# Celestial arrangement for the Cube World

An earlier question here concerning a cube-shaped planet got me thinking.

Suppose an artificial world-sized engineering project as described in this answer

The K-II civilization that built it would stock it with interesting life, just as we would fill a garden pond or terrarium. If that civilization still exists, they would be watching.

What kind of mechanical arrangement could provide for different planetary analogs on each face? I'd like to have regular sunlight (like ours) on 4 faces, with rising and setting. But, 2 faces have red dwarf suns that are fixed in the sky.

For example, the planet could be in orbit around a neutron star, with the main sun at a trojan point (L4) and a red dwarf in L1.

The problem is that the planet's axis won't turn to stay pointed at L1. In general, the planet rotation needs to be roughly in the same direction as its orbit, to keep the 4 "belt" facets turning under the sun.

There are things like statites to allow something to hover over the pole, and that could be a mirror to implement the red dwarf. But, I want something more durable. It should be stable over geologic time with minimal corrections.

The stars themselves don't have to be normal. They can be (relatively) low-mass and nearby constructed suns, so there is some flexibility in the mechanics. I don't even mind having them turn on and off! A constructed sun would still be too large and heavy to simply orbit the planet: the planet would be lighter.

Any ideas on how to arrange things? The big problem is how to keep something unmoving when everything is moving to remain in orbit.

If the planet were locked with its orbit than the near face would be non-moving. So how do we get sun movement over 4 other faces? I like the idea of a statite or some less durable implementation for the second red face, and this has indeed been lost before the present time in the story.

I don't mean to allow the motions to be arbitrary, still powered by mysterious means. The system should work according to normal laws of gravity and mechanics, once it has been set up.

So the example, "The problem is that the planet's axis won't turn to stay pointed at L1." Is problematic because "just making it turn" via unknown technology is not a hard-SF answer. I want a mechanical system that will move naturally according to known laws.

• Does the system get simpler without the red dwarfs? Instead of rotating the cube world so that it has two dark sides, couldn't you rotate the cube between opposing corners and get all six sides illuminated? – Green Jul 29 '15 at 23:45
• I want one or 2 sides to be very different, as an environment for a radically different planet. – JDługosz Jul 30 '15 at 0:11
• Can't they create a Dyson cube around your planet cube? the idea is allowing sunlight to ricochet inside and each panels can orientated itself to control amount of light. – user6760 Jul 30 '15 at 2:26
• If world is build, why to bother themselfs with unnecessary complicity, Just build 6 thermonuclear reactors - make sun's from them, for each side. You will have control over intensity. Reactors are open, 95% radiation, in form heat visible light etc will illuminate sides without conversion etc. Just start reaction and keep it going. Make moon from fuel, will be enough for long long time. – MolbOrg Jun 16 '16 at 2:05
• @MolbOrg How do you keep them in place? Unlike a normal star, will it last for geologic time without a repair man? – JDługosz Jun 16 '16 at 2:10

Cube orbiting a neutron star tidally locked no rotation.

Red stars* at the L1 and L2 points with a yellow star* in a polar orbit of the cube.

*Assuming you can make artificial star like objects much smaller than the planet.

• I'd worry about having an artificial star that can last for millions or billions of years with out the curators taking care of it. I like the idea of the yellow sun not being the central mass in the system. – JDługosz Jun 17 '16 at 14:57
• Btw, what are you using to draw the picture? – JDługosz Jun 17 '16 at 14:57
• That picture was made using Microsoft paint – Josh King Jun 17 '16 at 14:59
• Oh, problem: the orbit of the yellow fake-star will not turn to match the synchronous rotation of the cube. The yellow circle will stay in the same plane. – JDługosz Jun 17 '16 at 15:00
• The yellow orbit would need a slight precession equal to the cubes orbital period so it would line up over the cube throughout it's orbit. It would take some precise orbital tuning to make it all work perfectly, but entities capable of building the cube and mini suns should have no problem with it. – Josh King Jun 17 '16 at 15:31

Assuming that this cubic planet has a uniform mass distribution within its volume, it will not have a uniform gravitational field like that of a spherical body or a point mass, significantly complicating all orbits but geostationary ones. The variable gravitational field as the planet spins will also nudge objects out of the L1, L2, and L3 Lagrangian points, as these locations are dynamically unstable.

The two red dwarfs could be of equal mass and sit in circular orbits around their mutual center of mass. The binary red dwarf pair orbits in a plane perpendicular to its orbital plane around the star. The planet would be located at the center of mass around which the stars orbit, but the stars would really be orbiting each other because the planet's mass is negligible. The stable point at which the planet sits is like the L1 Lagrangian point The stars could then turn on only when they were over the poles (or only over one pole). This would produce a day/night cycle at each pole. However, the red dwarves would produce frequent eclipses of the primary star during two periods each year (when the orbital plane of the red dwarf binary is aligned so it passes through the primary star).

However, as there is no known mechanism allowing the stars to turn off, so one could instead have a large plate made of something like graphene orbit each star. Each plate would have an orbital period of half that of the binary star pair, phased so that it would block the star when its orbit went over the non-polar faces. As the plates would orbit symmetrically, the force on the planet from the plate orbiting one star would be cancelled by the force from the plate orbiting the other star. If red dwarf lighting is only desired at one pole, then the plates can have orbital periods equal to that of the red dwarf binary. However, the dwarves might be visible in the skies above the non-polar faces in this arrangement. I am also not certain of the ability of the graphite plates to resist tidal forces.

If one wants continuous polar illumination, no eclipses, and doesn't like having the planet at a point where it is vulnerable to small external perturbations, a different solution is required: Place red dwarves at the planet's L4 and L5 points (although given the mass ratio, it is maybe better to describe the planet as being at the Lagrangian points of the stars). Then place a pair of large parabolic mirrors at the planet's L2 point. The mirrors should be connected to each other so that they move and rotate as a single object (they are too far away from the star and planet for tidal forces to matter much). The mirror pair will have a rotational period equal to the orbital period of the planet, so that they will always point at the red dwarves. Inside each parabolic mirror, a secondary mirror near the focal point would concentrate the light into a beam. The beam from each parabolic concentrator would be directed out a hole in the back of the primary mirror, and reflect off of a planar mirror to direct it out perpendicular to the ecliptic plane. A rod made of something like carbon nanotubes would be attached to the mirror pair along its rotational axis and also extend perpendicular to the ecliptic plane as far as is structurally feasible. Mirrors at the ends of this rod will direct the light beams from the two planar mirrors into the atmosphere over the planet's poles. The atmosphere could then diffuse the light and refract it downwards. Illumination on the polar faces would vary in both angle and magnitude depending on the time of day due to the cube world's rotation and non-spherical atmosphere. Polar lighting would always be at a low angle to the horizon and would be largely indirect. The mirror system has no moving parts and is a single object. However, a system of reaction wheels and ion thrusters is required to keep it in orbit in the long run because the L1 point is dynamically unstable. Perturbations would come from moons of the cube world or from any other planets.

• "Assuming that this cubic planet has a uniform mass distribution within its volume," it does not. As described in the linked post, it is hollow with mass concentrations in discs on each face, slightly thicker around a rim of each disc. The corners don't contribute much to the mass, so I suppose I can address that with other details designed to make the mass appear to be nearly a spherical shell, and uniform with radial symetry along the axis of rotation. Thanks for pointing that out. – JDługosz Aug 1 '15 at 7:17

You can 'roll' the cube along its orbital path while rotating it on the axis perpendicular to the ecliptic plane.

I really wish I had a way to easily animate this, but I don't, so we'll take it in steps. If you have a cube handy to hold this will be simpler to picture. Holding the cube upright, rotate it so it spins to the left (or right). Now while keeping that rotation, turn the cube end over end making sure the four sides seen during the rotation remain facing you. Got it? Now, your face is the center star, keep doing what you're doing and spin in your chair. The four sides are seeing sunrise and sunset (with a slightly strange sun path in the sky) and the top and bottom are rotating in order to move with the orbiting red dwarf suns.

I haven't looked at any math for this but intuitively there is some ratio of rotations and rolls that will work and many that will not work, but I think there are rotation and roll angular velocities which that will allow it.

Am I totally off or should I try to animate it?

• Without applying torque, the body will only rotate along a single axis which is fixed in space. How do you get a "rotation and roll"? – JDługosz Jul 30 '15 at 0:12
• This site paulrhayes.com/experiments/cube-3d might help with visualization. It easily shows rotation on two axii. This is a fascinating question. I wish I could contribute more. – Green Jul 30 '15 at 1:31
• I can imagine a cube moving in such a manner. It's just not something that occurs without power and internal stresses. The angular momentum of the cube should be a constant. In the example scenario I can certainly imagine turning the axis to keep pointing to the center, but that's not unpowered natural motion. – JDługosz Jul 30 '15 at 7:20
• @JDługosz Does it need to be unpowered? – Samuel Jul 30 '15 at 7:22
• Yes. It should run like clockwork for millions of years after the builders left. It's also a matter of how much power that would take: do you realize the size of the rotational inertia of a planet? – JDługosz Jul 30 '15 at 9:59

I suggest a system somewhat different from Josh King's answer, but instead of one red star being closer to the center of mass of the system, have them both along the same vertical axis as your cube world, which also rotates about its vertical. This trio then orbits synchronously with a Sol-sized yellow star around an extremely massive black hole, neutron star, what have you, near the center of mass of the whole system. Here is a conceptual (not to-scale) rendering:

Here the yellow star and the red ones would each be on the order of 1 AU from the cube world, which itself would be several (dozen? hundred? Whatever it takes...) away from the supermassive center of the system. So long as the yellow star and cube-red-stars system complete their orbits about the center in the same period, this should achieve the desired effect without any need of artificial stars.

• What keeps the red stars in such a formation? I’m missing something. – JDługosz Aug 5 '16 at 22:43
• I suspect you could pick orbital elements such that those two red stars have an identical orbital period to the cube world, but in that case, the two red stars won't be maintaining their position relative to the cube world (and you will have all sorts of issues with making the system long-term stable; even long-term enough for a planet to be able to form). If the bulk of the mass in the system is in the super-massive black hole (or whatever), then everything (including the stars) will be orbiting the SMBH. Orbital mechanics is unintuitive (only?) if intuition equals Earth-based expectations. – a CVn Aug 5 '16 at 22:59
• And I won't even start on the issue of the black hole's accretion disk and what it'll do to the planet... – a CVn Aug 5 '16 at 23:00