In the Tychonic model, retrograde motion is equally explainable and makes perfect sense.
EVERYTHING you observe can be explained with Tycho’s geoheliocentric model.
This is the key. It’s a lot harder to come up with laws of motion that account for the motion of the planets in Tycho’s model. Probably not impossible, but the laws of motion would be a lot more complicated than Newton’s laws. Of course, someone who accepts the Tychonic model would say, so what? The laws of motion are what they are, and if they’re complicated, that’s just the nature of reality.
Don’t you have to have epicycles in the Tychonic system to account for that? Eliminating those was the biggest simplification of the heliocentric system over others.
How do geoheliocentric systems allow for the Earth’s rotation? Tycho’s system didn’t have it, but we know from other evidence (Focault’s pendulum) that it does.
And in fact, which origin is “better” depends on what is it we’re trying to calculate.
One of the oldest, simplest, yet nastiest tricks played by physics teachers upon their students consists of giving them an exercise which if solved just as given is very complicated (think, “Earth in the center and everything must be circular”) but with a change of coordinates (“let’s move the Sun to the center… now we need less circles”) and maybe notation or concept (“what if we don’t force circles? With elipses we need a single equation for each orbit”*) becomes a lot easier.
Car A runs towards car B at 60mph. Car B runs toward can A at 45mph. Things such as the force with which they’ll hit each other are a lot more complex if you keep it like that than if your first step is to “fix” either car and say the other one is running toward it at 105mph.
This was a change in geometry. But the kind of mindset change required is similar as going from, say, vectorial to polar notations. Or from thinking of planes as “surfaces” (as I spontaneously do) or thinking of them as “square matrices” (as my chrystallography teacher did).
If you want a real challenge, try integrating something over a cube… in spherical coordinates.
And within the context of GR, you can actually construct laws of motion to enable the Earth to be stationary at the center of the Universe, while still producing exactly the same observables as in the usual model, but they’re a heck of a lot more complicated, as well as being extremely arbitrary.
Strictly speaking, humanity doesn’t “know” the answer to this question. Either model (the simple model or the complex model) could be correct, if both models align with all measured observations.
But a simple model is more useful because you can apply it and calculate it much faster. So it’s better to use the simple model, even though there is a very tiny chance that the complex model is actually the correct one.
It’s not so much that humans don’t “know” the answer to the question, it’s that the answer to the question doesn’t really exist. What exactly would be the difference if the Sun ‘really’ orbitted the Earth, but God manipulated everything so that any measurement you take shows the Earth orbiting the sun? Since every way you look at it it works like our model, how does the ‘real’ answer affect our lives? I mean, my laptop could be entirely a prank - God could have just made a piece of space look like a laptop to people, and light up when we press where a button appears to be, and change what it displays when I type on what looks like a keyboard. But how is having a laptop that’s really a divine being perfectly impersonating a laptop perfectly any different than just having a laptop? If there is a difference, then it means that the divine being is no longer impersonating a laptop so you’re fighting the hypothetical.
I was trying to distinguish the difference between belief and assuming the truth is the position best supported by evidence.
Good scientists don’t “believe” in anything. They assume that the best supported position is true, but state their assumptions. For some fields, there is a large amount of uncertainty, and there are several possible theories that fit the sum of the evidence. (one recent, relevant one is whether or not simple caloric totals or actual nutrient profiles are the primary cause of weight loss and gain.)
The truth is you can use established physical theory to model the Sun-Earth system with the Sun having fixed coordinates or the Earth having fixed coordinates, with both models making the same predictions. And so in the sense that one correctly models the Sun-Earth system, so does the other.
Physicists are aware that the same physical situation can be modelled in different ways within the same theory and the freedom to chose different models is called gauge freedom. Gauge freedom exists simply because physical theories have redundant degrees of freedom and rather than each unique physical situation being represented by a unique configuration of of the theory, it is represented by an equivalence class of configurations.
Therefore the question of whether the Earth goes around the Sun or vice versa from a cold theoretical point of view is non-problematic as it is a moot question. However sometimes too much choice can be a bad thing as we really want the configuartion of the theory that makes calculations the easiest, which will be the one in which the extraneous degrees of freedom are suppressed. A procedure for choosing such a configuration is called gauge fixing. In a system like the Sun-Earth system the simplest choice is usually the one in which the centre of mass of the system is at rest. As has been pointed out the common centre of mass of the Earth and the Sun lies somewhere off-centre within the Sun.
Actually, yeah, it is. The same answer works for geostationary satellites: you might ask, if they aren’t orbiting, what keeps them from falling. Brace yourself, 'cause this is a doozy: frame dragging. Relativistic frame dragging, from the mass of the vast outer cosmos, rotating around the stationary earth once per day.
(And, while the cosmos would be moving much faster than the speed of light, this doesn’t violate relativity, because nothing is moving within the cosmos FTL. The cosmos itself is moving. This is why, in real cosmology, the expansionary/inflationary model is permitted. Space itself “moved” FTL, but no object moved FTL with respect to the cosmos.)
Even The Bad Astronomer has acknowledged that this interpretation is legitimate. It is not in any way supported by evidence, but as an example of abstract mathematical manipulation, it really does work.
No, because I wouldn’t ask myself that. If a satellite is at a height where it circles the Earth once every 23.9 hours, it is orbiting, and if a satellite is at a height where it circles the Earth once every 24.1 hours, it is orbiting, but if a satellite is at a height were it circles the Earth every 24 hours, it isn’t orbiting?
A satellite in a geostationary orbit wouldn’t care if the Earth suddenly accelerated up to a 10 hour rotation, and it wouldn’t care if the Earth suddenly slowed down to a 250,000 hour rotation.
I was addressing the issue of a non-rotating earth, with the cosmos whirling around it once a day. In that framework, a geostationary satellite isn’t “orbiting” but just sitting in space.
One might well ask, what keeps it from falling. And the outré answer is frame-dragging from that madly whirling cosmos.
That’s also the answer to Isilder’s question about the trajectory of a Mars rocket.
(I’m not making this up! It’s seconded, not only by The Bad Astronomer, but also by Martin Gardner, in an old “Mathematical Games” column from Scientific American.)
Ah. My bad. But in that scenario, wouldn’t frame drag also act as a tidal effect on the Earth, dragging against mountains and such and eventually making the Earth’s rotation “universe synchronous?”
I don’t know about synchronizing the spin/whirl…but it would have the (observed!) tidal effect on the earth of producing a tidal bulge – the earth’s shape as an oblate spheroid. (Martin Gardner mentioned that one.)
Very quickly let me say I don’t believe in this! It’s only an available mathematical model – and a hideously complicated one, of no real use to anyone.
So! Occam’s New Razor says the preferred theory, out of all plausible theories, is the one that we puny humans can most easily compute! Sounds good to me!
But, I can’t help but thinking that this would have been all the more useful in the olden days, before supercomputers, rather than in modern times.
Nowadays, what with supercomputers and all, there’s really no longer any reason (other than “tradition” I suppose) to prefer the simple theory over the complex theory, as long as they’re computable.
Right now, as of 2017, you still have to type in the rules for whatever model you want to use into the supercomputer, and test it, and worry about parallelism and all that. The supercomputer makes evaluating the model faster, but it’s going to take about half the time to program it for a model that is about half as complicated. Since programmer time is very expensive, simpler models are still better.
In addition, even with things like machine learning, where models can be learned automatically, simpler models can be exponentially faster to converge on. That is, the computer can learn a model that is half as complicated in a lot less than half the total number of data points. So even in this coming age of AI, AIs will pick simpler models inherently.
It would be more accurate to say that once you open your mind to a heliocentric frame of reference, an elegant physics of simple forces emerges.
But the geocentric model doesn’t collapse - it simply ends up looking awkward and over-complicated. Nonetheless, it’s quite useful for certain practical purposes, such as celestial navigation.
Even before Copernicus, there were complaints about the necessity to add epicycles on top of epicycles just to get the positions right. The heliocentric model has its complications too. To be really precise you can’t just use simple ellipses – you have to allow for perturbations by other planets. That’s how Neptune was predicted, in fact.
Also planetariums. At least the mechanical ones. Now-a-days, I expect they’re digital and it isn’t an issue.
