# Would two people standing on opposite sides of a flat world be able to see the same constellations?

Quick drawing illustrating what I mean:

Two people (humanoids, between 1 and 2 metres tall) are standing on the ends (less than 1km from the edge) of opposite faces of a flat world (approximately 20km thick) and staring out into space. One of them describes the constellations they are seeing: a wolf, a feather, whatever people see in stars. Can the other person see the same stars?

I imagine that no matter the distance separating the two people, the answer will always be "Yes, as long as the stars are sufficiently far away", so I guess then the question becomes: how far away do the stars need to be in this situation?

• @AlexP Please don't answer in comments and then comment that another answer is wrong. Make this an answer, so it can be up- or down-voted. Oct 20, 2022 at 17:16
• @ZeissIkon: L. Dutch's answer is not wrong; on the contrary, it is correct, but incomplete. I would have downvoted it if I thought it was wrong. The comment is a suggestion of how to complete it. And my calculation is not an answer, it is just a calculation. Oct 20, 2022 at 18:27
• How is the structure moving? You asked for hard science, so it's important to know if it is rotating and through which axis. And the distribution of masses, so it is possible to know if it rotates with stability. If it rotates chaotically it will expose the whole sky to both people. farside.ph.utexas.edu/teaching/336k/Newton/node71.html Oct 20, 2022 at 23:57
• @BillOnne This world does rotate around two axes, so eventually both will be able to see the same constellations, but I was mainly asking about seeing them at the same time. Oct 21, 2022 at 9:54
• flat worlds have traditionally a dome above the disc with little lights as stars, so they would see completely different domes.
– ths
Oct 21, 2022 at 13:17

## Depends on how close to the edge they are

Overlapping fields of view of two observers on opposite sides of a disk world. The field where both observers can see an object is purplish sector; note that the farther away from the edge they are, the narrower the common sector is. Own work, available on Flickr under the Creative Commons Attribution license.

For clarity, let $$h$$ be the height of an oberser, $$H$$ the thickness of the disk, and $$d$$ the distance of the observers from the edge.

The angular size of the overlapping part of their fields of view is $$\alpha = 2 \arctan \frac {h}{d}$$

In the question, $$h$$ is given as 2 meters; so that

• if they are 2 meters away from the edge, the common field of view covers 90°;
• if they are 20 meters away from the edge, the common field of view reduces to 11°;
• at 200 meters away from the edge, the common field of view narrows to 2°; and
• at 1 kilometer from the edge the common field of view is a thin thin thin sliver of about 0° 14ʹ.

The distance $$D$$ between the edge of the disk and the nearest object which can appear in both fields of view is $$D = \frac {dH}{2h}$$ from considerations of similarity of triangles; in the question, the thickness of the disk $$H$$ is given as 20 kilometers, so that

• if the observers are 2 meters from the edge, the nearest object which they can both see is at 10 km from the edge of the disk;

• if the observers are 20 meters from the edge, the nearest object which they can both see is at 100 km from the edge of the disk;

• if the observers are 200 meters from the edge, the nearest object which they can both see is at 1,000 km from the edge of the disk; and

• if the observers are at 1 kilometer from the edge, the nearest object which they can both see is at 5,000 km from the edge of the disk.

The part of the surface going from their feet to the edge will shield vision of part of the sky, so their field of vision will only partially overlap, as you can see in the below schematic.

The shorter the distance from the edge, the larger the overlap. The limit, with both observer standing on the edge, would be the half sky in front of them. A would see something above their head which B would not be able to see because it would be under their feet.

In formulas, calling $$d$$ the distance from the edge and $$h$$ the height of the observer, they would miss a portion of $$arctan (d/h)$$ of their field of view due to the presence of the bottom. Their common arc of view would then be $$\pi - 2\cdot arctan (d/h)$$

• The overlap also becomes larger if the observers are taller. Oct 21, 2022 at 0:18
• In practice, on a flat world d/h is going to be massive though, there will be less than 1 degree of overlap between 2-meter tall people once you're farther than 229.18m apart. Oct 21, 2022 at 0:26

# Same Constellations?

Yes, they would see (practically) the same constellations along the band of sky they can both see. I assume this is the area you are talking about.

Otherwise, this is a trivial question: they would see different constellations outside of the swath of sky they share because there is a (another assumption!) sight-blocking planet between the two viewpoints. Since the internet has its fair share of pendants who take joy in pointing out the obvious, I ought to include this for completeness.

# How Far Until They're Different?

It depends. How far away are the stars? Are any visibly close to each other? How much movement in stars' position qualifies as "different?"

There a phenomena called "parallax." This is the driving factor for change in constellations in this question. Astronomers use this (and the Earth's yearly trip around the sun) to calculate distances of far away stars. Wikipedia informes us that heliocentrism was argued against because the parallax effect wasn't particularly observable at the time. This is, of course, no longer the case!

We could have stars easily disappear if they are (visually) close to another. However, for an observer on a non-megastructure planet (like Earth!) this isn't likely to happen. You can play with some numbers to figure things out a situation which works...

Consider, however, the sky as seen from our nearest star Alpha Centauri. Astronomers have calculated that the sky looks nearly the same at 4.37 light years away!

The take away here is that, for most sizes of things we consider terrestrial planets, even if it is disk-shaped, these two observers will see the same constellations. They would need to be radically far away to see anything different. (With the caveat of "while looking at the same section of sky.")

• Surprisingly, while people on a space ship near Alpha Centari will see more or less the same constellations as people on Earth, people in Puna Arenas (latitude 53° south) see (mostly) different constellations from people in Murmansk (latitude 69° north). There is band of constellations around the celestial equator which they can both see, there are northern constellations which can be seen from Murmansk but never from Punta Arenas, and there are southern constellations which can be seen from Punta Arenas but never from Murmansk. Oct 20, 2022 at 18:38
• @AlexP Nevermind being in different sides of a planet, I can do this in mere feet. By having two people stand on either side of a sufficiently high wall, you can cause different sets of constellations to appear for each person. Such situations are obviously not on topic for this question. Even cursory reading shows that it is concerning the view mostly in-plane of the disk. Oct 20, 2022 at 18:52
• They are on "opposite faces of a flat world". From the question. The very tall wall is the 20 km thick disk which separates them. Oct 20, 2022 at 19:15
• "the internet has its fair share of pendants" - must ... resist ... obvious ... bait Oct 21, 2022 at 14:56

How “flat” is this planet? Earth is flattened out a bit by its rotation and a planet spinning much faster would be much flatter. While the Earth orbits the stars in the sky shift because the axis of rotation differs from the axis of the orbit. Through the year a person anywhere on Earth could likely see all the same stars as someone else anywhere else on Earth. These two people might have to climb a small hill and/or clear out some trees to get a good view but it seems to me everyone on this planet will see all the same constellations.

If the axis of rotation, axis of orbit, and a few other parameters are such then it is likely that there are portions of the sky in which someone on one side can’t see what someone on the other side can. I’m thinking of the North Star and Southern Cross, two points of navigation in the sky. These points are helpful for navigation because we know what they look like and that they closely approximate the Earth’s poles painted in the sky. People in the northern half of Earth generally can’t see the Southern Cross. If close to the equator, at the right time of year, and on a hill or in a ship’s crows nest, then the Southern Cross is visible.

If the North Star and Southern Cross, or this flat planet’s equivalents, can both be seen where these two people are then it would appear to me that they see everything the other sees, just not at the same time.

How far away would a star have to be to be visible by both people? My guess is it has to be far enough away to not irradiate them to death. Dead humanoids aren’t going to be stargazing.

• There are substantial differences between northern and southern constellations: astro4dev.org/north-vs-south-constellations-moon-phases The Earth's "flattening" is only about one part in 300, far from the disk world suggested by OP: en.wikipedia.org/wiki/… Oct 21, 2022 at 16:42
• No, you cannot see all the stars from an arbitrary point on Earth; only if you sit right on the Equator can you see all the stars. For example, I live in Bucharest, at latitude 45° north; I can only see those stars which are north of 45° south. From Bucharest I can never see the Southern Cross, the Toucan, the Chameleon, or the Peacock. To be able to see the Southern Cross (of which the southernmost star is at 64° south) I would need to travel at least 20° south, 1200 geographical miles, to Aswan, the ancient Syene. Oct 21, 2022 at 18:12
• @AlexP My comment of seeing all the same stars was assuming given enough height. The further from the equator the higher one needs to be. At the poles the heights required would be incredible but at least theoretically sound. Oct 22, 2022 at 1:47
• @MacGuffin “The further from the equator the higher one needs to be.” — If you account for the axial tilt, anyone between the tropics of Cancer and Capricorn is eventually able to scan the asymptotically whole sky over the course of a year. Exactly on these tropics some objects will show up only once a year for a split second over the reference horizon, which may happen during daylight; the Earth is not the reference geoid too. Realistically, move a few arcminutes closer to the equator. But that's still quite a wide belt! Jan 7, 2023 at 1:38