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Three natives who study their version of science on the surface of a large rotating habitat located in a cylindrical shape in the space between our solar system and Alpha Centauri, are trying to figure out the basic physics, equivalent of our Newtonian mechanics. How would they come to the truth of the matter?

Research thus far has included: a couple of 'Isaac Arthur' videos on the subject on Youtube, and a thorough reading of the Rama series by Arthur C. Clarke as well as the Ringworld books by Larry Niven, and an AIAA article entitled "Artificial Gravity Visualization, Empathy, and Design" by Theodore W. Hall. I also used 'SpinCalc' at this link by Theodore W. Hall.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ It really depends on how large the habitat is but if you look at the "sky" and see the curvature of the habitat, then it's pretty easy to tell the shape of the world they live on. $\endgroup$ – A. C. A. C. Nov 30 '17 at 17:16
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    $\begingroup$ @sphennings I disagree. Asking what ways are available with which to discover that one lives on an interstellar habitat is different than asking what an individual should do. $\endgroup$ – Stephan Nov 30 '17 at 18:18
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    $\begingroup$ Are you sure you want a hard science tag on this? $\endgroup$ – Mołot Nov 30 '17 at 18:27
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    $\begingroup$ Duplicate? How to hide the fact that you're in an O'Neill cylinder? $\endgroup$ – rek Nov 30 '17 at 18:30
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    $\begingroup$ You need to offer more details. What does day look like on this habitat Is there a pho-sun? Pho-stars? i.e point light sources? etc. $\endgroup$ – Firelight Nov 30 '17 at 18:42
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A "natural philospher" who studies his environment will notice effects consistent with a rotating habitat. The coriolis forces may not be noticeable with human senses if the habitat is big enough, but spring-based scales might be used to measure them. (This could grow out of efforts to assure fair weights in the markets or some such.)

Additional measurements could be made on a children's carousel or the like.

The "natural philosopher" would then have to come up with a consistent theory which matches the observable effects, and invent new experiments to support or challenge the theory. This might actually be easier than inventing Newtonian mechanics plus a theory of gravity, because gravity does not get in the way.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ Coriolis effect is only relevant to objects moving with respect to the rotating reference frame. A merchant in the market weighing something with a spring scale is not moving. A merchant on a boat is moving, but any changes in the weight would probably be too small to see over just the rocking of the boat. On a cylinder the centrifugal force is equal everywhere so it would be effectively unmeasurable. $\endgroup$ – Snyder005 Nov 30 '17 at 23:25
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    $\begingroup$ Remember the question is tagged hard-science. Such questions require a higher level of proof than normal questions. Sources should be cited to back up any claims. $\endgroup$ – sphennings Dec 1 '17 at 0:33
  • $\begingroup$ @sphennings, I explained that and how the scientific method applies. $\endgroup$ – o.m. Dec 1 '17 at 5:56
  • $\begingroup$ @Snyder005, once the "natural philosopher" has developed those springs he'd experiment with them in different conditions. $\endgroup$ – o.m. Dec 1 '17 at 5:58
  • $\begingroup$ @Snyder005 depending on the rotational axis wouldnt a scale at ground level measure heavier than if the user was closer to the axis (assuming up), this would in theory make an object lighter the higher it gets. $\endgroup$ – Mauro Dec 1 '17 at 13:14
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I'm assuming an enclosed cylindrical colony 600 kilometers across (so they can't just look up and see the other side of the world, or look out and see the stars rotating much too fast), and with no access to the endcaps. Such a colony would be rotating at 0.055 rpm, or about one rotation every 18 minutes.

Honestly, your medieval philosopher isn't going to be able to tell that this isn't a flat world. The easy test (drop an object and see where it lands) isn't precise enough: an object dropped from head height will land about 0.3 mm to the side of where it should, well within the medieval margin of error.

So let's move forward to the Renaissance, and have Galileo drop a pair of cannonballs off an Italian bell tower, 60 meters off the ground. We'll use a well-built tower rather than the Leaning Tower of Pisa, and, to make the effects obvious, we'll have him drop the balls off the spinward side of the tower.

There's a 0.17 m/s difference in tangental velocities between the top and bottom of the tower. The balls fall for three seconds, and then there's a pair of distinct "cracks" as they strike a balcony a third of the way up the tower, having drifted about half a meter anti-spinward (or, in a non-rotating reference frame, the colony rim rotated 5145.1 meters while the tower top, and the co-moving cannonballs, rotated 5145.6 meters).

Galileo's determined to prove that objects fall at the same speed regardless of weight, though, and he keeps dropping cannonballs off the top of the tower, trying to get them to hit the ground. He quickly notices that his ability to do so depends on which side of the tower he drops them from.

This information spreads to other natural philosophers, and when someone works out the equations of motion, those equations show distinct coriolis and centrifugal terms. These are the same equations that describe motion on a merry-go-round or other rotating object, and the conclusion is obvious: we live on a rapidly-rotating world. Since we don't go flying off into space, we must be on the inside.

(Incidentally, you can do the same experiment here on Earth, but the greater radius and slower rotation speed make the effect far more subtle. Galileo's cannonballs only drifted by about 10 mm during their trip down the Leaning Tower.)

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  • $\begingroup$ You don't need a Galileo to discover the rotating frame, you just need an archer who fires straight up in the sky. If the arrow goes up at 50 m/s (180 km/h), it will reach a hight of about 125 meters, which should be more than enough to witness the effect. The archer will also consistently witness the arrow turn in a specific direction due to moving horizontally for a moment. $\endgroup$ – cmaster Dec 1 '17 at 9:12
  • $\begingroup$ @cmaster, the air in the cylinder is co-rotating with the rim, and the arrow is strongly affected by aerodynamics. That's why Galileo is using cannonballs in his drop test. There's also the issue of precision: Galileo knows his tower is vertical relative to local gravity because it's a rigid structure that can be surveyed; if your archer is off in his aim by even a tenth of a degree, his arrow will come down half a meter away from him. $\endgroup$ – Mark Dec 1 '17 at 18:52
  • $\begingroup$ The aerodynamics will just slow the arrow in the direction of its travel relative to the air, not change its direction. And it's the aerodynamics that will make the arrow turn in a tell-tale fashion. You are somewhat right with your remark on the precision of this method. However, an archer aiming for a far-away target will notice that all arrows will be slightly deflected in a specific direction, and that he will need to correct for that effect. Hitting a target over a long distance will be quite a unique challenge in this world... $\endgroup$ – cmaster Dec 6 '17 at 8:40
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With medieval tech, they wouldn't have the concept of space. Their world would be the universe (everything there is). Their world is a cylinder. Everyone can see that.

They would likely not have any concept that the cylinder is spinning (no external frame of reference). However, unless the radius is huge, they would know that if you jump high enough, you will land in one direction (anti-spinward). They would likely have a name for that direction. So, there would be no need for a compass. Toss a rock high up in the air and see which direction it falls.

Math:

Word problem since I don't know mathlab:

The forces acting on a person standing on the surface is converted to a velocity vector in a direction tangential to the rotating surface in the direction of rotation. If we assume that the curvature is large enough to be essentially flat relative to the size of the jump, from a non rotating, out side perspective, he appears to jump in a triangle with each side composed of the combination of his jumping vector and the momentum imparted by the station with the top of the triangle being at the peak of the jump. If t is the time it takes him to reach the peak of his jump, 2t is the time for him to reach the ground. We take the hypotenuse of his jump to the peak and double it:

Djump = 2( sqrt (Dup + Dforward1).

If you compare that to the distance the surface moves:

2 x Dforward2,

you see that he travels a longer total distance jumping than the surface moves but, if you solve for Dforward, you will see that his jumping forward distance is shorter than the surface distance forward. the higher the jump, the more pronounced this will be.

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The only way for them to find out is if someone goes below the ground and finds a window in the floor or have someone or something tell them the truth.

Look at Gene Wolfe's The Book of the Long Sun series for an example of the type of society you are talking about.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ I think you're wrong about the anti-spinward jump. Your expectation seems to rely on the notion that the person (mid-air) will lose his sideways momentum, but I see no reason why you'd expect that. It's not due to air friction (since the air is rotating too, the least friction is encountered by moving along with it), nor general physics (as momentum is retained when no outside force acts on you). Can you elaborate on why you'd expect a sideways displacement during an upwards jump (from the native's perspective)? $\endgroup$ – Flater Dec 1 '17 at 9:43
  • $\begingroup$ (maybe I forgot to mention: notice that the atmosphere is rotating, not just moving sideways) $\endgroup$ – Flater Dec 1 '17 at 9:44
  • $\begingroup$ @Flater, rotating air: what in all of their experience and lore will tell them that atmosphere is not suppose to do that? $\endgroup$ – ShadoCat Dec 1 '17 at 18:35
  • $\begingroup$ @Flater, jumping: see my edit. $\endgroup$ – ShadoCat Dec 1 '17 at 19:03
  • $\begingroup$ From their point of view (rotating as well), the atmosphere isn't even rotating, so that's a moot question. We don't notice the rotation of the Earth either, because we're part of the rotation. I mentioned the air rotation not because they observe it, but because it means the natives and the atmosphere don't move relative to eachother (from a frame of reference of someone who's on the "ground" there) $\endgroup$ – Flater Dec 2 '17 at 16:49
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From your description of the rotating cylinder's habitat, it sounds like we can consider it to be in basic isolation. There are stars and such in the sky that appear to move in regular intervals across the sky, but they all just track half circle motions. This would be akin to watching the stars move in the sky at the Earth's equator.

The way to distinguish a non-intertial reference frame from an inertial reference frame would be to measure "spooky" unidentified forces that appear. In the case of a rotating reference frame, these would correspond to the Coriolis force and the Centrifugal force. In an inertial frame, the force on an object is

$F = m\vec{a} = m \frac{d^2\vec{r}}{dt^2}$

however in a rotating reference frame, this becomes

$F = m\frac{d^2\vec{r}}{dt^2} + [2m\vec{\omega} \times \frac{d\vec{r}}{dt}] + [m\vec{\omega} \times (\vec{\omega} \times \vec{r})]$

Where $m$ is the mass of an object, $\omega$ is the angular velocity vector of the rotating reference frame, i.e. how fast the cylinder is rotating and in which direction, and $\vec{r}$ is the position of the object in the rotating frame (note: I use $r$ to emphasize that, since this is a cylinder, the easiest coordinate system to use, for our purposes is the cylindrical coordinate system). Where there are two new terms (note: the $\times$ symbol above is a cross product, which is very important since we are dealing with position, velocity, angular velocity vectors). The first is the Coriolis force and the second is the Centrifugal force.

Deviations from Earth

It is very important to realize this is a different case from Earth. Many of the "spooky" effects of the rotating frame are easy to notice on Earth because one can change their distance from the rotation axis, e.g. by traveling from the Equator to the North Pole, and the direction of the force changes with respect to our horizon (ground).

Ex: Centrifugal Force always points outwards from the rotation axis. At the equator it points perpendicular to the ground (straight up in the sky). At higher latitudes, it will not be perpendicular. In our case, the centrifugal force will always be perpendicular to the ground.

Centrifugal Force

Probably the first to come to mind, if we look at the third term it depends on the objects position and how fast and which direction the cylinder is rotating. It will change the perceived force of gravity of an object by some amount and could theoretically be measured, given a knowledge of Newton's Law of Gravity $F=mg$, however it is most readily noticed by its varying effect due to changing an objects position. Unfortunately for your scenario, due to the cylindrical symmetry all points on your cylinder experience the same Centrifugal Force, and hence it is more likely that its effect would be folded into the gravitational force, i.e. $F=m(g + C)=mg'$ for some constant C

Coriolis Effect

This one depends on the rotation and the velocity of an object. You may be familiar with this causes objects to change from straight line trajectories when traveling West/East on Earth, but this does not occur at the Equator. What happens instead is that objects will deflect upwards or downwards, depending on if they are traveling the same direction or opposite direction to the rotation of the cylinder (see Eotvos effect).

What this means is the only deviation you could observe would be that the force of gravity would increase/decrease depending on which direction you were traveling in, by a magnitude:

$\Delta F = 2m\vec{\omega} \times \frac{d\vec{r}}{dt}$

The greatest deviations would be seen between an Westward and Eastward moving object. But how could you possibly measure this?

Measuring the Coriolis Effect

The magnitude is determined by how fast your cylinder is rotating and how fast your object is traveling. You can tune this to your liking for plausibility reasons.

  1. Measure with a gravimeter. Basically a spring with a weight on it, where you measure the compression of the spring to determine the gravitational force. Put it on something traveling west and something traveling east. This depends on the technologically prowess of your civilization, and likely your best bet for traveling object would be a boat. Things like waves would probably ruin any sensitivity your gravimeter had and the boat would be too slow moving.

  2. Measure changes in how fast things fall. I could envision an experiment where you fire a cannonball (or similar projectile) towards the East and measure the time it takes to fall (or distance it travels) and then repeating by firing the cannonball to the West. There will be difference in fall time/distance traveled, but the scale of this might be too small given other sources of error (such as elevation changes, precision of measurement).

Both of these greatly depend on what technology is available and how scientifically advanced your society is. Remember there are limitations to how fast you can spin your poor natives before they fly off or something. And more importantly there should be a reason to try some of these experiments. No one spends lots of time and effort on an experiment unless they expect to see interesting results, especially if they risk their reputation, or worse, their life.

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With a pendulum!

We had a similar problem on Earth, a long time ago- trying to convince everyone that the Earth rotated in a simple, intuitive way. Leon Foucault came up with the idea of using a pendulum to prove this- the pendulum swings back and forth, while the Earth rotates underneath it, often causing dominos or some other marker to be knocked over.

In your world, this might be discovered by the use of pendulum clocks. As your culture progresses, they might notice that these clocks lose accuracy over time. A large, easy to track pendulum is then built to be "the most accurate" and then the precession becomes large enough to see with the eye. This would trigger a whole debate about the Coriolis force.

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    $\begingroup$ That wouldn't work in a cylindrical habitat. A foucault pendulum does not precess at the equator, and in a cylindrical habitat, everywhere is the equator. They might be able to notice that pendula in different orientations have varying half-periods when swinging in one direction vs. the other, but that would require some fairly sophisticated (non-pendulum-based!) timing equipment. $\endgroup$ – Logan R. Kearsley Nov 30 '17 at 18:18
  • $\begingroup$ They measured gravity with pendulum clocks and determined the obliqueness of the Earth in Newton's day using the variations. I would think that's a harder problem than finding the radius measures from above rather than below the earth. $\endgroup$ – user25818 Nov 30 '17 at 20:26
  • $\begingroup$ If Foucault pendulums don't work right in cylindrical habitats then that's how I would know... except he lived in the 1800s. This question boils down to how to demonstrate a Coriolis effect or a lack thereof. +1 $\endgroup$ – Mazura Dec 1 '17 at 8:37
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They'd find out simply by observing their environment and then making deductions, sorry if that sounds trite I'll explain.

They'll have a day/night cycle but with no apparent cause. There's no sun to disappear under the horizon and no moon or stars to take its place. So why is there day & night the natives ask themselves ?

Likewise the seasons, how are they implemented and how do the natives observe them ? How did seasonal crops evolve with no apparent reason ? Why do animals hibernate ? Why do the local fauna have fertility cycles (spring) ?

Large bodies of water will mimic tides, but why would tides exist with no nearby planet or moon ?

If they observe their environment for long enough they'll have enough questions that can't be answered by observation or hand waved away by religion.

Medieval tech is reasonably sophisticated but resource intensive. This was a level of tech that was building cathedrals, pyramids and Stonehenge. They may not have had telescopes but they knew enough about astronomical observations and celestial mechanics to make accurate calendars and use them to plan the agricultural year ahead. Their lives literally depended on them being able to read the night sky.

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    $\begingroup$ You're confusing "primitive" with "medieval". They most certainly had telescopes in medieval times. It was the early age of steel, chemistry, and physics. $\endgroup$ – Stephan Nov 30 '17 at 18:21
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    $\begingroup$ Generally I agree with you, but pyramids were built in ancient era and Stonehenge exists for ages. We even don't know was Stonehenge built $\endgroup$ – ADS Nov 30 '17 at 18:39
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The only reason we ever stopped thinking we were the center of the universe was because the stars and planets didn't track neat lines across the sky. As a cylinder, all the stars would move in parallel lines, and with no other bodies to contradict the assumption, they would never have a reason to assume they weren't the center of the universe.

That said, it'd probably be pretty easy to tell it was a cylinder, as they could just walk to the edge and see the flat end caps. if they were inside, it's even easier, as you are completely enclosed.

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You need to read 'Orphans of the Sky' by Robert A. Heinlein. He gives one of the earliest descriptions of a generational ship including the detail that the passengers cannot see outside and, due to a mutiny, lose their understanding that they live inside a spaceship.

In this story the ship is rotating long-wise so each 'deck' has lower apparent gravity as you go 'up' and while the specifics for how you get a cylinder to rotate in such a way could be explained away as the writers prerogative, it could be easily satisfied by having the axis of rotation be in the middle where the other half is just never explored and can be of equal size / mass or it could be much smaller but contain lots have high-mass equipment so it just seems like the ship is flipping end-over-end. Regardless of that, even if you have the cylinder's axis of rotation go through the long dimension, the same physics would apply, apparent gravity would go down as you aproached the axis of rotation. The people inside might not be able to prove they are inside a starship but they would still have to explain why gravity changes based on location.

As Heinlein showed, humans are not just rational beings but quite as good at rationalizing based on incomplete data.

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In many ways:

  1. They could see the other side. Or the shadow on a moon or other stations next to them.
  2. They lived on another planet and know the flight path of projectiles should be different. That would be more of a feeling. Cause if you look at that tennis simulator you wouldn't say "Oh we are in a spinning cylinder" here. Maybe the answers from physics SE here help you.
  3. They could just walk along it until they came back to the beginning. And then measure there curvature.
  4. They find out that if you let drop something a given distance at different heights, it changes how much energy you get. You would just need clay and a heavy ball to prove that. So did we find out, that E=mgh (<-would be different for them) and E=1/2*m*v^2 (<-would be the same).
  5. They find a book about it and test/believe it. (When people today believe the earth is flat, you need for nothing proof -.- ) Maybe even only a children book that explains earth and easy experiments to prove the earth is rotating. They test it and it doesn't work. So now they wonder on what they live.
  6. The station wobbles and they get something like earthquakes.
  7. With MAGIC...Ahem, sorry, I mean SCIENCE. And you just don't explain more :-/

PS: They could find out gravity exists, but highly unlikely until they see stars and planets. Some experiments: https://www.youtube.com/watch?v=Ym6nlwvQZnE

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