Making Earth the Center of the Solar System

[Rhidian]

Long ago it was thought that everything in the universe revolved around the Earth, then thought to be the center of the universe. Geocentric maps of the solar system depicted nice circular orbits of the other planets around the Earth. Since then, scientific advances and astronomical observations have shifted our model of the Solar system to a heliocentric model centered around the Sun. All of the planets orbit the Sun in a well defined elliptical pattern.

That's all well and good, but completely disregards the importance of the Earth to humanity. Given that the origin of coordinate systems are relative, I think it would be interesting to translate the heliocentric model of the Solar System into an up-to-date Geocentric model. Instead of the nice circular orbits of past maps, there would be crazy loop-de-loops for all of the celestial bodies as they orbit around the Sun as (from the Earth's POV) the Sun 'orbits' around the Earth.

I suppose that the brute force way of generating such a Geocentric map would just be to calculate all of the positions of the celestial bodies and transform them into a coordinate system with Earth as the center. But would there be a way to have some sort of mathematics associated with the new orbits to predict their position relative to the Earth at a given point of time?

[jwenting]

maybe it's time you realised that humanity is utterly irrelevant on the scale of the solar system.

It has been tried, read up about epicycles.

In fact it was the utter idiocy of that system which first led astronomers to think there must be a more logical explanation for how the solar system works, and that putting the sun at its center was a good way to make things much easier.

[spudman2]

Well, jwenting, this is a completely silly pursuit, but maybe it's time you realized that humanity is a rather silly animal. I'd like to see a map like this, maybe make it into a poster with both the heliocentric and geocentric models printed on it. And such a chart might not be useless; since the heavens can, at the moment, only ever be observed from Earth, having a chart that predicts where those bodies would might be useful.

[Rhidian]

maybe it's time you realised that humanity is utterly irrelevant on the scale of the solar system.

It has been tried, read up about epicycles.

In fact it was the utter idiocy of that system which first led astronomers to think there must be a more logical explanation for how the solar system works, and that putting the sun at its center was a good way to make things much easier.

Humanity may be irrelevant on the scale of the solar system, but Earth is of great importance to humanity, and I wanted a nice transition line into making a geocentric map. Thanks for mentioning epicycles though, I didn't realize that was the term used previously.

Yes, this idea makes things much, much, harder, and isn't likely to be used since the heliocentric model is simpler. However, I thought it might be cool if something like this could be made.

Starting off simple, I think it would be best to see what the brute force method would result in with a time limit of 1 year or 1 month of orbiting (since a complete map over infinite time would prob. just be an indecipherable mess of squiggles).

[K^2]

Yes. I've posted this before, but let me re-summarize the laws of motion for a Geocentric system, because it's unlikely I'll find them now. In all of this, I'm going to basically treat Sun as barycenter of the system, but this might need corrections for finer computations of orbits.

1) All bodies in heaven attract each other with the force proportional to the product of their masses, and inversely proportional to the distance between them. (Newton's Universal Gravity still holds.)

2) All bodies in heaven are repelled from the Earth's axis of rotation by the force proportional to their mass and distance from that axis. (Centrifugal term for Earth's rotation.)

3) All bodies in heaven are acted on by a force which lies in a plane parallel to the plane of the ecliptic, is perpendicular to the track of the body through that plane, and is proportional to body's mass and component of its velocity through that plane. (Coriolis effect. No easier way of putting it, I'm afraid.)

4) All bodies in heaven are acted on by a force which is directed parallel to the line connecting Sun to Earth, and is proportional to the mass of the body and inversely proportional to the square of the distance between Sun and Earth. (Accounts for Earth's annual track around the Sun.)

Each of these has its own "universal constant", which you can actually compute from Earth's orbital parameters in Heliocentric model.

[Idobox]

Easy, have the Sun and Moon turn around Earth, and all the other planets turn around the Sun. It's a specific form of epicycles.

And I suppose it could be a normal step for Copernicus to develop the heliocentric model: "hey look: it works if all the planets are turning around the sun, but, hey, if look from the sun, it looks like Earth is turning around too".

[Scotius]

I guess i will never understand why people are so enamored with geocentric system. It' complicated, ugly and inacurate (not to mention outdated like heck) - about only thing it's good for is stroking the ego of members of Homo sapiens species.

[K^2]

I guess i will never understand why people are so enamored with geocentric system. It' complicated, ugly and inacurate (not to mention outdated like heck) - about only thing it's good for is stroking the ego of members of Homo sapiens species.

It's not inaccurate. It's possible to describe universe from Geocentric perspective with almost as much precision as any other frame. And it has a certain elegance to it. It's not so much about Earth being the center, as about any arbitrary point being as good a center as any other. I'd find an Areocentric or Selenocentric system just as exciting.

[maccollo]

This is actually something I'm working on =P

Jupiter's motion as seen from the earth over a few years.

Each orbit is a day, altho there are less days per year than 365 to make things easier to observe.

Each half finished torus is a year on earth

The complete up and down motion is a year on Jupiter

Here's the inner planets motions over a few years. Unlike the outer planets, the inner planets distance to earth varies more, and so their motions are a bit crazy.

By filtering out the daily rotation of the earth the changes in the orbits become more apparent.

Edited January 30, 2014 by maccollo

[lajoswinkler]

Mind that the heliocentric model wasn't correct. Copernicus got at least one thing wrong - he put the Sun in the center of the universe, not "the Solar system".

It took some time before we figured out what's the real deal.

[K^2]

Mind that the heliocentric model wasn't correct. Copernicus got at least one thing wrong - he put the Sun in the center of the universe, not "the Solar system".

It took some time before we figured out what's the real deal.

And would you mind telling us where the center of the universe actually is? At least, point in the general direction.

[maccollo]

And would you mind telling us where the center of the universe actually is? At least, point in the general direction.

I am the center of the universe.

[ZetaX]

Time for a session in the total perspective vortex.

[lajoswinkler]

And would you mind telling us where the center of the universe actually is? At least, point in the general direction.

Please cease with this passive-agressive behaviour. You have enough knowledge that you should've understood my point.

His heliocentric system defined the whole universe as rotating in orbits around the Sun. This has nothing to do with Hubble's discovery that the whole universe expands, where each point could be considered the center. For Copernicus, the universe was static and perfect, with the star in the center.

[Idobox]

To be honest, Copernicus was not able to measure the distance of stars, so they were all super far and looked still. His hypothesis was the simplest that could explain all the observations, it was not a mistake.

He also pointed out his model was not able to predict events perfectly and needed to be improved.

[Kerbart]

No scientist is ever completely right. We build upon what we know and what we are able to see. Copernicus, with not even a primitive telescope at his disposal, brought our vision of how the universe is put together a thousand times closer to reality than the large hadron colider and its thousands of scientists ever will.

Yes, he put the sun in the center of the universe. But the step of taking the earth out of the center was a giant leap forwards in understanding the universe. It's like saying that the Wright brothers weren't really flying "since they didn't cross the ocean." Well, given where Copernicus was coming from and how much his model improved things I'd say he grocked the solar system pretty well.

I liked Macchollo's post. If all the information you have is the completely random movement of the "stars" (planets really, but even that was not known at the time), then figuring out how the solar system really works is nothing short of impressive.

[brdavis]

This is sort of curious, as I'm teaching this on Monday… so here's my take on it, for what it's worth.

The Ptolomaic (Earth-centered) system with epicycles was a good system - it predicted things rather accurately, and had a number of simplifying features (everything moved in perfect circles, for example. The Copernician (Sun-centered) system offered a couple of predictions - first, it predicted the distance to the outer planets (the Ptolomaic system didn't constrain that), which, while nice, they had no way to measure. It also predicted there should be a shift in the positions of the stars over the year… which was very pointedly *not* observed. So, observationally… the Earth-centered system made more sense. More specifically, Copernicus (who nicked the idea from the ancient Greeks - they, too, had proposed a sun-centered system) worked with perfect circles… and in order to get predictions as accurate as the Ptolomaic system, also had to add back in epicycles, deferents, and the whole load of baggage that went with it. By the time you patched the Copernician system up to the point where it worked as well as the Ptolomaic system… it wasn't any simpler. Far from it.

It really wasn't until Kepler took Tycho's data, tried to fit it to any existing model, and realized neither of them worked, that he invented a fix - not just Sun-centered paths, but eccentric paths, with varying velocities. With that, he finally had a system that could out-perform an Earth-centered one. and it still took about 100 years until some kid in his 20's explained it all while inventing calculus and integration in his spare time (Newton).

You don't throw out a model, or theory, until there's some good reason to. Copernicus really didn't have one - and in fact observers like Tycho had good evidence that Copernican theory didn't match the observations. It wasn't until Kepler tried to reduce Tycho's (astoundingly precise) data that there was any really good reason to pick one over the other… and as it turns out, what resulted was really a third, novel system.

[K^2]

To be more precise, Tycho did note that for parallax to be too small to measure, stars would have to be more than 700 times more distant than Saturn from the Sun. For all of the limitations of their understanding of cosmos, they had excellent understanding of geometry and geometrical optics. So it's not like they'd assume that if there is no measurable parallax, that there is no parallax at all. Possibility that stars were simply too distant for parallax to be measurable was understood. The problem was lack of understanding of wave optics, leading Tycho to greatly over-estimate the apparent size of stars. Even to a modern telescope, light from a distant star might as well be from a point source. However, even a point source results in an apparent disk of finite size. Brighter source results in a larger apparent disk, which is what Tycho was measuring, resulting in absolutely enormous predictions for sizes of stars.

[lodestar]

I guess i will never understand why people are so enamored with geocentric system. It' complicated, ugly and inacurate (not to mention outdated like heck) - about only thing it's good for is stroking the ego of members of Homo sapiens species.

That's absolutely wrong. First of all, it's not inaccurate. As someone else already pointed out, you can describe the universe from a geocentric model with almost as much precision as from any other frame of reference, and as a matter of fact, the coordinate systems used most often for space travel and orbital maneuvers are Earth-centered. Ultimately, it all rests in faith. If you want to believe Earth has a privileged location in the universe, or if you want to believe the distribution of matter in the universe is uniform and Earth is in some random corner. The math works both ways.

Complicated? Well... if you put the Earth in the center of the universe, you can explain most of the phenomena we observed so far with plain newtonian physics. If you are convinced beforehand that Earth can't be at the center of the universe and this is an unacceptable proposition, then things get really complicated.

Ugly? Personally, I think the Tychonean geocentric model is much more elegant. When you realize how the heliocentric model ultimately lead 20th century physics to nonsense like Dark Matter theory, it's hard to argue for the elegance of that system.

[lodestar]

And would you mind telling us where the center of the universe actually is? At least, point in the general direction.

Either Earth is the center of the universe, or the universe has an indefinite center. It's as simple as that.

[lodestar]

Long ago it was thought that everything in the universe revolved around the Earth, then thought to be the center of the universe. Geocentric maps of the solar system depicted nice circular orbits of the other planets around the Earth. Since then, scientific advances and astronomical observations have shifted our model of the Solar system to a heliocentric model centered around the Sun. All of the planets orbit the Sun in a well defined elliptical pattern.

Correction. Scientific advances and astronomical observations have shifted our model of the Solar System to a heliocentric model, and after that more scientific observations shifted our model to a relative model, with no definite frame of reference.

That's all well and good, but completely disregards the importance of the Earth to humanity.

Well... to disregard the importance of the Earth to humanity is one of the premises of modern science, formalized in the Copernican Principle, that assumes we are not in a privileged position in the Universe. Many physicists think we should believe in this out of modesty. As much as enthusiasts of modern science enjoy likening the acceptance of the conclusions of modern astrophysics and cosmology to "logic" and "enlightenment", it's ultimately a matter of faith. If you decide to not assume the Copernican Principle as valid, most of modern astrophysics and cosmology crumbles.

Given that the origin of coordinate systems are relative, I think it would be interesting to translate the heliocentric model of the Solar System into an up-to-date Geocentric model. Instead of the nice circular orbits of past maps, there would be crazy loop-de-loops for all of the celestial bodies as they orbit around the Sun as (from the Earth's POV) the Sun 'orbits' around the Earth. I suppose that the brute force way of generating such a Geocentric map would just be to calculate all of the positions of the celestial bodies and transform them into a coordinate system with Earth as the center. But would there be a way to have some sort of mathematics associated with the new orbits to predict their position relative to the Earth at a given point of time?

The exact mirror image of the heliocentric model of the Solar System into an up-to-date Geocentric model is a Tychonean model with the star movement centered on the Sun. There's no need for the scare quotes. There's absolutely nothing wrong with saying the Sun orbits the Earth and the other celestial bodies orbit the Sun and that's a perfectly valid model. No observation made from or near the Earth can give you any evidence for one model over the other. It's purely a matter of faith.

[K^2]

Ugly? Personally, I think the Tychonean geocentric model is much more elegant. When you realize how the heliocentric model ultimately lead 20th century physics to nonsense like Dark Matter theory, it's hard to argue for the elegance of that system.

And now you've gone off into the crazy lands. Dark matter is a consequence of general disagreement between observed trajectories and visible mass distribution. It's a problem in General Relativity as well, which is the most frame-invariant thing we've got by its very design.

[lodestar]

And now you've gone off into the crazy lands.

Oh boy, I hear that a lot. That was my reaction when someone made me think about this too, so no surprises here.

Dark matter is a consequence of general disagreement between observed trajectories and visible mass distribution.

Correction: consequence of general disagreement between modeled trajectories that interpret Hubble's red-shifts as velocity-shifts. Hubble himself acknowledge the problem, but accepted it and called it "inter-nebular material", since the only alternative would be placing Earth at the center, something he said was "an hypothesis that cannot be disproved but it is unwelcome and would be accepted only as a last resort in order to save the phenomena."

It's a problem in General Relativity as well, which is the most frame-invariant thing we've got by its very design.

Yes, but frame-invariance was introduced with Special Relativity precisely to salvage the heliocentric model after the Michelson-Morley experiment detected no relative movement of the Earth. Given strong evidence that Earth isn't moving and has to be in the center of the universe, you could either accept that and scrap the heliocentric model, or find a way to say that no matter where you are in the universe, if you look around, it looks like you are in the center. In that context, Make-Believe Dark Matter is not a problem, but a fudge factor needed if you assume Einstein's field equations to be valid.

Where I come from, that's called reductio ad absurdum. Dark matter is the EAS-4 Strut Connector of the current model of the universe.

Edited February 1, 2014 by lodestar

[Brotoro]

Dark matter has nothing to do with interpreting Hubble shifts as velocity shifts. Our Galaxy (and other galaxies) simply does not have enough visible matter to rotate as it does without flying apart. Similarly, the way galaxies in galaxy clusters can hold together with their observed velocities indicates that those clusters contain more matter than we can see.

[ZetaX]

lodestar: So how exactly are you explaining that the Michelson-Morley experiment gives the same result if you strap it on a car/plane(and, but as far as I know, untested, a satellite)¿ If the earth stands still, then that vehicle obviously doesn't.

Not even speaking about tons of other effects not taken care of by pre-relativity stuff (mercury or atomic clocks, anyone¿).