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In a geocentric universe...

Quinn

Breathtakingly blasphemous.
Quinn
Joined
Jan 6, 2002
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Inspired by the How fast? thread, but thinking in the opposite direction...

In a geocentric universe, with the Earth in the center and everything else revolving around it, what would be the linear speed of the most distant stars we can detect as they whipped around us in their orbit?

Here's what I came up with. Those who know more than I, please add or amend...

I had no idea how far away the furthest detectable stars are, but according to this article they're about 13 billion light years away. I don't know if that's generally accepted as accurate, or if it's screaming Daily Mail lunacy, but I'll run with it for the sake of the exercise.

If it's true, that means the length of their orbit around us (assuming it's roughly circular) would be 13 billion * 2 * ∏, which comes out to roughly 81.7 billion light years. So if they made that orbit in a year, they would be going 81.7 billion times the speed of light. But if they made it in a day, their speed would be that times 365. That comes out to about 30 trillion times the speed of light, or 5.5x10^114 mph.

Is that generally right, or have I gone horribly astray somewhere in this question of purely theoretical fantasy physics?
 
Sounds about right.

Bear in mind that according to relativity, the speed of light is constant in all inertial reference frames. A frame that rotates with the earth isn't inertial, and light does all sorts of funny things in such frames. So in a frame like that c isn't necessarily the speed of light... which is why the light emitted by those stars whipping around us can be moving so fast.
 
Probably just a typo - but "5.5x10^114 mph" can't be right. Thats 550 trillion googols mph.

I didn't do the math - but whenever I see 10 to the power of a three digit number - its generally a combination/permutation thing - or its wrong.
 
My mental calculation gives it as on the order of 10^24mph.

Very rough and ready, but 10^114 is way off.
 
Oh! Oh! Here's a video that'll make you want your three hours back watching it. :)

 
I did some similar calculations for a response to a complete moon-dog moron on YouTube who goes by the handle Megasage007. He'd posted a video arguing that the Earth really is stationary at the center of the universe.
 
Of course there is a "simple" solution to this. That is that the galaxies aren't moving but that the space they are in is rotating around the Earth.

There is a further problem with the geocentric model - consider that a far galaxy is in same plane as the solar system, and then contrast it with one at same distance that has a "polar" relationship to the solar plane. Are they moving in terms relative to their location (ie the "polar" one stays in same position, so not moving), or does each have individually the same revolving relationship to Earth such that they are all whizzing around in different directions?
 
Foster Zygote said:
I did some similar calculations for a response to a complete moon-dog moron on YouTube who goes by the handle Megasage007. He'd posted a video arguing that the Earth really is stationary at the center of the universe.
Click to expand...

Well, there's nothing wrong with using coordinates in which the earth is stationary, non-rotating, and at the center of the universe. The laws of physics allow you to choose any coordinate system you like, including that one, and derive correct predictions for all physical experiments (the predictions will be identical regardless of which coordinates you use).

Some coordinate systems are much more convenient than others. Geocentric coordinates where the earth isn't rotating are great for doing calculations related to navigation on the earth's surface, but terrible for astronomy.

Does this mean the earth is "really" at the center of the universe? Of course not - it means you can put the center wherever you want.
 
sol invictus said:
Well, there's nothing wrong with using coordinates in which the earth is stationary, non-rotating, and at the center of the universe. The laws of physics allow you to choose any coordinate system you like, including that one, and derive correct predictions for all physical experiments (the predictions will be identical regardless of which coordinates you use).

Some coordinate systems are much more convenient than others. Geocentric coordinates where the earth isn't rotating are great for doing calculations related to navigation on the earth's surface, but terrible for astronomy.

Does this mean the earth is "really" at the center of the universe? Of course not - it means you can put the center wherever you want.
Click to expand...
That's interesting - so we can't directly observe anything about the motion of the universe which rules out the geocentric model?

However that model would require some pretty extreme forces acting on the rest of the universe to keep it spinning around us wouldn't it? We have no explanation for such forces - and the traditional model doesn't require any extra mysterious forces.

Therefore surely we can conclude that the geocentric model is false (or at least extremely implausible)?. Not from direct observation of the motions - but from the difficulty in explaining the motions.

- Drelda
 
Quinn said:
Inspired by the How fast? thread, but thinking in the opposite direction...

In a geocentric universe, with the Earth in the center and everything else revolving around it, what would be the linear speed of the most distant stars we can detect as they whipped around us in their orbit?

Here's what I came up with. Those who know more than I, please add or amend...

I had no idea how far away the furthest detectable stars are, but according to this article they're about 13 billion light years away. I don't know if that's generally accepted as accurate, or if it's screaming Daily Mail lunacy, but I'll run with it for the sake of the exercise.

If it's true, that means the length of their orbit around us (assuming it's roughly circular) would be 13 billion * 2 * ∏, which comes out to roughly 81.7 billion light years. So if they made that orbit in a year, they would be going 81.7 billion times the speed of light. But if they made it in a day, their speed would be that times 365. That comes out to about 30 trillion times the speed of light, or 5.5x10^114 mph.

Is that generally right, or have I gone horribly astray somewhere in this question of purely theoretical fantasy physics?
Click to expand...


Don't geocentric models generally involve the stars being on the inside of a sphere of (comparatively) modest diameter?
 
slyjoe said:
If the earth is the center of the universe, it would also be the center of the solar system. How did we rule that out?
Click to expand...
Not necessarily, the Sun could be the centre of the Universe and everything revolve around that, including us. Given the distances involved it would be indistinguishable.
 
slyjoe said:
If the earth is the center of the universe, it would also be the center of the solar system. How did we rule that out?
Click to expand...

If I understand Sol_Invictus's point correctly - we didn't rule it out through direct observation - ie we didn't observe any motions in the solar system that would be inconsistent with the earth being the center of the solar system.

However we did find it really hard to explain those motions when we assumed the earth was the center of the solar system. Once we tried putting the sun at the center it was much simpler to explain.

So I think both geocentric models (universe and solar system) are similar - we can't falsify them through observations - but in practice we do because the alternative is much simpler.

- Drelda
 
drelda said:
If I understand Sol_Invictus's point correctly - we didn't rule it out through direct observation - ie we didn't observe any motions in the solar system that would be inconsistent with the earth being the center of the solar system.

However we did find it really hard to explain those motions when we assumed the earth was the center of the solar system. Once we tried putting the sun at the center it was much simpler to explain.

So I think both geocentric models (universe and solar system) are similar - we can't falsify them through observations - but in practice we do because the alternative is much simpler.

- Drelda
Click to expand...

I remember reading a bad astronomy article about the observations - retrograde motion and phases of Venus (where a new Venus is always larger than full Venus), and maybe Jupiter moons, that were indications that the solar system orbited the sun.

I agree you can always make your reference frame the stationary earth, but is seems the last 400 years of observations were direct evidence that we orbited the sun.

The OP worked out the speed of the farthest stars if the earth were the center of the universe (forget about relativity for a second). Just try Neptune and see what its speed would be. ;)
 
wollery said:
Then the answer to your original question is "Occam".
Click to expand...

All for that, but are you saying that Occam is the only reason for not assuming geocentrism? Maybe I'm misremembering, but for the solar system I thought we had some observations that made the earth centered solar system untenable.
 
slyjoe said:
All for that, but are you saying that Occam is the only reason for not assuming geocentrism? Maybe I'm misremembering, but for the solar system I thought we had some observations that made the earth centered solar system untenable.
Click to expand...
Well, you need to come up with a new gravitational model to account for the motions of the planets and stuff, but other than that...
 
drelda said:
If I understand Sol_Invictus's point correctly - we didn't rule it out through direct observation - ie we didn't observe any motions in the solar system that would be inconsistent with the earth being the center of the solar system.

However we did find it really hard to explain those motions when we assumed the earth was the center of the solar system. Once we tried putting the sun at the center it was much simpler to explain.

So I think both geocentric models (universe and solar system) are similar - we can't falsify them through observations - but in practice we do because the alternative is much simpler.
Click to expand...

That's not quite right. In our modern understanding, not only are both models consistent with all data, they are absolutely identical models. An imperfect analogy is the same book translated into different languages - except that always changes the meaning slightly, whereas this is truly, mathematically equivalent. That means that all physical predictions are identical - so data can only either falsify both or be consistent with both. It can never falsify one but not the other.

It's very similar to changing from Cartesian to spherical or rotating coordinates in Newtonian dynamics - the laws of physics (like F=ma) look very different in the two coordinate systems, but they are exactly the same laws, and make exactly the same predictions. Same goes here, just a bit more complicated.

wollery said:
Well, you need to come up with a new gravitational model to account for the motions of the planets and stuff, but other than that...
Click to expand...

It's not "new", it's just coordinate invariance.
 
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