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15:40
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A: A planet with a square orbit?

Anders SandbergLet us consider what forces are needed for a square orbit. As Newton pointed out, as long as there are no forces it will move in a straight line... so there must be no gravity along the sides. Then suddenly the moon turns 90 degrees, which implies a lot of force accelerating it. So there must be ...

J...
J...
Not that it matters because the four fixed corner assumption is physically impossible anyway, so there is no "in practice" to worry about. This can't happen.
Tristan
Tristan
@J... in principle we could have the four planets connected to each other by light rigid braces. If the planets are far enough apart the forces between them ought to be small enough that making the braces light enough is possible whilst maintaining sufficient rigidity. The actual limitation here would be getting enough material to produce the braces, as well as actually constructing them. It would also require that the planets have no individual rotation, but instead the entire assembly rotates as a whole (which may mess up the orbit, I'm not sure)
J...
J...
@Tristan Space is vast. I don't think you've considered the numbers. Fantasy will need to be invoked at some point to make this plan work. "Rigid" is not possible over such distances.
Tristan
Tristan
space is vast, but the forces between the bodies drop off fairly quickly. If the planets are far enough apart to barely be felt then the necessary station-keeping force from the brace is trivial. The braces could therefore have a tapering cross-section, being wide at the base mostly to support its own weight. This weight could also be used to provide some of the centripetal force needed for a rotating assemblage, allowing you to also cut the cross-section needed (similar to space elevators using the weight of the cable to keep the top in place)
you'd need an extremely empty region of space, and a loooooooot of material, and the ability to construct this assemblage on such a large scale, but in principle those are all engineering challenges not ones of physics, so it is not correct to say that the four fixed corner assumption is physically impossible
J...
J...
@Tristan Physics does not allow materials with the required properties. What you think of as "solid" objects aren't on this scale. Our intuitions are wrong in such an environment and you cannot use them to guide your thinking. Do the numbers. You could maybe achieve this for some time with small objects in an isolated void, but not stars or planets large enough to be called planets (ie: gravitationally self-rounded).
@Tristan "to provide some of the centripetal force needed for a rotating assemblage" - it can't be allowed to rotate or the squircle orbit becomes impossible.
Tristan
Tristan
15:41
are you sure rotating makes the orbit impossible? The exact details with obviously differ, but the same logic gone through in the answer itself ought to apply just as well to the rotating case
and obviously the situation wouldn't be able to last forever, this entire thing is dealing with unstable orbits to begin with, but given a light orbiting body, and the whole thing being distant from anything else then the only forces we need to concern ourselves with for the assemblage are from each massive object to the centre of the assemblage. This means our braces only need to resist compressive forces, and we don't have to concern ourselves with any bending forces
by moving the heavy bodies far apart, the compressive forces we need become as small as we like
so the only place for physics to come in here, is if it's impossible to build a sufficiently tall tower to reach from the massive body, to the centre of the assemblage
which definitely seems like an engineering problem, not a physics one
J...
J...
No bending forces? What do you think makes the planet turn around the corner? Have you calculated what torques look like on lever arms measured in astronomical units? Go do the numbers - don't trust me. It is impossible.

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