanding as stevendaryl briefly mentioned earlier.

Stevendaryl said nothing about the "Earth expanding", which is exactly the wrong way to explain this, and leads people to conclude that GR is a bunch of nonsense.

He says that the surface accelerates away from the center. But that doesn't imply movement away from the center (expansion). He also gives a much better analogy:

Think of spacetime as the surface of a globe, and think of the time axis as being measured North-South, while spatial distances are measured East-West. Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

 

[PeroK]

Here's a thought experiment:

We take two balls at a large distance apart in space. They are at rest. So, we have a rest frame.

We introduce the Earth close to one ball (the second ball is so far that the Earth's gravity is negligible).

If the Earth moved to the first ball, then that ball would remain at rest in the inertial frame we have established.

But, in this inertial frame, the first ball would move to the Earth.

We could also establish an inertial frame in which the Earth is at rest and then bring a ball near the Earth. The Earth would effectively remain at rest.

Isn't it obvious that the Earth has a massive influence (whatever your theory of gravitation) on a ball; whereas, the ball has almost no influence on the Earth?

 

[Wes Tausend]

Stevendaryl said nothing about the "Earth expanding", which is exactly the wrong way to explain this, and leads people to conclude that GR is a bunch of nonsense.

He says that the surface accelerates away from the center. But that doesn't imply movement away from the center (expansion). He also gives a much better analogy:

I agree Stevendaryl does a good job explaining an aspect of gravity.

I think you have the wrong post from Stevendaryl. I quote the one that I referenced below.

There is a sense in which it is correct to say that the surface of the Earth is accelerating upward: there is an upward force on the surface of the Earth, and this force causes the surface to accelerate upward relative to a freefall path (or geodesic). All parts of the Earth are accelerating upward, in this sense (I wouldn't call it "falling" upward, falling means traveling in the absence of any forces holding you up, and that is not the case with the surface of the Earth; the surface of the Earth is held up by contact forces from the rocks below). This notion of acceleration, relative to a geodesic, or freefall path, is local, so different spots on the Earth are accelerating in different directions.

How is it possible for opposite sides of the Earth to be accelerating in different directions, without the Earth expanding? I think it's helpful to think of a lower-dimensional analog. Think of spacetime as the surface of a globe, and think of the time axis as being measured North-South, while spatial distances are measured East-West. Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

Stevendaryl was clear that Earth is not expanding and is trying to avoid a scenario where it could be. I merely pointed out why it is a good thought experiment to think of it temporarily that way. I think most people know the difference beween reality and a thought experiment, so no one need be "mislead", or think GR non-sense. The bubble thought experiment, if carried to conclusion will stall.

Otherwise the bubble expansion idea is a very, very good approximatization of exactly how the Equivalence principle works, a valuable tool and I'm surprised and hurt you can't see that. It is very similar to Einsteins rendition of a "chest drawn up by a cable", along the lines of Poincaré's thoughts, and can be carried far further than I did. On the other hand, If there is some serious flaw to the chest or bubble equivalence idea, I need to hear it.

Wes
...

 

[A.T.]

...inertial frame ... whatever your theory of gravitation...

But the definition of inertial frame depends on which theory of gravitation you use. In GR "inertial frames" are just local approximations and there are no valid global inertial frames, when gravity sources are around.

...then that ball would remain at rest in the inertial frame we have established...

In GR the free falling ball does remain at rest in an local inertial frame, and so does the center of the Earth.

 

[A.T.]

I think most people know the difference beween reality and a thought experiment, so no one need be "mislead", or think GR non-sense.

Unfortunately I have seen many concluding that GR is nonsense after being exposed to such non-sequitur explanations, and I cannot even blame them. We know the Earth doesn't expand, so assuming that it does explains nothing.

 

[PeterDonis]

If the Earth moved to the first ball, then that ball would remain at rest in the inertial frame we have established.

No, it wouldn't. Moving the Earth close to the first ball curves spacetime, so the "inertial frame" you established is no longer a valid inertial frame.

We could also establish an inertial frame in which the Earth is at rest

No, you can't. There is no valid inertial frame that covers the entire Earth. The best you can do is construct a local inertial frame at the center of the Earth, but this frame will only cover a small region around the center; it will certainly not extend all the way to the surface and beyond.

You could also construct a local inertial frame in which the surface of the Earth at a particular point (say, just beneath a ball that is falling) was momentarily at rest. But the "momentarily" is crucial: the surface of the Earth will not stay at rest in such a frame. It will accelerate upward, while the falling ball will move at a constant speed. So again, there is no inertial frame in which the surface of the Earth at any point is at rest (for more than a single instant).

 

[PeroK]

But the definition of inertial frame depends on which theory of gravitation you use. In GR "inertial frames" are just local approximations and there are no valid global inertial frames, when gravity sources are around.

In GR the free falling ball does remain at rest in an local inertial frame, and so does the center of the Earth.

Thanks for this explanation. I'm still teaching myself SR and I haven't taken the leap to GR yet. But, it seems odd that one can't take an experimental view of what is happening from outside the system. E.g. from outside the solar system, from my naive perspective, one should be able experimentally to conclude that the Earth orbits the sun and not vice versa.

Kepler was a pure observationist for example. He had no knowledge of Newton's or Einstein's or any theory of gravity. He concluded by observation alone that the planets orbited the sun. That might be theoretically invalid from the GR perspective. But, how can it be observationally or experimentally invalid? If that is what you are saying. "And yet it moves"!

 

[PeterDonis]

from my naive perspective, one should be able experimentally to conclude that the Earth orbits the sun and not vice versa.

More precisely, the solar system, to a very good approximation, can be described as an isolated system of matter surrounded by empty space, with a definite center of mass, and that the object whose trajectory is closest by far to the trajectory of that center of mass is the Sun. We describe this informally as the planets orbiting the Sun (though a more precise description would be that the planets and the Sun all orbit their common center of mass).

But to say that the Earth orbits the Sun "and not vice versa" is to assert a preference for a certain system of coordinates (one centered on the Sun--or on the common center of mass), which is not, in principle, valid. Certain coordinates may be more useful than others, because the description of the solar system looks a lot simpler in terms of them, but that doesn't make other coordinates invalid; it just makes them less useful for certain purposes--but not for others. Try describing your route to the grocery store, or the path of an airplane flying from New York to London--or even the trajectories of the Apollo missions to and from the Moon--using coordinates centered on the Sun. In Earth-centered coordinates, the Sun does "orbit" the Earth; even our common language still says the Sun "rises" and "sets", instead of that the Earth turns to make the Sun visible or not visible from our location. Different coordinates are useful for different purposes.

He concluded by observation alone that the planets orbited the sun.

Actually, he concluded by observation alone that a description of the solar system that had the planets orbiting the Sun was a simpler way to account for the data. So he was really just discovering what I said above, that the physics of the planets and the Sun looks simpler in coordinates centered on the Sun (or, more precisely, on the solar system's center of mass).

 

[Wes Tausend]

Unfortunately I have seen many concluding that GR is nonsense after being exposed to such non-sequitur explanations, and I cannot even blame them. We know the Earth doesn't expand, so assuming that it does explains nothing.

Then you know more than Poincaré. He wasn't so absolutely sure we would be able to know. Poincaré eventually came within an inch of solving SR before Einstein and I admire him too.

If it makes you more comfortable, we could easily assume Earth does not expand for the explanation and that would be very conventional and along the lines of how Einstein personally developed the relativities. In GR he basically assumed that the vacuum of space was "vacuumed in" (curved) by the resting firmament of steady state matter. To explain thusly, one can nearly imagine the particles, the field lines, of nothingness being vacuumed by earth, very much faster as nothingness approaches the vortex ever closer. And that stretching vortex, causing a far reaching drift of nothingness towards earth, thereby drawing the moon close and keeping it in orbit, corraled in an invisible funnel cloud. Or a meteor rolling right over the edge straight on. Pretty much like the bowling ball stretching the blanket close to large mass. :)

Wes
...

 

[A.T.]

Pretty much like the bowling ball stretching the blanket close to large mass.

From bad analogy to the worst analogy.

 

[PeroK]

More precisely, the solar system, to a very good approximation, can be described as an isolated system of matter surrounded by empty space, with a definite center of mass, and that the object whose trajectory is closest by far to the trajectory of that center of mass is the Sun. We describe this informally as the planets orbiting the Sun (though a more precise description would be that the planets and the Sun all orbit their common center of mass). ...

I understand all your arguments about being free to choose any coordinate system. If you are saying: whatever the theory, whatever the experiment, you can always choose whatever coordinate system you like, then I'd agree with that.

I was trying to argue that, experimentally, you could show that the Earth has a bigger influence on the "motion" of a ball than the ball has on the Earth. And that the sun has a bigger influence on the motion of the planets than the Earth does (take the Earth out of the Solar system and would Jupiter even notice?). Yes, there would be a perturbation, but not much more I imagine.

It seems strange to say: it's equally valid to view the Sun as orbiting the Earth and Mars orbiting the Sun. But, then, why does a massive object in one case orbit the small object, but in the other case the smaller object orbits the larger one. I can't see a theoretical explanation for that.

Maybe this way of thinking has no scientific value. But, anyway, here's my question:

If the Sun is orbiting the Earth and Mars is orbitting the Sun, how do you explain that using classical physics? Without resorting to a model whereby both planets are "actually" orbitting the Sun? In order to explain this, you have to put the Sun at the centre, I thought?