# Sun-like sky objects in a flat world?

I'm positing a non-planetary world but within Euclidean space. This world has things that resemble mountains (but probably not plate tectonics). Elevation varies considerably, but on average it is perfectly flat as far as any inhabitant could tell. If they were to do the various experiments Flat-Earthers should do, they'd discover that their world wasn't spherical.

Inhabitants experience "falling" which gives approximately 1G of acceleration. But if the extent of the world is infinite, true gravity would have collapsed this into some sort of singularity, so it's probably not gravity as we know it.

There are no stars in the sky, or any typical astronomical bodies. This causes a deep black darkness which is only broken up by a strange phenomenon... appearing out of the eastern sky is a giant fireball that streaks across the sky to the west. It is visible for a long time as a faint bright dot (the inhabitants call these stars) before it appears directly overhead (or close enough to it) to provide a period of several hours with "daylight" and warmth. When it is overhead it will appear far larger, but as soon as it does it starts receding into the western sky where it is visible as a "star" once more.

If this world has periodic day/night cycles of approximately 24 hours, can anything be inferred about the size of the "sun" or its altitude? For how long will the eastern and western stars be visible in the night sky before they're too faint to perceive with human eyes (assuming no obstructing mountains/elevation on the horizon)? How far north/south can one travel before it is perpetual night or they freeze to death? Are future suns visible in the east during daylight (and past suns in the west)? How fast do these suns travel? What color are they, can they be roughly the color of our own sun?

How much can any of these things vary without the people on the surface being wiped out (either by a sun flying too low/slow and frying them, or their world freezing, etc)?

• @Bitterdreggs. No. They only move in one direction. There are just many of them. Several might be visible at once especially at "night". They're not orbiting (or being orbited around), and it wouldn't be clear what keeps them in the air, so to speak. – John O Jan 24 at 17:59
• Ok, if you want there to be an infinite stream of suns passing over your world, so what is the actual question? Could you narrow it down from the five that you ask. If we don't know your physics then we can't tell you anything about your suns. – Tantalus' touch. Jan 24 at 18:02
• One interesting observation is that if your world is infinite in every direction and the suns fly by in single line, the livable area will be only inside infinite band under the suns, with infinite frozen land north and south from there. – michalsrb Jan 24 at 18:20
• Without defining how your universe works much more specifically it's impossible to give you a science-based answer. Perhaps you should consider removing the tag or perhaps exchanging it for science-fiction. – Tantalus' touch. Jan 24 at 18:47
• @Bitterdreggs. Anything not specified should be considered to work the same way. Is gravity itself required to know (for instance) how high and what size the sun is to provide enough light and warmth in such a scenario? – John O Jan 24 at 20:12

The apparent magnitude of the sun as seen from Earth is -26.75; when a celestial body with this brightness shines we consider it to be 'daytime'. Conversely when the full moon (magnitude -12.74) shines, we still consider it to be 'night time'; the sun is 400,000 times brighter than the full moon.

Since apparent magnitude follows an inverse square law with distance, this means that 12 hours after midday, the passing sun is at least 632 times further away than it was at perihelion; actually slightly more because there will be two moon-brightness objects in the sky (one advancing and one retreating). You can increase this ratio for a darker night.

We still don't have a fully-constrained problem in terms of working out the distance to the 'sun highway', but we can still put an upper bound by assuming that we still have the speed of light as a universal speed limit. If the maximum distance the suns can travel (relative to the observer) between midday and midnight is 12 light-hours, or 86.5 AU (about the diameter of the solar system out to the Kuiper Belt), then the maximum distance at perihelion is only about 20 million kilometers (0.14 AU), much less than the orbit of Mercury. In order to remain habitable, the suns need to be much more compact and cool to still provide a non-cooking amount of illumination.

At that distance, though, you could travel for hundreds of thousands of kilometers away from the 'equator' before any noticeable change in radiance, or even a perceptible change in the inclination of the suns. If you shrank the system by a factor of a hundred, though, so perihelion is at 200,000km (half the distance from the Earth to the Moon), and suns shot off (at $$\mathrm{3000\ km\ s^{-1}}$$) to a distance of 0.87AU, then you'd see a 1% change in brightness after the first thousand kilometers away from the equator. Working out what that would translate to in terms of climate and weather patterns on a flat world is a much more challenging question.

• Thank you. You've nailed this. – John O Jan 28 at 14:10

The inhabitants can calculate the height of the “star” by using simple trigonometry with people positioned at different points in its path and synchronized watches.

Knowing its height the size of the star can then be calculated by measuring its angular diameter and again using trigonometry or even simpler similar triangles.

It is impossible to say how close or far these stars could get. It would depend on the exact number, their frequency, temperature, speed, altitude, diameter, atmospheric properties and much else.

• The original poster stated that his world was within Euclidean space. I interpret that to mean we can assume distances, angles and measurment in general still work as we would expect. Otherwise the question makes no sense at all. – Slarty Jan 24 at 19:00
• Assume all geometry/trig works as it does in the real world. – John O Jan 24 at 20:17

Since Newtonian/Einsteinian physics clearly don't apply here, I see no reason these "stars" and "suns" couldn't be actual hydrogen-fusing stars, just flying across the (infinite?) flat world at a (handwaved) speed and (handwaved) density such that they provide the day and night cycles.

If they stars have the same population distribution as those in our universe, there will be many more of the smaller, cooler ones than there are of the very large, extremely hot ones, but since physics isn't involved here (maybe it's all magic?), there's nothing preventing these stars from flying at altitudes determined by their mass, such that their light and heat as seen at ground level is nearly constant from one to the next.

Of course, there's also no reason they need to be what we'd call stars. They could as easily be flying balls of combusting coal, chariots carrying various gods, or immense, cordless spotlights flying through the sky. Since you've thrown physics out the window, you can make up whatever seems good to you.