If an orbiting space station is built with extended arms that have a diameter of approximately 1 A.U. and then rotated at slow velocity the objects at the arms extremities will rotate faster than objects at the hub. The structure doesn’t need to be 1 A.U. (about 93,000,000 miles) but it’s a good size, it could be made one Earth diameter or even the distance between the Earth and the Moon, approximately 200,000 miles.
Obvious problems are getting enough material to build the arms, stress on the arms as they rotate, and finding enough space where you aren’t going to wipe out a major civilisation. But really, these are minor problems and don’t require any sort of exotic materials or special technology we don’t already have.
It will be interesting to observe the exhibit-able properties.
First, a small time dilation effect will be observable between the hub and the arm’s extremity.
Second, the biggest problem I foresee though, and one I am not sure how to figure out the effects of, is that the ends of the rotating arms will really be moving quite fast in relation to other parts of the structure.
What will that do to electrical wiring?
To the physical properties of the material that makes up the structure?
If one part of the structure is undergoing a time dilation effect, however minor, what will that do to the overall structure?
You have the paradox that certain parts of the structure will be older (or younger) than other parts of the structure?
You will also have the paradox that someone sat at the exact centre of the structure looking out along one of the arms will see the arm bending and trailing behind.
In fact, eventually someone looking from the centre down one of the arms should see the arm either disappear or detach itself from the structure due to the frame of reference getting further and further out of synchronization.
With a structure 1 A.U. in length, rotating at 1 revolution per hour, the rotational speed at the extremity would be equal to the circumference of the structure as it rotates. So 93,000,000 * PI This means that the rotational speed would be 292,168,116 miles per hour.
The speed of light in a vacuum is about 186,000 miles per second, or 669,600,000 miles per hour.
So the rotational speed of the arm would at the ends would be close to 43% of the speed of light.
At that speed the ends of the arms may require some sort of shielding to protect them from collisions with space dust, micro-meteorites, etc.
Interestingly if you think about it, isn’t the Earth itself undergoing some sort of effect such as this? A person on the equator is travelling faster, and hence undergoing a different frame of reference, to an observer at the North Pole.
Is this an inherent property built-in to relativistic physics that a single chunk of matter, i.e. the Earth, cannot undergo relativistic changes, or is it due to the mass of the Earth and the effects of gravity warping space-time?
Interestingly this structure would not necessarily be required to be rigid. It could be made out of a very strong “rope” (for want of a better word) and spun like a bolas. The center motion of a bolas does not appear to be a rotation of a constant fixed axis but appears, from observation, to describe an ellipse and is more of a circular back and forth motion very similar to how female breasts move in an elliptical orbit when a woman runs.
Any objects at the end of the structure could be sling-shotted in to space at extremely high velocities.
Or they could be sling-shotted at planets too, a 1,000lb weight travelling at a significant portion of c would impart enough energy to obliterate a major metropolitan area such as London. Though the calculations for the orbital mechanics may be beyond us at this time, thank goodness.