[Tom Bishop]

Sometime back Sandokan had suggested that the acceleration and speed buildup in UA might seem more reasonable if the Earth was undergoing circular motion on a very large scale at an unnoticeable radius. I assume that he had meant something like this:



The Earth is presumably in some sort of cosmic flow or vortex. In this way the Earth does not really gain speed in relation to the rest of the universe after making a complete circuit around the phenomenon.

[Roundy]

In this way the Earth can continually accelerate, but not really gain speed in relation to the rest of the universe as it moves around the phenomenon.

Interesting but it seems unlikely to me. Can you show math demonstrating that this circular motion would cancel out the appearance to the rest of the universe that it's gaining speed? I'm having trouble picturing how that could work.

[JSS]

Sometime back Sandokan had suggested that the acceleration and speed buildup in UA might seem more reasonable if the Earth was undergoing circular motion on a very large scale at an unnoticeable radius. I assume that he had meant something like this:



The Earth is presumably in some sort of cosmic flow or vortex. In this way the Earth does not really gain speed in relation to the rest of the universe after making a circuit around the phenomenon.

If it's going in circles and accelerating wouldn't it still continue to get faster and faster?  Even in a circle, constant acceleration will build up.

However if you tilt the plane of the Earth 90 degrees so it faces upwards to the center and then spin it around at a constant speed and somehow kept it tethered to the center of the phenomenon or carried around by the vortex, you could have 1g of force applied downward at a constant speed. At the scales involved, I'd guess the Coriolis force would be immeasurably small and wouldn't be an issue.

[BRrollin]

Sometime back Sandokan had suggested that the acceleration and speed buildup in UA might seem more reasonable if the Earth was undergoing circular motion on a very large scale at an unnoticeable radius. I assume that he had meant something like this:



The Earth is presumably in some sort of cosmic flow or vortex. In this way the Earth does not really gain speed in relation to the rest of the universe as it moves around the phenomenon.

Interesting. So is the idea that the earth still undergoes UA as it travels the path? Or is in uniform circular motion?

I ask because if you rotate the plane of the earth so that looking “up” from the surface would be at the circle’s center, then we could have the correct weight one earth and never face the “relativity” problem.

This would work too - the math would hold. Of course, this also insists that the Earth is finite - since one cannot have an infinite plane rotating about a finite radius of curvature - this would introduce additional forces as one travels away from the North Pole - in the single pole model, anyway.

Thanks Tom! This is very interesting to think about.

/edit - I see that JSS arrived at the same idea as I while I was composing this message. Apologies for the re-statement and duplication. JSS was first.

[Tom Bishop]

Yes, the acceleration speeds would build up in the circle, but to the rest of the universe there are no drastic (relational) speed changes. Look at this diagram:



In relation to Points A and B the xy coordinates are the same after a complete circuit.

It would be like spiraling into a black hole. The speeds increase locally to extreme rates, but that would be unrelated to the outside universe.

[Tom Bishop]

I suppose that it is possible that Sandokhan actually meant that UA is caused by circular centripetal force, like when swinging a bucket around, and the water stays flattened against the bottom.



If this is what he meant, then perhaps it is possible that the Earth is the bottom of the bucket, moving at a constant speed around the circle, with a 9.8 m/s/s imparted in g acceleration.

[BRrollin]

I suppose that it is possible that I am misinterpreting what Sandokhan meant, and that he meant that UA is caused by circular centripetal force, like when swinging a bucket around, and the water stays flattened against the bottom.



If this is what he meant, then perhaps it is possible that the Earth is the bottom of the bucket, moving at a constant speed around the circle, with a 9.8 m/s/s imparted in g acceleration.

Yes, this is what I think JSS and I meant when we suggested rotating the Earth. I think the math would work for this version, but I’m worried about the previous version (see your penultimate post).

In the previous version, then the translational speed still increases, and so this wouldn’t  fix the relativity issue.

I think one interesting consequence of the “bucket Earth” is that it should impose a constraint relation on the uniform circular speed and the radius. That is:

g=v^2/r.

Since we want to feel g on the surface, then the square of the speed divided by the radius of curvature must equal this value.

Do you have any thoughts on what either of these two values might have to be, roughly?

[TomInAustin]

Yes, the acceleration speeds would build up in the circle, but to the rest of the universe there is no drastic (relational) speed changes. Look at this diagram:



In relation to Points A and B the xy coordinates are the same after a complete circuit.

It would be like spiraling into a black hole. The speeds increase locally to extreme rates, but that would be unrelated to the outside universe.

I guess this would have to include all of what we call the visible universe?

[BRrollin]

Yes, the acceleration speeds would build up in the circle, but to the rest of the universe there is no drastic (relational) speed changes. Look at this diagram:



In relation to Points A and B the xy coordinates are the same after a complete circuit.

It would be like spiraling into a black hole. The speeds increase locally to extreme rates, but that would be unrelated to the outside universe.

I guess this would have to include all of what we call the visible universe?

I’m not following. Why would it need to include all that?

[JSS]

Yes, this is what I think JSS and I meant when we suggested rotating the Earth. I think the math would work for this version, but I’m worried about the previous version (see your penultimate post).

In the previous version, then the translational speed still increases, and so this wouldn’t  fix the relativity issue.

I think one interesting consequence of the “bucket Earth” is that it should impose a constraint relation on the uniform circular speed and the radius. That is:

g=v^2/r.

Yes, that is exactly what I meant by my post, using centrifugal force for gravity while moving at a constant rate. I ran some calculations in another thread about what speeds would be required to orbit a Flat Earth around the Sun in this as well as some details on how to work with that equation that might be helpful for reference.

[TomInAustin]

Yes, the acceleration speeds would build up in the circle, but to the rest of the universe there is no drastic (relational) speed changes. Look at this diagram:



In relation to Points A and B the xy coordinates are the same after a complete circuit.

It would be like spiraling into a black hole. The speeds increase locally to extreme rates, but that would be unrelated to the outside universe.

I guess this would have to include all of what we call the visible universe?

I’m not following. Why would it need to include all that?

Becuase if we were zooming around a circle our view of the universe would constantly change right?   Stars would be useless for navigation etc

[BRrollin]

Yes, the acceleration speeds would build up in the circle, but to the rest of the universe there is no drastic (relational) speed changes. Look at this diagram:



In relation to Points A and B the xy coordinates are the same after a complete circuit.

It would be like spiraling into a black hole. The speeds increase locally to extreme rates, but that would be unrelated to the outside universe.

I guess this would have to include all of what we call the visible universe?

I’m not following. Why would it need to include all that?

Becuase if we were zooming around a circle our view of the universe would constantly change right?   Stars would be useless for navigation etc

I see. But if the circle was large enough then maybe our view wouldn’t change noticeably even over long periods of time. I think that is kind of the point of the model.

[Bikini Polaris]

Yes, the acceleration speeds would build up in the circle, but to the rest of the universe there are no drastic (relational) speed changes. Look at this diagram:



In relation to Points A and B the xy coordinates are the same after a complete circuit.

It would be like spiraling into a black hole. The speeds increase locally to extreme rates, but that would be unrelated to the outside universe.

Black holes are very precise objects that exist due to gravity, if you allow for their existence you are basically saying that earth's gravity is mainly due to mass. You cannot admit them in FE models. That said, acceleration in our own framework would still build up and our kinetic energy would be increasing constantly, and that would maybe refute external structures helping the rotation.

But, I LOVE the bucket theory of gravitation! It has many less issues than UA!

[Tom Bishop]

There is a centrifugal force calculator where you can play around with the fields and get some possible values for a centrifugal acceleration of 1g.

https://www.omnicalculator.com/physics/centrifugal-force

(Mass field can be any value and won't affect acceleration or velocity fields)

Centrifugal acceleration: 1g
Tangential velocity: 100,000 mph
Radius: 126,626 miles

Centrifugal acceleration: 1g
Tangential velocity: 250,000 mph
Radius: 791,413 miles

Centrifugal acceleration: 1g
Tangential velocity: 500,000 mph
Radius: 3,165,652 miles

Centrifugal acceleration: 1g
Tangential velocity: 1,000,000 mph
Radius: 12,662,609 miles

Centrifugal acceleration: 1g
Tangential velocity: 2,000,000 mph
Radius: 50,650,437 miles

[Longtitube]

There is a centrifugal force calculator where you can play around with the fields and get some possible values for a centrifugal acceleration of 1g.

https://www.omnicalculator.com/physics/centrifugal-force

(Mass field can be any value and won't affect acceleration or velocity fields)

Centrifugal acceleration: 1g
Tangential velocity: 100,000 mph
Radius: 126,626 miles

Centrifugal acceleration: 1g
Tangential velocity: 250,000 mph
Radius: 791,413 miles ..................

...

...

That calculator is a good find! I ran your figures through it myself to see how long each rotation would take:–

Tangential velocity (Tv) 100,000mph    Revolutions per year (Rpy) 1101  which is about 3 a day!
Tv 250,000mph    Rpy 440.45
Tv 500,000mph    Rpy 220.2
Tv 1,000,000mph      Rpy 110.1
Tv 2,000,000mph      Rpy 55  (6.64 days per revolution)
Tv 20,000,000mph    Rpy 5.5 (66.4 days per revolution)
Tv 200,000,000mph  Rpy 0.55 (1.88 years per revolution)

I think 1.88 years per revolution is still a bit quick to not notice. However, the last calculation is:–

Tv 671,000,000mph which gives 0.164 revolutions per year, or about 6 years per revolution

– but this is an upper limit to the period of revolution, because it's a fraction short of the speed of light in a vacuum.

I hope I haven't made any glaring arithmetical error here...

[Regicide]

Just be warned however, if this is considered for the explanation, there would be some observable differences between this and a linearly accelerated plane/ gravitationally correct planet. Check out this video for a quick and easy demonstration of the anomalies caused by centripetal acceleration.

I know that if the circle was big enough the anomalies would be hardly noticeable, but they would still be observable.

[Longtitube]

That's really weird on the small laboratory scale. On a smallish scale, dropping an object would show oddities too – it wouldn't fall vertically. It might be interesting to find out at what scale that wouldn't be measurable.