# How would a torus world (donut shaped) have to rotate in order to have a stable day / night cycle in all of its regions?

In this universe, mass and gravity work differently so stable torus planets are possible (donut shaped).

How would a torus world orbiting a single star have to rotate in order to have a stable day and night cycle on all of its regions? For example if it was constantly in a horizontal position from its star and rotated as such, the inside of the ring would be eternally dark. So I believe its rotation would likely have to be both horizontal, vertical and complex so that all its regions would have similar constant day and night cycles.

Assume this torus world has a total surface area similar to Earth's, a similar distance from its sun, 12 hour days and nights, etc, etc. (If that information is necessary for any reason.)

• – Mołot Apr 20 '17 at 16:09
• Ok so if you want some semi-serious reading, check out this article. – MozerShmozer Apr 20 '17 at 16:54
• You can have a toroidal sun pasisng inside it, expanding and coming back passing outside it – jean Apr 20 '17 at 20:26
• You don't need to change mass and gravity to make toroidal planets possible, you just need to put a sufficient spin on the torus. – Mark Apr 20 '17 at 20:30
• Plantes are donut shaped... stars are donut shaped as well? That would make astronomy observations very interesting :) – PaperBirdMaster Apr 21 '17 at 9:02

# A Day/Night Cycle for All Points

1. Lay the torus down so it's in line with the plane of its orbit. (That is, it's "laid flat".)
2. The planet must rotate about an axis that is perpendicular to it's orbit, like Uranus.
3. The planet must also rotate such that it's axis of rotation is always perpendicular to the orbit, like a tidally locked planet.

So yes, the planet is rotating about two axes, but one of them is rotating much more slowly than the other.

There is also the oddity that people on this inside will have "short nights" and "long nights," because the sun will be blocked by the far side of the planet (a short night) and then because the sun goes under their horizon (a long night). People on the outside of the ring will just have long nights. So the duration of a night will change based off of geographic position, but the duration of those night(s) will be consistent.

This will also result in 4 points which are in perpetual twilight, almost like the earth's poles in their summer. I suggest calling them the twilight lands.

# Spin it like a top

If you set it on its side so that one could see the sun through the hole in the middle from an orbit further out. then spin it around that axis, You'll have a day/night cycle similar to earth's. The outside will be normal, and the inside will have eclipses in the middle of each day.

Edit: Now that I think about it some more, the inside will spend most of their time in twilight. Either from the eclipse, or from all the light reflecting back at them from the ground "above" them.

• It seems like the north and south inner poles would be pretty dark... What happens to the center if you give it a wobble? I'm trying to visualize but I'm no good at this stuff. And of course the thickness of the planet matters, if you have a very thick planet and a very small hole the center gets almost no light anyway (like a deep mine shaft)... Now I want a donut. – user3067860 Apr 20 '17 at 21:11
• Except the sun shines right through that "mineshaft" twice a day. A wobble just extends or shortens the day depending on location, much like Earth. – amflare Apr 20 '17 at 21:39
• A couple of minutes of direct sun twice a day (for a very, very narrow mineshaft) seems to qualify as "not much" to me. – user3067860 Apr 20 '17 at 21:49
• Its not just a couple minutes, its ~50% of the rotational time. – amflare Apr 20 '17 at 21:52
• The bottom (center) is pretty dark when the sun isn't right overhead, which doesn't last for that long...definitely not half the day. – user3067860 Apr 20 '17 at 22:42

Orbiting a sun that is far away is always valid like amflare has stated but it is limiting. But if you are messing with physics, there's a few fun things you could do. Especially if the "sun" travels around the planet.

• The sun oscillates up and down shooting through the center of the torus. This would leave a cold outer edge and an always lit inner edge. You'd also have North Days and South Days.
• The sun (or suns) draw a helix or screw pattern as they loop in and out of the "hole" and also travelling around the circumference of the donut. The inner side would always be lit some amount each day though changing with seasons but the outside would have dark seasons.
• Skip a spherical sun completely and go with a varying size torus of heated plasma that goes up through the middle (while small) and travels around the outside (as a larger ring) before getting smaller to fit inside again. People on the outer edge would only see an arc of light sweep across the sky, the rest would see a ring. If planets have a stable shape as tori, suns might also follow the same pattern.
• You can get a figure-8 pattern through the hole as well. This page doesn't have a diagram of it, but goes into a lot of detail about torus shaped worlds. – Draco18s no longer trusts SE Jul 3 '17 at 4:32

I'll admit it. You nerd-sniped me on this one. I had to figure out what the day night-cycle on a toroidal planet was like. It happens to be that mapping a torus to a map is really easy, so after setting up a simple script in Blender3D, I was good to go. For reference, the top and bottom of the animated image is the smallest possible circle in the torus: ie the inside circle/edge.

First up, some axis (taken from some other website):

First up, spinning on the Z axis while the sun points at it from the side:

As you expect, we get a patch of brightness (the side facing the sun) while the rest of the planet is either facing away from the sun or shaded by the center.

How about we rotate it by 90 degrees so now the Z axis starts facing the sun and rotate it around the X axis (As per amflares answer):

Wow! That's fancy. The day and night goes in opposite directions depending on where you are. And that's not inside vs outside either (remember, inside is the top and bottom edge). You'll notice it creates a line twice a day. That's when it is 'face' on to the sun (sun is on the Z axis). You could live in that - the whole planet get's illuminated at some point during the day - but I have no idea how timezones will work. I feel that something would be pretty messed up here.

So let's try another tack. Rather than spin it along directly along an axis, let's give it a 45 degree tilt:

Aww. That's even more messed up.

Right, I'm out of ideas for how your planet should spin. I'd say go for the "spinning it like a top" - ie not around the hole.

• What if it is both 1 and 3? If the planet is spinning about its Z axis but the Z axis precesses about another in-between axis? If you've ever spun a coin on a tabletop and watched as it winds down and falls flat, the last spinning stage approximates what I mean. – Asher May 2 '17 at 15:27
• Bear in mind that spinning it along the Z axis at any time has no effect on the distribution of light/dark, only it's specific position. So it will look like the last one but sliding horizontally at a different speed. – sdfgeoff May 2 '17 at 21:20
• one reason it matters is that two axes of rotation also allows for two different rotation rates, allowing for seasons and even more interesting effects. A single Z-axis rotation may be considered a day while a full 'wobble' about the precessional axis takes five days or thirty days or 57.79 days. This would have varying effects. In fact, a tilted (with respect to orbit) Z-axis even without a wobble creates seasons on a toroid just like in a sphere. You'd even have regions where the sun doesn't set for several days in summer, etc. – Asher May 3 '17 at 1:32

This is a totally different suggestion but if you are messing with physics anyway....

Have the sun stationary in the center of an enormous torus and then rotate along the internal axis of the torus. It would rotate in a way that the outer edge would become the inner edge during the day.

Unless you handwave a lot of stuff through magic, landmasses would get closer together during the day and farther apart during the night. Because the outer circumference is larger than the inner.

This kind of world can only exist in a universe of magic or a universe with a super science race that has a really odd sense of humor.

I think you are mistaken about what is referred to as a "ringworld". Ringworlds are generally not torus (donut) shaped worlds that rotate on one axis and orbit on a different axis. Ringworlds generally are rings around a star, with an internal radius equal to the orbital distance. As such, they only need to rotate in one manner (about the star's center of gravity).

Day and night cycles are usually created by a smaller ring of alternating transparent and opaque segments that orbits inside the main ringworld at a faster pace.

If you're imagining a torus orbiting a star not at its center, it would also have to rotate along the axis tangential to the orbit in order to permit light to reach the far side of the ring. This axis would constantly be moving as the torus rotated about its own center of gravity to create the forces necessary to simulate gravity.

Edit: Thinking more about this second case, you could tilt the ringworld enough to let light hit the far side of the ring, then tidally lock the ringworld to the sun. Day/night cycles would come naturally by way of the ringworld rotating about its CG.

• Yes, I meant torus. I will edit the question to clarify. Thanks. – Noble Apr 20 '17 at 16:05