Technically, Earth Does Not Orbit Around the Sun (2014) 256 points by gojomo on June 15, 2019 | hide | past | favorite | 200 comments

 The center of gravitation is also just a simplification, or how scientists call it: "a model". Actually everything gravitates around everything else, as the article also explains.Models, or simplifications, aren't bad though. Because what value can you get out of "everything gravitates around everything else"? Not much. But if you use a model, you can use the model to explain what happened in the past and use it to make an approximated assumption about the future. You can use it to guide decisions, and you can use it to focus on more details in other areas. E.g. if you don't use the actual trajectory of everything but a model, you can still calculate where Mars will be when you reach it if you start right now from point X on Earth. Of course the center of Mars will not be at exactly the same point, but it will be a good enough approximation that you can start planning resources required to get there, and it can help you decide if "now" and point X are good inputs to that travel plan.Models are a good, helpful tool. They are just not explaining everything, and that on purpose, and as a human we always need to be aware of that models are just models and not reality.
 > Because what value can you get out of "everything gravitates around everything else"?Expensive numerical simulations!
 Simulations with numbers are also models. You can make them indefinitely more complex and still have a model that is only an approximation of reality.
 > In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.
 I would say, rather, that models are not approximations of reality, but descriptions of it.
 Just like the maps are not the territory, but like maps, models/descriptions can become out of date.
 Nope. You can use them to make predictions, but they are not in themselves predictions.
 Or semi-esotheric bestsellers!
 Indeed. As I learned from a link posted to HN the other day, apparently there is a name for this tension between the accuracy and comprehensibility of models: Bonini's paradox.
 > Models are a good, helpful tool. They are just not explaining everything, and that on purpose, and as a human we always need to be aware of that models are just models and not reality.Do we have anything else but models?
 It is repeated in all these super-pedantic threads. All models are wrong. Some models are useful.
 > Actually everything gravitates around everything else, as the article also explains.What helped me understand it the most was an answer to this question:"Where does the Solar System end""When the dominant gravitational influence is not the Sun"it seems like it is always a loaded question because it is relative to the body being talked about and not its own moons, but it really just comes down to gravitational influence.
 Let’s say all the planets’ orbits decayed and ultimately spiraled into the sun. Wouldn’t that be a possible end to the solar system? I mean it’s just be a sun at that point. But I think the Sun would still be the dominant gravitation force.
 Would require all asteroids, debris and everything in the ort cloud to be in it too, which would be impossible.But honestly not sure what semantic nuance you are playing devil’s advocate on
 I was actually surprised that if all the planets were lined up, the center of mass would be outside the surface of the Sun. I had always assumed that the Sun was so massive that the center of mass was almost fixed and certainly always within its surface. I guess I hadn't factored in the fact that the planets are so far away and the Sun so small that their masses could have such large measurable outcomes on the center of mass of the system.
 Well, 'the Sun so small' is a phrase I have never seen before.
 No? Never saw videos like this one? https://youtu.be/i93Z7zljQ7I
 There is always something bigger, isn’t it...
 Well it is outside the surface right now, no need to imagine all planets being perfectly lined up.
 I wonder wether this center of mass moving around in the sun, is producing - time delayed of course- the "sun-weather" aka, the dark spots and solarflares..Something else:Technical the orbit, is a spiral of the whole system around the center of mass, slightly deteriorated by remainders of old interactions.Which got me thinking, if you run a astronomical simulation backwards- can you computate old interactions and "gone" missing bodys from that? Use celestial motion as a sort of archive-trail to go back along?
 This idea about solar weather affected by the planets was just in the news
 Thank you for sharing. The link within the article about Rossby waves was also very interesting!
 I've had very similar thoughts concerning coronal hole locations on the suns surface. I've also wondered too if the 11 year sunspot cycle is related to a dark mass orbiting the sun, or the solar polar field alignment that flip flops a regular intervals.I'd suggest lurking around the stream of thought and materials coming from Ben Davidson and the Suspicious Observers community if this interests you.
 Or Jupiter. Its year is 11.9 Earth years.
 I think our ability to look backwards is limited by the precision of our instruments and the precision of floating point computation.Any error in our measurements would be magnified as we look backwards to the point that the simulation would at some point significantly diverge from reality, I wonder how many years back you can look before that happens?Also floating point error would compound on top of that.
 Typically the error due to your numerical integrator that runs Newtons law backward in time (or forward for predictions) is larger than the floating point error after a few time steps and it is not uncommon to run for millions of time steps. This is not just true for the trivial but terrible Euler integrator, but also for high-order symplectic integrators. I know that my office mate has run simulations of planet systems with different codes and they tend to diverge at around 100 million years. They still look like the same system, but orbital phases disagree.The uncertainty in the orbital elements (current orbital position and velocities) from which you start is not a major problem as long as all bodies are well separated. But our model would for example completely miss the body that crashed into the young Earth and left us with a moon.
 Floating point error is far far smaller than measurement error and missing data.
 Is there a reason you couldn't use whole numbers in place of decimals?
 The problem still exists. It's less so specific to floating point numbers and more so a product of the limited number of states any data type can hold. Integers and floating point numbers are both still 64 bit on most modern computers, unless you are using big-int structures which are much more computationally intensive.
 Granted, I'm no mathematician, but...If we have a limit of 2^64 for \$x, can't we set \$y = representive of multiples of \$x's upper limit?\$y = 5 = 5x2^64What's the reason for not being able to sub-divide numbers and operations into smaller, more manageable forms?
 Eh, was that rule not circumvented with conway? You can compress more data into a given numeric format, by moving the complexity into rule systems- aka determinstic games? Like a big number of chess games, or a group of possible games growing from just a sequence of letters and numbers.The tradeoff for this limited space is though a complex ruleset and to recreate the data, lots of computation.
 I'm no physicist, but isn't the 3-body problem relevant here too?
 Only in the sense that you couldn’t directly compute the locations at arbitrary points in time given current positions and velocities.The three body problem doesn’t stop you from running a simulation and getting the correct answer.
 I think the point was that n-body systems with n>2 are chaotic, such that very small differences in starting position lead to massive differences as time unfolds.Wouldn't this make it very difficult to do the highly precise detective work needed to find alleged former solar system bodies? Or are simulations accurate enough these days?
 Not an expert, but I think n>2 means that chaotic behavior is possible, but not inevitable. Consider an isolated sun-earth-moon system, that doesn't appear to be chaotic. Simulating a "3-earth" system would, AFAIK, usually be chaotic.I'd be happy to be corrected, of course.
 That sounds correct. I would guess that systems like that can be approximated fairly accurately as nested 2-body problems.
 Couldnt you make a backwards scenario filter, that kills simulations that run against evidence? Like - if this planet ceases to be, or that condition is not fullfilled, you are history.
 In college I took a great "Philosophy of Physics" class, where on the first day the professor asked everyone to write one page on whether the Earth revolves around the sun, and the final project was another paper on the same topic, so we could see how nuanced a question it was and how our views had evolved over the course.With that said, I don't think there's any valid answer besides "you can define your terms and points of reference such that it does or doesn't; there's no particular physical reality to the matter".
 An interesting tangent: At the time of Gallielo, the church used the Tychonian model of the solar system.In the Tychonian model, the earth is the center and the sun revolves around the earth. But the other planets revolve around the sun! You will notice this is practicallty the same model as the Copernican model except for the arbitrary definition of what is "the center".The only observable difference was the relation to the firmament which in the Tychonian model revolved around the earth but in the Copernican revolves around the sun. If the Copernican model was correct, some parallax to the stars should be observable. Now we know this is not observable due to the distance to the stars, but this was not known at the time.
 It's not arbitrary. The only two choices that work are the real center of gravity, and the observer's position with the real center of gravity orbiting the observer and everything else orbiting the real center of gravity. If Tycho chose Jupiter as the center of the orbits, the planetary orbits would have the same problem of epicycles as the older models.
 You can claim that any arbitrary point is "the center of the universe" if you acknowledge that the planets rotate around the sun, not around the designated "center". If you choose Jupiter as the "center", there would still be no observable difference and you wouldn't need additional epicycles.
 What precisely do you mean by “the same problem with epicycles”? You can fix Jupiter at the origin. You use exactly the same equations, except that the sun is using the equation that used to describe Jupiter (with an extra negative sign) and the other planets add in the term describing the Sun’s motion.Earth is no different than any other planet (or other celestial body in a stable orbit relative to the solar system) in this respect. Hell, you could make the Moon the center of the solar system - the math works just fine.
 If observer is on the Earth then equations for Jupiter will not work for describing the apparent motion of the planets.
 this isn't entirely true. At the time of Galileo, Tycho was presenting his model (and was a militant enemy of Galileo). Tycho's model was either used or not depending on more local scientific stances, but it wasn't entirely popular.
 An interesting read is On the Revolutions of Heavenly Bodies by Copernicus, even if you just read the introduction. It’s an appeal to the Pope regarding the scientific nature of his conclusions. Regardless, they still excommunicated him years later for going against what was thought the authority of scripture.
 He was never excommunicated as far as I know, and the book was only published after his death. The church did suppress the book though.
 >An interesting read is On the Revolutions of Heavenly Bodies by Copernicus, even if you just read the introduction. It’s an appeal to the Pope regarding the scientific nature of his conclusions. Regardless, they still excommunicated him years later for going against what was thought the authority of scripture.This... is completely false. Copernicus never faced adversity for his heliocentric model.
 Thanks - I was confusing the stories of Copernicus and Galileo. Galileo’s works, based on Copernicus’s ideas, were declared heretical. While not excommunicated he was persecuted by the church.
 no, Copernicus was never excommunicated, although "On the Revolutions of Heavenly bodies" went through various stages of requiring errata pointing out it was only a hypothesis and even a ban
 Claiming that "there's no particular physical reality to the matter" I don't understand at all. I can make sense of that to a limited degree as a variation on the saying "all models are wrong..", but you seem to have extended that to say that there is no 'right' possible (ie the 2nd part of that saying, that "...but some models are useful").A naive reading of what you said suggests eg. no spaceflight is possible because no astronomical (or any...) calculation is reliable. Can you clarify?
 What I mean is, if two people disagree about whether the Earth orbits the sun, there aren't any experiments where we'd expect them to predict different results. They're both describing the same physical reality, viewed from different frames of reference.It's analogous to talking about someone throwing a ball on a train. A person on the train can say the ball moves relative to the train, and someone outside can say the ball and train are both moving relative to the Earth, and a guy in a spaceship can say that all three are actually moving relative to the sun. But choosing one of those claims over the others is purely a matter of convenience or perspective, not of physical reality.
 IIRC objects experiencing acceleration (e.g. planets orbiting each other) are not subject to Galilean relativity like objects that are moving at a constant velocity (e.g. ball being thrown on a train). So when planets orbit each other, there is only a singe valid frame of reference.
 The disagreement can exist because "orbits" is left under-defined. If you say A orbits B if A makes circles around B and B creates a bigger gravity field, then everyone will agree; they'll also agree on the fact if both objects have roughly equal masses, then it is true to say that both A orbits B and B orbits A.
 But that is not what "there is no physical reality to the matter" means, if one chooses not to use any relative point there is still an objective distance between each object with respect to every other object and accelerations for each of those distances.
 "The matter" in that quote is the matter of whether the Earth orbits the sun or vice versa. Naturally there's observable physical reality to distances and whatnot, but if you use the laws of physics to make predictions about those observables, the math works regardless of which body you assume the others revolve around.
 You might find Bertrand paradox interesting regarding this aspect.
 While I think the connection with what GP wanted to convey is tenuous, Betrands paradox _is_ interesting, and even more so E.T. Jaynes' solution.As with most paradoxes, it's about how a seemingly innocuous question turns out to either be underspecified to have an answer, or tricks even the mind of mathematicians to assume too much.Here it's about what it means to have a "random chord of a circle"; several simple ways to generate random chords lead to very different results, but true randomness should not be easy distinguishable from other true randomness...E.T.J's solution to invoke the maximum ignorance principle to require any source of random chords to be size- and translation-invariant (because those dimensions are not specified in the problem) seems elegant.Now, comparing to orbits, or to balls on a train, the thing here is: all these different viewpoints, although very different, do lead to the same result. Even if you calculate stuff; and if I'm not mistaken, that's because of relativity (Galilean relativity should be sufficient for the train example to work, the more modern ones for the rest).
 What they mean is that you may take whatever point in space to be your immobile frame of reference and describe all motion with respect to that point. It happens to be convenient to take the center of the Sun as such a point when doing calculations relevant to the solar system but it's not more 'valid' than literally any other point in the universe. You just have to change the equations a bit.
 No, they actually dispute the „physical reality“ which is completely wrong: the actual words:“there's no particular physical reality to the matter”
 No, they said "there is no physical reality to the matter", where, judging by context, "the matter" is the question of whether the Earth revolves around the Sun.The conclusion that there is no physical reality to this is based on the what @aluren mentioned - you can take any immutable point of reference and describe the movements of the others from it using the same laws of physics, thus "the matter" becomes one of philosophy and choice of point of reference rather than physics itself.You may disagree with this point but I don't think anyone disputed the existence of a physical reality, they simply moved one particular question out of its domain.
 Changing the point of reference will change your mathematical model, sure, but it will still describe a movement around a barycenter, and the statement remains true whatever your philosophy. Numerous ways to model a phenomenon don't deny its existence.
 Again: not denying the existence of the phenomenon, only removing it from the realm of physical reality to that of philosophy and mathematical point of reference.Still very much existent.
 The laws of motion are the same in every reference frame, which means that statements like "X revolves around Y and not vice versa" are not "physically real" in the same way as "X and Y attract each other gravitationally" is, because they select one reference frame as privileged.
 > The laws of motion are the same in every reference frameInertial reference frame, right? Otherwise you need to add in fictitious forces.
 Rotation is different from motion.Rotating around a point still applies in any frame of reference. Spin a top and the axes of rotation is independent of your frame of reference. Pick an atom on that top and it’s rotating around a specific point in any frame of reference.
 This goes back to the ambiguity of the definition of orbit. If I have a system with two points involved in some sort of rotational motion, then there isn't a "best choice" for which point should be considered the origin of my coordinate system.
 If you mean exactly 2 abstract points in Euclidean geometry then sure. 3D objects are not points which is the first issue. Relatively also cares about accelerating or rotating reference frames which applies to both point masses.The center of mass in a two body system is a nice inertial reference frame which simplifies calculations.
 The "physical reality" of describing motion is transformations relative to a frame of reference. The origin (eg where you put 0,0,0) of that frame is a mathematical choice; it's not a real physical thing.
 That the formulas can be calculated relative to any reference point doesn’t change the fact that the physical reality is ellipsoid movement of planets around the Sun.
 Even as you insist on choosing a privileged reference frame for, say, aesthetic reasons, it's still not all the planets moving around the Sun. Did you not read the article? It's all the planets and the Sun moving around the barycenter. If you try to think through what your words even mean, you'll realize that they don't even mean anything, much less describe a physical reality.
 > you'll realize that they don't even mean anything, much less describe a physical reality.Wrong.https://en.wikipedia.org/wiki/Ellipse#Planetary_orbits"In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun [approximately] at one focus, in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation.More generally, in the gravitational two-body problem, if the two bodies are bound to each other (that is, the total energy is negative), their orbits are similar ellipses with the common barycenter being one of the foci of each ellipse. The other focus of either ellipse has no known physical significance. The orbit of either body in the reference frame of the other is also an ellipse, with the other body at the same focus."The existence of barycenter it a physical reality. The elliptic movement is a physical reality. Compared to all other distances, the barycenter is for all the motions of all the planets effectively Sun. Even it it is approximation, it's a good approximation. Even if it moves and is sometimes a little outside of the Sun surface, it's still compared to the other distances practically there.Sun.It was known even three centuries ago, but now some "philosophers" think that they "relativize" that away. No. It's there.
 > The existence of barycenter it a physical reality.A barycenter is a mathematically defined point that we choose because it makes equations simpler. There's nothing physically real (i.e. directly observable) at the location.Consider: if you fire a cannonball it will follow a parabolic path, and that parabola will have a focus, right? But that doesn't mean there's anything physically real about the focus of the parabola - it's a mathematically abstraction we invent because it's useful for describing the cannonball.> some "philosophers" think that they "relativize" that away.The relativity we're talking about comes from Einstein, not philosophers. Deciding whether the Earth revolves around the sun or vice-versa ultimately boils down to choosing a frame of reference, and one of the grand results of relativity is that there really is no absolute frame of reference we can measure from.
 > Consider: if you fire a cannonball it will follow a parabolic path, and that parabola will have a focus, right? But that doesn't mean there's anything physically real about the focus of the parabolaThe parabolic path is physically real, it will not go any other way.The same is with the paths the planets make: their form is real, they don't take any other.If you try to draw these paths on scale, you have to draw the ellipse (which for many planets is hard to distinguish from circle, the measurements had to become precise to learn that). Also, you have to place the Sun directly in one of the foci of the ellipse.All of these steps you have to do to make a picture that corresponds to what is measured and observed -- to make a picture reflect the physical reality.You obviously agree that much. So when you then write "whether the Earth revolves around the sun. ... I don't think there's any valid answer besides "you can define your terms and points of reference such that it does or doesn't; there's no particular physical reality to the matter"."You are confused with the fact that the calculations can be done using different frames of reference to make a statement that "there's no particular physical reality to the matter."The particular reality is the ellipsoid paths and the Sun in one of the foci, and whichever calculations you do, you have to reconstruct that physical reality. These shapes and that the Sun is actually in one of the foci is what you can't "relativize away."> Deciding whether the Earth revolves around the sunb or vice-versa ultimately boils down to choosing a frame of referenceIt doesn't. The Sun is in the focus of the ellipses made by planets around it. The opposite doesn't hold.> there really is no absolute frame of reference we can measure from.And that has nothing to do with the fact that the Sun is in the focus of the elliptic path of each planet and not the vice versa. The planets do make that path around the Sun, what can be simplified to "they rotate around the Sun." If you ever tried to draw it it would be obvious to you too.So you were just confused after taking that "Philosophy of Physics" class.
 > The Sun is in the focus of the ellipses made by planets around it. The opposite doesn't hold.Certainly the opposite holds - if you draw the Sun's orbit from a planet's frame of reference, you'll draw an elliptical path with the planet at one focus. That's the whole point here, that neither drawing describes observable reality any better than the other.I don't think I'm making any headway here so I'll defer to Einstein:> Can we formulate physical laws so that they are valid for all CS [coordinate systems] ... ? If this can be done ... the struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS could be used with equal justification. The two sentences, 'the sun is at rest and the Earth moves', or 'the sun moves and the Earth is at rest', would simply mean two different conventions concerning two different CS. Could we build a real relativistic physics valid in all CS; a physics in which there would be no place for absolute, but only for relative, motion? This is indeed possible!(from The Evolution of Physics)
 The orbits of the planets don’t behave “regularly” when observed from the Earth, exactly because they orbit the Sun and not the Earth.
 What does it mean for the earth to orbit the sun or vice versa?
 > points of reference such that it does or doesn'tIt's too bad (but not surprising) that you couldn't have gotten a bit deeper into general relativity where even the idea of "points of reference" gets a lot tricker. Even though there's a lot of pop-science talked about "space time" I find most people don't really grasp how really challenging of an idea it truly is.Newtonian physics and special relatively are quite happy to imagine one observer looking at another from a particular frame of reference. The classic example is of course watching someone driving while you are in a train. Special relativity seems really crazy at first because you realize the length of the car can change if either of them are going close to the speed of light.But GR does away with this idea that you can understand the universe at all while sitting on a train. In GR frames of reference only exist locally in infinitesimally small units of space and time and are defined by being simple such that all particles being observed move in straight lines. The big insight of GR is that the question "which 'revolves' around the other" is the wrong question because the only way to understand the universe is in slices of space and time where everything moves straight (well you can't ever get 'everything' straight, so even then you just worry about getting it right for a few particles at time).In GR when you jump forward and land on the ground in front of you, you moved in a straight line the entire time. This sounds impossible because we can't imagine a single frame of reference where we could observe this. And that's what makes GR so hard to understand because the jump forward can only be understood by looking at the way those infinitesimal local reference frames change, but there is no general frame of reference that we can find where we can clearly observe this. In the exact same way that calculus understands a curved line as an infinite sequence of perfectly straight lines, GR understands curved space time as an infinite sequence of perfectly straight frames of reference.It is, in fact, much more complex than the simple case of trying to understand who is right from the two reports of two observers seeing each other on passing trains.
 > In college I took a great "Philosophy of Physics" class, where on the first day the professor asked everyone to write one page on whether the Earth revolves around the sun, and the final project was another paper on the same topic, so we could see how nuanced a question it was and how our views had evolved over the course.A lengthy and enjoyable read of the original controversy is "The Great Ptolemaic Smackdown."[1] (I prefer to start there, as it's easy to tell whether you are interested in reading after the first few paragraphs, but he did put a ToC together, too.[2])
 > Philosophy likes to make things all seem like perception and mental frame of reference, and sometimes it is with people, but the earth’s trajectory relative to the sun doesn’t change if we think about it different or define terms differently.That's exactly the point here - answering the question of which revolves around what boils down to deciding which body is stationary, and that depends entirely on your frame of reference. Viewed from the Earth the sun is moving, and viewed from the sun the Earth is moving, and viewed from somewhere else they both move relative to one another. But none of those viewpoints is any more physically real than the others - they're just choices for where to put the origin of the coordinate system, as it were.That is, if you wanted to predict how the planets will move in the future, you could start from any of those assumptions and still make correct predictions. That's what I mean by saying there's no physical reality to the matter of which frame of reference you choose.
 > Isn’t the article linked here exactly the correct and valid answer of whether the earth orbits the sun?Is it though? I'm genuinely curious. For example, in our current reference, earth almost always is orbiting the sun, but what would happen if the entire system was not contained in the galaxy but in the middle of space (not attached to any galaxy), how would the planetary orbit change?Another question would be if our solar system was closer to the center of the galaxy, would the orbits of the planets stay the same or would they be skewed because of gravitational forces from the center of galaxy + other solar systems?> Another valid answer to whether the earth orbits the sun might be 99.87% yes and 0.013% no.I'm not sure if you're an astronomer or have a weather of knowledge or PhD in this topic but from the article, the answer is given as "Technically, what is going on is that the Earth, Sun and all the planets are orbiting around the center of mass of the solar system," writes Cathy Jordan, a Cornell University Ask an Astronomer contributor." That would be the only correct answer it seems. If the center of mass happens to be direct center of the sun or skewed one way or other is irrelevant to the fact. However, I could be wrong in my understanding.
 > there's no particular physical reality to the matter"Completely wrong. The physical reality is reflected by calculating Newton‘s formulas, which give the center of mass somewhere inside or very close to the Sun, as the article explains.
 By that argument we actually orbit the centre of the galaxy, with the sun causing a minor wobble on top of that orbit.It depends on your frame of reference.
 Some frames of reference are very close to being inertial frames, and others aren't. There's a big difference between inertial and non-inertial frames. In non-inertial frames, you have to introduce fictitious forces in order for the physics to work out.In short, the universe cares about acceleration, but not constant motion. Accelerating frames are different from non-accelerating frames.
 We are accelerating away from the center of the universe though.
 There is no center of the Universe. If the Universe is flat or negatively curved, then it is infinitely large, and if it is positively curved, then the volume is finite, but space is periodic.Space is intrinsically expanding, and that expansion is accelerating. That's quite different from acceleration in Newtonian physics. The statements I made about acceleration are in the context of Newtonian, pre-Relativistic physics, and are only approximate in a Relativistic framework.
 looks towards the great attractor and sighs
 Only someone without basic physics literacy would jump from the fact that "planets revolve around the center of mass of the solar system" to the clickbait conclusion "earth does not orbit around the sun". They missed that approximation is a prerequisite for a scientifically meaningful representation of the real world.
 I liked it. The clickbaity title leads the reader to learn what a barycenter means.
 "Everything in the solar system orbits around that point."Depends on exactly how pedantic you want to be. Technically everything in the solar system orbits the barycenter of the galaxy and intra-system movement is the same type of low-distance high-frequency wobbling the author chose to dismiss with regards to the motion of moons around planets.
 Are you sure that the neighboring galaxies have no effect and it is just about our galaxy? ;-)
 If you get that pedantic you must delve into relativistic center of mass and center-of-momentum frame. The speed of gravity is the speed of light. Sun's gravity affects earth with 8 minute lag.I'm told that you do the math at that level it's almost the same as in the Newtonian model, which is surprising. I never understood the math but it's related to the fact that changes in stress-energy tensor of matter are continuous. Mass+energy moves gradually from place to place, there are no sudden jumps. Earth accelerates towards point point where the Sun is in future. Not the same point as Newtonian mechanics with instant gravity says it should be, but close enough to hide relativistic effects of gravity most of the time.
 Does this mean even the sun orbits around that point?
 Yes.
 Fascinating. Basic physics question: the linked Wikipedia page on barycentre suggests that the further away a planet (in a 1 sun 1 planet system), the further the barycentre is from the centre of the sun. How does that work in the context of the declining force of gravity as a function of distance? I would have thought that the further a planet , the less pull it can exert on the sun. Does gravity not work that way?
 Think of it like this: if the planet were inside the sun, at the very center, that's where the barycenter would be. If the planet were then to move steadily away from the center of the sun, the barycenter would also move steadily (though more slowly) away from that point. As that planet steadily moves away from the sun, there is no point at which the barycenter will stop and start moving back toward the sun.
 The barycenter is a balancing point. If you were trying to balance two objects on the ends of a see-saw, if you move one object farther away, the balance point has to move toward it (you're actually balancing moments of inertia, which are functions of radial distance.)If your gravitating objects are in an orbit, they also have angular momentum and moments of inertia.
 You're right that a nearer small body pulls the large body with a greater force, but after one full orbit the large body has been pulled rightward just as much as it has been pulled leftward. The missing piece is: for how long is the force exerted before the situation repeats?A distant small body exerts a smaller force for a longer time, and a nearby one exerts a greater force for a shorter time.It comes down to how much time and how much force. The law of graviton plus Kepler's third law plus some algebra ought to show that you get a larger circle with a weaker force over a longer time (not an obvious result).
 You hit upon a very important point.Suppose that you have a 2 planet system: A sun type star (mass 210^30 kg), an Earth type planet 1 AU from the sun (weight 610^24 kg), and a Jupiter type planet (mass 2*10^27 kg) that is 1000 AU away from the sun.The distance between the Earth type planet the center of the star could be nearly constant.The distance between the Earth type planet and the barycenter would not be nearly constant -- it would not "orbit" the barycenter in a circular orbit.I may be wrong and I would be very happy if someone corrected me.(Note: I think the barycenter would be about 5 AU from the star!)
 The barycenter determines the point around which the system rotates, the intensity determines the speed.
 I believe this is false in the sense that Mercury's orbit is more centered about the center of the Sun rather than the barycenter of the solar system (center of mass).
 That might be, but the real statement would be more like that the solar system rotates around the barycenter of the solar system, for sure the moon revolves "more" around the barycenter of the earth-moon pair than that of the whole solar system.
 The planet's pull on the sun and the sun's pull on the planet decline at the same rate (they're both proportional to 1/r^2). So the barycenter will always be the same proportion along the line between their centers of mass.
 It has less pull, but it orbits slower and therefore has a longer time to pull on the Sun.
 The Moon also revolves around the center of mass of the solar system. In a sense more than it does around the earth. In particular Moon's orbit around the barycenter is convex - the popular picture of Moon's orbit having loops is wrong in that sense.
 My illustrative story from a few years back, was that if Earth were to vanish, the Moon's orbit would merely smooth out a bit, losing a slight ripple. Whereas if Jupiter were to vanish, Io would zoom away, perhaps even leaving the solar system, or impacting the Sun.
 > the popular picture of Moon's orbit having loops is wrong in that sense.Do you mean the moon never moves 'backwards'?
 Yep. Here's a discussion with diagrams and numbers: https://astronomy.stackexchange.com/questions/10979/moons-or...
 https://qph.fs.quoracdn.net/main-qimg-c8ca8c109ecb9dacdaa829...Something like this
 It never goes backwards and it never "bends in" towards Sun.
 I think it's better to say it never "bends out" away from the sun, which is a different way to statue that it's orbit around the sun is convex.
 Isn't the title incorrect? As in: it does orbit around the sun, but the center does not coincide exactly with the center of the sun. Or maybe there are other used definitions of the term "orbit around"?
 I suppose there's no hard line between a single object being the actual center of orbit and a many-body problem. I think the interesting thing to me is that the barycenter is often far enough from the center of the sun to not be within the sun at all. But that's about it.
 If one is going to play the “well technically“ game then we need to describe the motion with relativistic physics rather than Newtonian physics.
 Also you can't just treat the solar system as a point mass if you're inside it. Earth does orbit the sun but it is also perturbed to some degree by every other mass in the universe.
 An annoying and tedious game, played often by physicists...
 The sun moves at about 828,000 km/hour around the glactic center. Thus, it moves about 7250 million km each year.The distance from the earth to the sun is about 150 million km.Therefore, the earth's "orbit" is actually a very elongated helix.
 With respect to the galaxy's frame, sure. With respect to the earth or sun, not so much.
 One of my simulation software projects for a class last century was to try and recreate the slight “wobble” stars have from suspected orbiting planet pulling on them.The simulation proved they could but it took a fairly large planet in a closish orbit.Planet finding techniques have improved considerably.One problem I remember having was Setting the initial state so the planets didn’t just slide off my coordinate system with a constant velocity.
 All scientific theories are approximations, but some are better approximations than others.For example: one of the reasons that the flat-earthers get as much traction as they do is that "the earth is flat" is actually a reasonable approximation in some circumstances. "Flat" is actually just a special case of "round" where the radius is infinite. If the distance scale that you are concerned with is small (e.g. the size of your own body) and you don't care about small errors, then infinity is a not-entirely-unreasonable approximation of the radius of the earth.Of course, this all falls apart as soon as you start to care about anything that is more than a few thousand body-lengths away from you. But it's a mistake to say that the flat-earthers are wrong in any absolute sense. They aren't. They're just using a bad approximation for the realities of modern life.Unless you're sending a spacecraft to another planet, "the earth orbits around the sun" is a perfectly fine approximation.
 > But it's a mistake to say that the flat-earthers are wrong in any absolute sense. They aren't.I'd say they're absolutely wrong in the sense that they make the flawed claim that people who assert that the Earth is an oblate spheroid are absolutely wrong, or worse, are engaged in some kind of conspiracy to hide the truth.
 Fair enough. My point is just that the claim that the earth is flat is not entirely indefensible under the right circumstances, and so any proclamation that a particular position is wrong (e.g. "The earth does not orbit the sun") calls for a certain amount of humility and awareness of context.
 Well, actually, it isn't orbiting just around the center of mass of the solar system (solar system barycenter), but that is just one of the two foci of the earth's elliptical orbit. The error is of a similar magnitude as assuming the center of the sun vs barycenter of the solar system.If you're going to be pedantic, get it right.This article is a much better technical explanation of the orbit, including both the moving center of mass and the elliptical orbit: https://socratic.org/questions/is-the-sun-directly-in-the-ce...Oh, and the earth's orbit is also distorted by proximity to other gravitational masses, most notably the moon, but we're not going to be /that/ pedantic.Side note: the phrase "Well, actually," was banned at my house. Not sure why...
 I don't know what definition of "orbit" the author is using, but what he explains is how scientists define it.
 The article quotes Cathy Jordan,"Technically, what is going on is that the Earth, Sun and all the planets are orbiting around the center of mass of the solar system".I believe that the statement is a good approximation for the orbits of trans-Neptunian objects or any other orbiting object that is more than 40 AU from the Sun, but I think it is a bad approximation for Mercury, and not a good approximation for the Earth. When I say it's a bad approximation, I mean that it would be more accurate to say "the Earth and Mercury orbit the center of the Sun" than it is to say "the Earth and Mercury orbit the barycenter of the Solar System (center of mass)".Any comments by someone more qualified that me would be appreciated (I took about 6 courses in physics and 2 courses in astronomy in college and I graduated over 20 years ago).
 In a 2-body system on the complex plane, can't you basically take any point as the origin and describe the motion of te bodies in terms of a complex Fourier series, with the interpretation that the bodies orbit a circle on a circle ... on a circle ... around your chosen point?Edit: Basically Ptolomy did that the 2nd century AD.
 The word you’re looking for is: epicycles
 Since gravitational waves travel at the speed of light there should be a delay as well where the gravity of one body is affecting another from where it was not where it is. For earth that is where the sun was 8 minutes ago. Technically the galaxy might be orbiting something too.
 In fact, this is not how it works. My understanding is that whatever the gravitational force is carried by (ie. gravitational waves) is also affected by the velocity and rotational velocity of the gravitating object (in this case, the Sun), so the Earth really is attracted to the Sun’s current position, not where it was 8 minutes ago. Of course, this only works if no net forces are applied to the sun in those eight minutes, but that’s almost definitely the case. I believe, although it’s been a while since I did the calculations, that if this were the case then the galaxy would gradually become funnel shaped before eventually dissipating after the center gets too far away from the rest. It would have similar effects on the solar system as well.
 > current positionCareful there, buddy.
 Okay, yes, current position is not quite correct, but you can replace each instance of it with “the position of the Sun after the same amount of time as it takes for light to get to the Earth from the Sun, according to an observer that is stationary and on neither,” but that’s a mite clumsy (and still not totally correct, but good enough)
 What does “stationary” mean?
 Poor wording there as well :)Perhaps “not experiencing net force“
 You have reinvented inertial reference frame, but that doesn’t give you what you want either.
 I recall hearing that another effect in GR compensates for the delay of gravitational waves to make a binary system act according to newton's laws.
 Fine, it orbits sagittarius A'*' with some very small wobbles caused by sol.
 >Every single object in the solar system, from the gargantuan sun to the tiniest speck, exerts a gravitational pull on everything else.Actually: in the universe, not just solar system.
 every person who finished some school should understand that speaking about motion without reference frame is meaningless.Is such frame is proper to Earth (yeah, go google what proper frame is) then the Sun does revolve around Earth. If the frame is not proper to Earth or Sun then they both rotate around common center of mass which is (relatively) near Sun’s center but does not coincide with it.
 > "Everything in the solar system orbits around that point."Does this mean even the sun orbits around that point?
 Yep. Thats the cool thing about the center of mass: its always the center of rotation for a set of moving bodies.
 Of course the point isn't a point, the solar system is moving relative to the galactic centre, which is moving relative to other galaxies. And space itself is changing.So as, pointed out elsewhere, we choose our points of reference and they're pretty arbitrary when you consider the whole Universe.
 How much, in terms of percent variation, could this be? 1%? 2%? When is it going to become significant?
 Wow, is that catnip-clickbait for the Flat Earth Society...
 Then technically, nothing orbits any other single thing.
 As the saying goes: all models are wrong; some are useful.
 >As the saying goes: all models are wrong; some are useful.models being wrong/right/useful/etc. is just a model of a relation between a model and [an aspect] of reality [or whatever else] the model is supposedly modeling.
 Sure. It's also very useful.
 > As the saying goes: all models are wrong; some are useful.It's important to also recognize that everything we believe about the world except raw sensory perception is a model and, ipso facto, wrong, though perhaps useful.
 Surely you mean "including raw sensory perception" ;)
 The fact of the occurrence of the raw sensory perception is not necessarily a model; the interpretation of external causes is.(Though it's possible that the actual mechanism of sensory experience involve modelling, but the only way we could draw the conclusion that that is the case is through a model of the mechanism which has the problem of all models. All other belief about the external world is necessarily a model.)
 The fact that sensory information is limited, does not make it wrong. It's a certain perspective on reality, and we can easily accommodate for that.For instance, we know that a stick isn't actually bent when it goes into water, even if it looks like it is.More generally, we have no practical problem dealing with reality using the information given by our senses. It's not a problem in our daily lives and it's not a problem for going to the moon, Mars, creating microprocessors, etc.Sorry for busting up the "deny knowledge to make room for faith" parade.
 > The fact that sensory information is limited, does not make it wrong.If you reread the comment you are responding to, it says raw sensory input is the only thing that is not wrong, not that it is wrong.> For instance, we know that a stick isn't actually bent when it goes into water, even if it looks like it is.We don't even know that there is a stick, even if it looks like there is, but we do know the sensory data itself. In fact, there very idea of “a stick” (or discrete objects more generally) is a useful, but still wrong, model.> More generally, we have no practical problem dealing with reality using the information given by our senses.We have lots of practical problems dealing with that, and lots of practices adopted specifically to mitigate those problems. The historically recent invention of the modern scientific method is itself a (far from entirely successful) method of mitigating a very broad and impactful class of pervasive practical problems with that.> Sorry for busting up the "deny knowledge to make room for faith" parade.Faith, where it concerns the material universe at all, is still a method of selectig models subject to the “all models are wrong, some are useful” rule, it's just a method of model selection that isn't focussed on predictive utility, so, insofar as prediction is your key metric for utility, it's inferior to the scientific method which is narrowly focussed on predictive utility.Pointing out that all knowledge of the material universe beyond the facts of raw sensory data is models that are at best useful but always in some respects wrong is certainly denying lots that is commonly claimed as knowledge, but it absolutely isn't clearing the field for faith by so doing.
 One of the ways philosophy goes wrong is by using trivial problems as examples. "Where is the stick", or "is this really a table in front of me" are the Hello World of epistemology. Just like you can't figure out which programming language is better than another by looking at Hello World, you can't evaluate a philosophy by its answer to where the stick is. You need to look at answers to hard problems, like "what should I do with my life?"
 > If you reread the comment you are responding to, it says raw sensory input is the only thing that is not wrong, not that it is wrong.My view is that raw sensory input is just information, so it's not wrong, and so we are in agreement there. Further, I am saying that knowledge can be derived from that sensory input, which is where we disagree.I see what you are saying, I failed to clearly distinguish these two cases when I used the term "sensory information."> We don't even know that there is a stickYes we do. But to "know that there is a stick" is subject to certain caveats. It's not an absolute, like being omniscient. For example, if something is a stick, it's still a stick, even if we actually live in the Matrix, or in the dream of an alien being. Because to be a stick is just a mental classification (i.e., concept) that we have created for a certain kind of thing evidenced to us by our sense data and by the use of reason.> is a useful, but still wrong, modelA model can be correct as long as it doesn't overstate its own power of generalization. There is a sibling discussion going that covers the fact that Newton's Laws are correct as long as they are understood to describe phenomena (i.e. evidence) actually observed by Newton, and then only to a certain level of fidelity; but not "correct" if you hold them to the standard of explaining everything.> Faith, where it concerns the material universe at all, is still a method of selecting models subject to the “all models are wrong, some are useful” rule,Faith doesn't select a model. A model is based on evidence of the senses. Faith dispenses with models entirely and just makes stuff up out of whole cloth. I see your point there, I just think you're using the word "model" too loosely and in a way that gives faith too much credit.
 > Faith doesn't select a model.Yes, it does.> A model is based on evidence of the senses.No, a model is an abstraction by which one conceptualizes phenomena, regardless of the basis. It seems true that a model not based on structured application of sensory observation is likely to be a poor model if you judge quality by how well it lines up with future sensory observations, but a model is not necessarily a good model.Faith, also, does not dispense with evidence of the senses, it just applied it differently.“I perceived X describing Y as true”, where X is a (natural or supernatural) authority figure is sensory data, as are positive sensations associated with a particular belief. Now, they aren't sense data that empiricism would treat as relative to the truth of the belief at issue, but that's a different issue.
 You're just arguing that a "model" based on make believe is still a type of model. I don't find that compelling.It's like saying a scientific theory not based on empirical information is still a scientific theory.I don't see why that point is worth defending. Except perhaps as a way to give bad ideas higher stature by lumping them in with good ideas.> Faith, also, does not dispense with evidence of the senses, it just applied it differently.No idea what you are talking about here. For instance, the only sense-based evidence I know of for Christianity or Islam is the historical record, and that isn't reliable enough to establish these beliefs as anything more than make believe. In other words, we can't see Jesus work miracles, which would constitute partial evidence for Christianity; the only evidence we have is that someone said they did a long, long time ago. I'm also not aware of evidence for Zeus or Thor or Brahma.> as are positive sensations associated with a particular beliefEmotions do not constitute evidence for religion.
 Your last long doesn't follow, as far as I can tell, from the rest.The first part of your argument reminds me of Searle's that a belief shared, external reality is implicit in every statement of faxt, e.g. it no sense to say that "there is snow and ice at the top of Mt. Everest, AND there is no shared, external reality."
 The last line is a reference to Kant, who made an argument roughly along the same lines as dragonwriter, and said he wanted to deny knowledge to make room for faith. He wanted to preserve religion in the face of the Enlightenment. So far, he has succeeded.
 Sure, but how of what is this reference apropos?
 and some are wronger than others.
 By the way, be careful who you tell this to.The anti-intellectuals will spin this to prove their own points without any understanding of math or physics.I've seen this happen, and they are very confident, their 'friends' don't know either. When it comes time, will anti-intellectuals trust scientists or their neighbor?
 I disagree with the need for a warning. I think it would be better if this were _more_ commonly used.So often debates arrive at a stasis like:> "You're wrong"> "No YOU'RE wrong"And there they sit, each side certain that the other is an idiot.The alternative is to admit that both parties are right according to their model, and that both models are wrong (because being right is not what models are for). I think this is better because the "which model is more useful" question sets up a lot more potentially fruitful interaction between opposite sides.The danger you're referring to only occurs in a setting where science is implicitly authoritative in the first place. If we drop that assumption, science still produces the most useful models, but finding the most useful one for your project becomes less adversarial.
 I'm going to remember this. It's a good way to have discussion if you're lucky enough to have someone who can abstract their personal views from the model that produced them.
 I want to believe that, but how do you evaluate models’ usefulness if you refuse to acknowledge facts and data, and just yell “fake news” when they point to a conclusion you don’t like?
 What do you hope to gain from combative dialogue with such people? Are you trying to change how they vote, or shop?
 It doesn't help that model outputs are often put forward as the main reason for doing something. For example with climate change. But often the problem being discussed is more complex than the single dimension that the science based argument relies on. You have to consider ethics, economics, social effects, and a whole host of other disciplines. People intuitively get this.You have to have an argument that will pursuade the uneducated, poorly informed neighbor first. And often model outputs just don't cut it.
 >You have to have an argument that will pursuade the uneducated, poorly informed neighbor first.An emotional/moral argument will be a coinflip with these people.Will they side with the sad story of X, or the anti-intellectual sad story of Y?I do not know the solution, I've seen others propose everything from hiding difficult to understand topics to calling them 'stupid' infront of their peers, etc...Engaging them with logic and argument makes the problem worse.Would be willing to hear ideas if people have them.
 On a similar topic: https://news.ycombinator.com/item?id=16974098Convincing people is hard and starting from the position "I know better than them" only makes it harder. I understand that sometimes people are just wrong or are using fact incorrectly, but often this get inflated to an extreme degree by the "smarter" side.For me an important distinction is whether people are using unsound arguments to support a position or are holding an unreasonable position. For climate change the problem (from our "let's save the planet" side) is that we want them to change opinion, not that they are misusing unsound arguments.To solve this the only way is to start a two way conversation where you can communicate how and why you believe is important and they can do the same. It is hard to convince people that do not want to be convinced, it is even harder to lecture people that do not want to be lectured.A good starting point is to show that you yourself are willing to reconsider their point of view as stuff like "calling them stupid" is the same as brewing social resentment.
 There are no shortcuts. You have to meet where they are, find common ground and build trust, both ways. It’s incredibly expensive and hard.
 Surely the mechanism for change is the political process. And at a smaller scale society is full of people trying to influence, change opinion and mainpulate. Surely you should just adopt those same methods?It would be interesting to try and model people more directly. Like what political campaigns do, but with a more noble intent. Use the data to discover how to serve people's needs.
 “The map is not the territory”This is a similar sentiment, but perhaps more useful initially in conversation with people who may get hung up on what “model” means. It can also lead to a fruitful analogy as people easily grasp why different kinds of maps are important.
 I’ve never heard this phrase but I like it.
 What is the meaning of being anti-intellectual and who are these anti-intellectuals you talk about?
 That saying is wrong.Newton’s Laws are absolute in a typical human context. A better model must explain everything covered by newton and more. Discovering that better model doesn’t make newton wrong.
 No, the saying is not wrong here. Newton's Laws are wrong, period. They explain some observational evidence to some degree of accuracy. That they're "absolute in a typical human context" is literally the point of the saying I quoted.
 This is the wrong way to think about models.Newton's laws captured part of what he observed at the time. And that's all a model is supposed to do.That doesn't make it wrong. It makes it limited. You could say it's a "low resolution" view of reality.If we limited our knowledge only to perfect models, we would be holding ourselves to a standard of omniscience, and we would never know anything.We clearly have good enough models to design hypersonic aircraft, to pick a semi-random example. But our models are not complete; we don't know everything. But our models are not wrong.Other commenters who warn that saying "all models are wrong" encourages anti-intellectualism and exactly right. That leads to a bad place.
 The opposite of wrong is correct. Newton's Laws are not correct, therefore they are wrong. Technically.I agree though that saying they're "wrong" has limited utility... Perhaps the more useful way of thinking about models is "give sensible predictions up to certain amount of accuracy in certain contexts".
 > The opposite of wrong is correct.I agree.> Newton's Laws are not correct, therefore they are wrong.They are correct as long as they are stated with the caveat that they are only known to apply to Netwon's observations, and then, only with a limited amount of fidelity.I haven't read Newton's original source material, so I don't know if he overstated the universality of his laws.
 I feel we're arguing a very minor point here. You seem to be hung up on this "models can be correct when stated with appropriate caveats". Sure. The "all models are wrong" saying has an implicit "at representing the observable reality in full fidelity".
 "All models are wrong" is the same as saying "All knowledge is wrong." That's technically incorrect and philosophically disastrous. Ideas like this have a huge impact on people in myriad ways.> The "all models are wrong" saying has an implicit "at representing the observable reality in full fidelity".No, it doesn't. This is exactly like saying "All knowledge is wrong" has an implicit "as knowing everything in full fidelity, i.e., being omniscient." You are holding models (or knowledge) to a completely ridiculous standard. They are not supposed to work the way you are implicitly asking them to work.
 > That's technically incorrect and philosophically disastrousHow can taking a particular epistemic stance be wrong? What non-epistemic basis would you use to judge it? It might be inconsistent with the stance you have chosen, but that doesn't make it wrong.And as far as it being disastrous, I know a number of very competent people that take that view--what disasters should I look for in their lives to see how disastrous their stance is?
 It's wrong if it contradicts the evidence of raw sense data or knowledge derived logically from the evidence of raw sense data.You can choose to reject even that, but there is no reason to make such a choice, and it would be supremely impractical to do so.> And as far as it being disastrous, I know a number of very competent people that take that viewThe view that knowledge based on sense data isn't really knowledge was advanced by Kant, and certainly helped make room for the Nazis. Marx also exploited the anti-knowledge ethos of the time with his dialectical materialism. Finally, religion thrives when the ability to know is denigrated; that was Kant's stated goal [1]. Religion is fundamentally dishonest and leads to an infinite plethora of evils.[1] "I have therefore found it necessary to deny knowledge, in order to make room for faith" -Kant, Critique of Pure Reason
 Sense data in itself can't be contradicted because it contains no propositions.As for knowledge logically derived from the sense data--it is exactly the choice: "which logic should I choose to interpret this sense data?" that is in question.If you choose a logic where all models are wrong and some are useful, then it won't contradict knowledge derived according to itself. If instead you choose some other way, you're again not going to run into any contradiction.The choice of an epistemic theory can only be about utility. Truth and falsity can only come later because they must be expressed in terms of the chosen theory.
 No, they're also wrong in a typical human context.Most people have a phone with GPS these days. GPS would flat-out fail to work entirely without correcting for time dilation effects in the satellites. Newton had no concept of time dilation (nor should he have, given his context).
 Interesting description of “relativistic” effects in the GPS system. http://www.tuks.nl/pdf/Reference_Material/Ronald_Hatch/Hatch....
 They are wrong in _that one example_. For most other day to day scenarios, Newton's laws are plenty accurate.I disagree with the poster about that saying. I think it's a fantastic saying.
 I'm not sure I follow your argument, perhaps you can help me understand. If you're saying that Newtonian Gravity breakdown in a specific case but are fairly accurate in other cases does that mean they're still universally correct?
 I'm saying that for most everyday situations, Newton's equations provide sufficient accuracy for people to achieve their goals. However, in the case of GPS, the system wouldn't work reliably if it was only using Newton's equations.Einstein's theory of gravity is much more robust and is highly accurate across a far wider domain. It can be used to implement a reliable GPS system.
 Pointing out that Newton sill isn't wrong doesn't mean he was ever right in the first place. It's simply not about right and wrong.He spun a good tale about the universe. Later somebody else spun a good tale that was better in at least one way. That's all.
 Well, the saying is a model for the relationship between a model and reality. Being a model, it's wrong, but it is useful.