# What would make scientists realize that they are on a toroidal world?

In my story, a portal is opened from the Earth to an alternate world. However, this world is toroidal in shape and has a surface gravity equal to that of Earth. It rotates around an axis that goes through the center of the circle perpendicular to all major radii, and its day/night cycle (assuming that it is inclined enough relative to its star that all (or almost all) of the planet will see sunlight at some point in most day/night cycles. At the location where the portal opens, conditions are very Earth-like (1 atm of pressure with similar Oxygen, Nitrogen, and Argon concentrations, comfortable surface temperature, and 9.8+/-0.1 m/s² of surface gravity after adjusting for centripetal force) and the toroidal shape is not obvious (i.e. on the outer equator).

Some quick sketches of how it rotates (green torus is planet, yellow sphere is its star, black cylinder is the axis of rotation), distances and sizes are not to scale, that I made in about 2 minutes: The axial tilt of the planet may be increased as long as the rest of the planet is moved so that the axis still goes the same way, if that is needed to not have parts in perpetual shadow.

I know that this toroidal shape should not be able to naturally form, but assume that plot device/advanced aliens/a wizard made it stable

What aspects of this planet would tip off the scientists that it is not a sphere like Earth? Would they see something in their surroundings or would they not notice until they either went far enough to see the toroidal shape directly or went into space?

Note that I am not asking for some test to prove that it is toroidal, but rather, something that people would notice is different and would result in them doing those tests or conclusively knowing. It would also be preferable if an ordinary person with a high school education can understand this demonstration (though they need not be able to recognize it on their own or even have been taught in school about it).

• Two points: The first is that such a planet could not exist; it would be forced into hydrostatic equilibrium and form roughly a sphere, or a spheroid. Second, how large is this planet (both the characteristic diameters)? If they're compact enough, it's possible that people could just see the other side. – HDE 226868 Dec 16 '16 at 0:44
• First: Ignore that and assume that it exists regardless of whether or not it should. Second: the major radius is much longer than the minor radius, but I have not decided upon much more than that – Jarred Allen Dec 16 '16 at 0:45
• "toroidal in shape and has a surface gravity equal to that of Earth" - on which circle? Because, you know, gravity will vary. – Mołot Dec 16 '16 at 8:05
• Can you include a sketch on how it’s rotating? Perpendicular to all Major radii makes me think “donut on the turntable in the microwave” but that leaves half of it in darkness. Sunlight everywhere every day makes me think of how the donut must rotate to land frosting-side-down when it falls off the plate. – JDługosz Dec 16 '16 at 9:33
• Not to scale -- to be taken literally! That little 100mm wide planet would get rolled up in the Little Prince's Katamari in 5 seconds flat! – Cort Ammon Dec 16 '16 at 15:03

## 7 Answers

The outside equator of a toroidal world isn't locally much different from the equator of a spherical world.

Assuming a physically correct toroidal planet (ie. one that maintains its shape due to physics rather than unobtanium or magic), the most likely clue that something's wrong is varying surface gravity. In order to keep the toroidal shape from collapsing into a sphere, the planet needs a fairly hefty spin: for an Earth-like planet, on the order of a rotation every few hours. This translates into a 30%-50% change in apparent gravity between the outside equator and the poles.

Alternatively, someone sufficiently observant would notice that the horizon distance is significantly anisotropic: for the "hoop" planet modeled on the site I linked to, the horizon is about 8900 meters away in the equatorial direction, but less than 4000 meters away in the polar direction.

Since this is a physically-correct planet, variations in the direction of "down" will not be present: the planet is in hydrostatic equilibrium, and the surface is everywhere locally horizontal (give or take minor variations such as mountains and valleys).

Most of the really exciting stuff that happens on a toroidal world (doubled seasons, odd day-night cycles, etc.) happens on the inner surface, and if you're there, you can tell something's wrong just by looking up and seeing part of the planet stretching across the sky.

• you would see that for a large planet? – djechlin Dec 16 '16 at 2:25
• @djechlin, see what? – Mark Dec 16 '16 at 2:38
• the earth going into the sky. – djechlin Dec 16 '16 at 2:39
• Under good conditions, you can see through 100-200 km of atmosphere. The atmosphere of a toroidal planet is about the same thickness as that of a spherical one with the same gravity and pressure, so most of the space between you and the other side of the world is vacuum. Seeing the far side of the the torus is no harder than seeing the Moon from Earth. – Mark Dec 16 '16 at 2:42
• @djechlin: From your point of view, six thousand years of astronomy is just something that happened to other people, isn't it. – A. I. Breveleri Dec 16 '16 at 2:58

You would notice some odd things when travelling.

Take a point on the outside of the torus. Travel in a straight line in a certain direction relative to the surface, let's call that direction 'west'. After a while, you get back to the place where you started, but you're approaching it from the 'east'. This is what you would expect, because it is what happens on a spherical planet as well.

However, when you travel 'north', it will take a lot longer to end up where you started, and most shocking of all, you never cross the path you took the first time.

This clashes with a spherical planet, but it doesn't require much immagination to see that the path you took fits perfectly onto a toroid planet.

## Looking during the day

If the torus is small enough, the other side will be visible in the sky. In this case, during the day at some point someone on the inside of the ring is going to look up and see something looking suspiciously like a planet obscuring part of the sky. This can later on be confirmed by telescopes to be part of their own planet.

## Star gazing

If the torus is too large to see the other side during the day, anyone sitting out at night star gazing on the inside of the ring would find part of the sky occluded. Subsequent investigations with telescopes could provide incontrovertible proof they are denizens of a torus.

## Astute map makers

Eventually cartographers are likely going to try to map the planet, and at some point, they will inevitably discover something is not quite totally spherical about their home.

## Bad cellphone reception

Once cellphones are developed, people will most likely notice that at certain times and at certain places on the planet, they cannot receive a signal from the carrier's satellite. Due diligence will likely result in discovering the far side of the torus is occluding their cell satellites.

## Failed space launches

If rockets are launched from the inside of the torus' hole and unexpectedly run into the other side of the torus, they will discover the true nature of their home.

• However the OP pointed out they are on the outside of the torus. – colmde Dec 16 '16 at 8:32
• What about non failed space launches? – Destructible Lemon Dec 16 '16 at 10:32
• @DestructibleWatermelon Then I suppose they could still be left unaware of their toroidialness. – Thom Blair III Dec 16 '16 at 11:02
• You'd think they'd notice something strange about it's shape, even if they didn't see the hole... – Destructible Lemon Dec 16 '16 at 11:29
• "If rockets are launched from the inside of the torus' hole and unexpectedly run into the other side of the torus, they will discover the true nature of their home." +1 for the image of scientists scratching their heads 'dang! anotherone c=gone. I just don't get it!' – Orangesandlemons Oct 22 '18 at 12:09

## Watch the sunset

No education required

If these scientists are deposited on the outside equator of the toroid, they probably won't notice anything different. The sun will rise and set as it does on a normal planet. The rest of the torus is occluded by the ground under their feet. Further, the torus is large enough that they won't be able to visually confirm that "north" and "south" have a much smaller diameter than usual.

However, on the internal equator, just look up at midnight. There will be a huge illuminated stretch of green and blue "sky" above them. It'll be hard to miss. They will be looking across the hole at the illuminated internal equator. If they arrive before sunset or dawn, the sun will set much before it reaches the apparent horizon because the sun will be occluded by the spinwise or anti-spinwise portion of the toroid.

## Torus at Noon

(The renderings of my own make and I'm very new to Blender. Oceans and land will come later.)

## Assumptions

• The toroid spins at 1 revolution per day.
• The 9.8m/s^2 gravity is along the outer equator of the toroid.
• The axial tilt of the toroid is sufficient to permit sunlight to illuminate the entire internal face of the toroid. (Sunlight can get through the hole.)
• The toroid is large enough that the scientists can't see

Gravity will behave really, really weird.

Assuming no technology has been used to alter the natural way gravity works, you will have extremely strong gravitational difference between the inner side and the outer side.

When on the inner side, the opposite side affects you much more (gravity scales with the distance), but in the - from your point of view - upward direction. The extreme case would be the center of the torus where it would even cancel out (provided the mass distribution is somewhat homogeneous).

Thus it could be possible to "jump through" the center to the other side (if the jump is strong enough and the jumping person/vehicle can survive the trip.)

How to figure it out if you can not move to the inner side or even a point where the horizon starts looking weird:

Assume we are on the outer side, the torus is huge and movement is restricted.

1. Drop an object from as far up as you can and measure the falling time. (Repeat a few times to reduce the impact of errors)
2. Mark (from your position) two orthogonal directions.
3. For these two directions move as far as you possibly can (but an equal distance) and repeat the measurement. If one or even both measurements start to deviate significantly (5%+) something is very wrong with your world…
4. If no significant enough deviation can be measured, go back to your starting point,
• +1 for first answer to mention this #1 most important factor. If the planet's gravity did not cause it to collapse in on itself into a spheroid, this would be the most obvious clue, besides actually seeing the other side: gravity changing depending on where you're standing. You could even potentially orbit (unstable) the barycenter. If the planet had atmosphere, it could possibly extend all the way to fill the center of the torus. If the planet was rotating, the inner ring would experience centrifugal force. And what if you stand on the north rim? Do you fall towards the surface, or barycenter – IT Bear Dec 16 '16 at 18:48
• Since we are talking of a planet-sized structure here, you would fall back to the surface. However a slight shift in position to the barycenter would probably occur. If it would be noticeable for a human is doubtful. Great, now I will spend the day trying to calculate it. * nerdsniped * – fer-rum Dec 16 '16 at 19:07
• Assuming the gravity is strongest in the center of the torus, it would imply that as you go from the outer side to the inner side, you'll feel the ground become slowly steeper and steeper. It could go even up to the point where you'd never be able to see that it actually is a torus, and just assume you are on some kind of continuous large-scale mountain which stretches in a ring. Well, you'd have to climb in order to get to the inner side. Animals might have adapted to that, and the inner part of the torus planet could be well habitable. – Battle Oct 22 '18 at 10:17

Looking at the Horizon

Depending on the landscape you might even see the different curvature by looking at the horizon. If the planet is covered with a kind of desert where you can look in each direction without getting blocked by dust or fog one might notice from a point at the outside of the torus, that the horizon of two directions (lets say north and south like in Ezras answer) is more far away, than the horizon in the other directions (West and East). One might as well see different curvature at the horizon, assuming that the differences between the outer and the inner radius of the tourus are very large (i.e. that the "hole in the middle" is big enough to make a huge difference).

This does not proof, that the planet is a torus (and no scientist would assume that directly from this) cause there are other shapes with the same unequal curvature. But it might be enough to make them think about the shape and want them examine deeper into this.

Compass will be useless.

On a spherical space, assuming there's electromagnetism going on between the poles, you can always find one of the pole using a compass. No matter where you are on the sphere, if you follow "North" then you end up passing through the North's pole.

On the other hand, on a toroidal space, there's no such thing as a pole. Making compass useless. If you find something equivalent to electromagnetic pole, then you won't be able to reach it (assuming it's in the empty space inside the torus).

• Couldn't this just be a result of a spherical planet having no electromagnetic field, so this would not be a hint to any such scientists. – Jarred Allen Jan 17 '17 at 4:36
• Jarred Allen's right that there are spherical planets without magnetic fields. However, if toroids can't have magnetic poles, that's a really interesting fact. Can you explain why they wouldn't? – Jetpack May 30 '18 at 17:56