Gravity in a world of infinite cylinders?

[Pds314]

How would Newtonian gravity behave in a world where everything is an infinite wire? Clearly the escape velocity would be infinite with only inverse distance as the strength, but could there still be functioning orbital systems inside this world? Would there be such a thing as escaping an object to get to a different? How would the orbits work?

[Entropian]

I think orbits would still function relatively normally, with an orbit around the axis of the cylinder.  There's a parallel to this in Coulomb's Law, just instead of Coulomb's constant and charges, you have the gravitational constant and masses.  Relevant link: http://farside.ph.utexas.edu/teaching/302l/lectures/node26.html

[Silavite]

Perhaps I'm misunderstanding the question, but I think that the dynamics of a world wherein all bodies are cylinders (whose the length approaches infinity) would simply collapse into the dynamics of a 2-dimensional system wherein all objects are circular.

[OHara]

Well, if the cylinders are somehow constrained to remain parallel, then yes the dynamics are the same as 2-D gravity.  But with force decreasing as 1/distance rather than 1/distance² , 2D gravity is different. 

The energy required to pull bodies apart increases without bound as log(distance) so as Pds314 says there is no escaping a body.

The orbits are no longer ellipses (but I think flattened at the far side -- probably someone will do the numerical integration and post an example).

The long axis of an eccentric orbit will no longer stay in one orientation (because the Lenz vector is no longer conserved) so the orbits will draw more complicated patterns.

[RCgothic]

I don't think it works as a universe. It's not stable.

One perfect perfectly long infinite wire, axial forces cancel out. But if it curves even a little bit, gravity will bend it. The system collapses.

Two perfectly parallel perfectly straight infinite wires can orbit each other as in 2d. But the moment they become not-straight or not-parallel they collide. The system collapses.

But until it does, axial momentum of a smaller object orbiting a wire would be conserved. You'd get orbital spirals. Circular or elliptical orbit would be a special case of zero axial momentum.

 

 

Edited August 25, 2020 by RCgothic

[Nuke]

if the cylinders were infinite then you wouldn't be able to localize gravity to a single point, all gravity sources become line sources. in addition all cylinders would have infinite mass as they have infinite volume. this would cancel out their infinite gravitational attraction. likewise changes in orientation would be impossible as they would have infinite moment of inertia (not sure if thats the right math terminology because moi is not a scalar quantity) and thus no amount of torque can change a cylinder's angular momentum. all in all it would be a very boring universe. if objects of finite volume also exist, then they might have some interesting orbital mechanics provided the gravity field is not infinite everywhere. 

Edited August 25, 2020 by Nuke

[sturmhauke]

Help us, @illectro, you're our only hope!

[K^2]

13 hours ago, Entropian said:

I think orbits would still function relatively normally, with an orbit around the axis of the cylinder.

There's much you get to keep with inverse distance gravity, but orbits stop being closed. So if you're in nearly circular orbit, yeah, these will work pretty similar to normal ones. But orbits that aren't circular are going to be pretty chaotic. You still get energy and angular momentum conservation, so objects still stay within a distance range, but you no longer get fixed points where they reach these distances.