# Visibility of curvature on other planets and moons

On Earth, a curved horizon becomes more clearly visible at an altitude of about 40,000 feet (12 km). I wonder what altitude that would be on other spherical bodies of our system. I'd say that if you consider the size of a planet or moon relative to Earth, you could determine the altitude at which the planet's curvature becomes visible, am I right? Such as the Moon has 0.27 the size of the Earth, so the altitude at which a curved horizon becomes visible would be 10,800 feet, right?

Other celestial bodies would then be:

Mars has 0.53 the size of the Earth, therefore 21,200 feet

On Mercury 15,300 ft

On Venus 38,000 ft (the horizon probably wouldn't be visible due to Venus' thick cloudlayer)

On Io 11,500 ft

On Europa 10,000 ft

On Ganymede 16,600 ft

On Callisto 15,000 ft

On Titan 16,200 ft (however same case as Venus)

On Triton 8,600 ft

On Pluto 7,500 ft

The four gas planets have no clear surface.

The above values are approximations from using 40,000 feet for the Earth.

• Could you give some example for your very first statement? To me the horizon never looked more or less curved from a high altitude airplane compared to sea level. Commented Apr 5, 2020 at 12:39
• @asdfex You mean airliner cruise altitude (30-35,000 ft)? I too saw it a bit I think, but from 40,000 ft on, it looks curved more clearly but it's an approximation. Just search the net for "curvature visibility altitude" or something. At cruise altitude you see a curvature a bit if you try to recognize it. Flat Earthers on the other hand will still claim that there's no curvature. But at 40,000 ft or higher the curved horizon becomes more clearly visible (such as from a Concorde).
– user35272
Commented Apr 5, 2020 at 13:11
• Don't get me wrong, I just doubt the "becomes visible at 12km" part. There's nothing special about this altitude. The rest seems fine, you can just scale everything up and down by the radius and expect to see the same curvature. Things might be slightly different due to missing refraction when there is no atmosphere. Commented Apr 5, 2020 at 13:53
• @asdfex Your comment is actually the answer. You should replace your comment by an answer. The given altitude is one that is barely achieved by subsonic airliners but was achieved and trespassed by the Concorde which flew up to 60,000 ft high (but most of its path flew at around 50,000 ft or so). Concorde passengers could clearly see the Earth's curvature. So I set the border at around 40,000 ft.
– user35272
Commented Apr 5, 2020 at 14:20

Whether a straight line appears straight or curved is highly subjective. It depends on your expectations, and the part of your visual field the line is passing through. Straight lines passing through fixation (the center of the visual field) usually appear straight but if they pass through the peripheral field, there is a "fish eye" curve which few people are conscious of.

For instance, imagine you are standing in the middle of straight, flat railroad tracks, looking at the horizon at right angles to the tracks. The track just in front of your toes starts at the horizon past your left shoulder (at eye height). It curves down to your feet, then back up to the horizon (eye height again) past your right shoulder. The rail appears curved.

But if you look down at the rail, the line now goes through fixation and appears straight.

We reflexly fixate on anything we want to see, so we are unaware of the fish-eye curvature in our peripheral vision.

The information processing in our visual system assists in filtering out fish-eye curvature. Our brain constantly adjusts the image it presents to our consciousness so that the image complies with expectations. "The eye sees what the mind knows." That's why eye witnesses are notoriously unreliable.

So, perceiving the horizon as straight or curved has a significant subjective component. If you are expecting to see curvature (you first Concord flight) and your fixation point is below the horizon, I bet you'll perceive that subtle curve regardless of altitude.

• The human visual system is such a hodge-podge of tricks that you can "get used" to using a curved monitor and have to re-acclimate to using a flat monitor of the same approximate size. Commented Nov 21, 2022 at 0:57