So, we all accept as fact now that the Earth revolves around the Sun, it’s more or less an invitation to mockery if you assert otherwise. But, if my understanding of relativity is correct, motion is relative to the observer. So doesn’t that mean that from the perspective of the earth, everything DOES revolve around the Earth, and likewise from MY perspective, the universe revolves around me? I have a feeling that since this isn’t taught in school there’s something wrong with my reasoning, what is it? I suspect it’s a gross misunderstanding of what “motion is relative” means formally.
My understanding is that you can assume that anything revolves around anything, but the heliocentric model is the easiest to grasp, and fits with newtonian physics best.
::shrug:: I’ve been content to nitpick people here on the Dope that say the Sun doesn’t go around the Earth for precisely this pedantic reason. I see no fault with asserting it.
But usually when people use that phrase, they mean “geocentric theory is false.” So really, this is just a case of where verbal oversimplification introduces error into the debate. It’s like when some people found it outrageous that asserting one’s “right to remain silent” required one to actually announce that to police. You have to just sigh and go “Yeah…that phrase isn’t meant to be literal.”
I don’t know if this adds anything, but the sun appears to orbit the earth not because the earth actually orbits the sun, but because the earth rotates about its axis. That is, if you assumed a geocentric universe, you’d have to assume that the sun and the rest of the observable universe all revolved about the earth once per day. You’d see that the sun and stars moved back more or less to their original positions each night, but the planets would seems to wander through the sky from night to night. Why is that? Also the position of the sun in the sky and which stars you can see changes as the year progress, so you’d need a theory for that as well.
If you plot the motion of the planets, you get something that looks like this. So of course the planets, including earth, revolve around the sun. The theory of relativity does not say “everything is relative.” It applies to inertial reference frames, and rotation is not inertial. For example, you can say, “is the earth rotating, or is the universe rotating around the earth?” But of course we know the earth is rotating. For one thing, there is an equatorial bulge due to its rotation. The the “motion is relative” idea is only applicable to comparing inertial reference frames.
Epicycles, of course. Planets not only revolve around the Earth, but around invisable objects as well.
Hmmmm…
Motion is relative given two inertial frames, right?
Is the earth orbiting the sun an inertial frame?
Not that gross a misunderstanding. You just need to add “constant straight-line” before “motion is relative”.
Speeding up, slowing down, or changing direction is NOT relative. You can always absolutely tell whether something is slowing or speeding up or changing direction. Which maybe seems a little strange if you can’t say absolutely how fast it is going, but if you think about it carefully, hopefully you can see how this can be possible.
Now going around in a circle, even at a constant speed, is changing direction all the time. So there’s no problem with relativity saying that one thing is circling around another, but not vice versa.
Though, once you look at how gravity works, it turns out that both the Earth and the Sun are in fact in orbit around the same point. It’s just that, because the Sun is so much bigger, the point is inside the Sun. So the Earth swings around a 93 million mile circle and the Sun just gets a little bit off-center to one side then the other of the central point.
Of course, the hard-core geostationary blokes, like the Tychonian Society and the Biblical Astronomy group, answer that “frame dragging” from the rotating cosmos pulls the earth’s equator outward…
The Bad Astronomer has pointed out that, if you really want to crank through the math, any point in the cosmos can be at the “center” of any degree of rotation you might choose. Mars could be at the center of the cosmos, spinning a million RPM retrograde, and the cosmos is spinning nearly as fast, prograde, to produce the observations we make today. The math, of course, gets so incredibly hairy that no one (sane) would bother!
(Martin Gardner also played with the idea in one of his Mathematical Games columns in Scientific American magazine…although I can only cite this from memory; I don’t have an index. He noted that the obvious objection – the distant stars would be moving faster than light – doesn’t really apply, since it is the cosmos itself that would be rotating, and nothing is moving FTL with respect to that. The same answer given to the same objection regarding the Expansionary Phase or Cosmic Inflation in modern Big Bang theories.)
It’s also been pointed out that, if you want to do the math, you can model the cosmos as “inside out,” and the stars are at the center of the hollow earth, while the ground under our feet is the “distant edge of the cosmos.” Here, the math is easy: just replace r with 1/r in a geocentric model.
It’s nothing but mind-candy, but kind of fun to play with in an abstract fashion. The only real sin is in believing that it is mandated by the almighty…
Sorry to bump a two month old thread, but I accepted this answer before, and after some thinking I may have re-confused myself. If my reference frame is moving at 4m/s relative to some outside observer. Everything looks like it’s moving at -4m/s to me. Now imagine my reference frame is at 5m/s, to me everything looks like it’s moving -5m/s.
Further, if I’m moving at 5 m/s and somebody is running along side me at 5m/s, it looks like they’re sitting still, if we both accelerate to 6m/s at exactly the same rate (same acceleration function), at any rate you care to sample the instantaneous velocity, we’re moving at the same velocity and therefore not moving in each other’s reference frames. What’s the functional, mathematical difference between me accelerating and most/all other objects accelerating?
Since rotation is just constant acceleration, it would look like everything is orbiting me. No, that doesn’t necessarily mean in a nice pattern, i.e. in a “circle” around earth, it would likely look like some bizarre loop-de-loop (imagine plotting the moon’s location relative to the sun over the course of a whole year), but it seems to me that on paper you could pick any arbitrary point you want and say things rotate around it (albeit not in a nice pretty ellipse/circle).
If you’re moving at a constant velocity in space, and another object is also moving at a constant velocity in space, there’s no way to say whether you’re moving and the other object is stationary, or you’re stationary and the other object is moving, or both of you are moving.
But if the relative motion between the you and the object is changing–that is, either you or the object is accelerating–you can tell whether you are accelerating or the object is accelerating.
Obviously, you can change the math to say that the entire universe is accelerating around you rather than you accelerating, but this quickly becomes very difficult if there are more than two or three objects in the universe.
Some of these posts are needlessly complicated. Look, if you want to say that the universe appears to revolve around the earth, you would be correct. If you want to say that the sun appears to revolve around the earth, you would also be correct. And, by the same token, if you spin around in your living room, you could say that it looks as if the room is revolving around you. And unless you insist that, “Yes, it is from my point of view,” forever, you won’t be able to comprehend that there are other points of view besides your own, i.e. ALL of them, in which the room does not appear to revolve around you. As for the sun/earth question, you can argue that it LOOKS like the sun is going around the earth, and so are the stars and the planets, but any other observer any place else in the universe will not see it that way. Invoking relativity here - in the physics sense - is a mistake.
Only in Mississippi, and when your mom is in town.
I think CC’s answer is as good as any in this thread. I’ll just add, for the stars to be in orbit around the Earth, their velocity would have to exceed the speed of light, which is impossible.
That’s what I wanted to know – so it’s not scientifically incorrect to assume a geocentric (or mars-centric, or andromeda-centric) model, just that it’s mathematically bonkers to keep track of?
No, it is incorrect, as the premise violates laws of physics, such as speed of light, theory of gravity and laws of motion.
You can kludge things so that the physics all works out, but it’s a horrid, unholy mess.
For any two bodies independent of other factors, they both revolve around the point in space that is the center of gravity of the two masses. The sun is so massive that the point happens to fall within it’s volume, but this is an arbitrary distinction and carries no actual physical significance. It’s merely a categorical convenience.
But this is unrelated to geocentric models which have to do with the way the orbital paths of all the planets look when drawn together.
Relativity does say that you can model any body as a motionless point with everything else moving, but this doesn’t make the orbital traces of the other planets look like circles around the Earth.
Generally speaking I suspect the most useful way to model multiple bodies is to make the center of gravity of gravity of the whole system be the zero coordinates.