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I want to know if a planet with an atmosphere identical to that of Earth could be big enough so that from no point in the lower atmosphere it would be possible to appreciate the curvature in relation to the horizon.

Essentially, I want to know if it's possible to have a planet so big it appears flat even from the highermost point of the mesosphere? The mesopause I think it's what I'm thinking about, as the limit to my question.

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    $\begingroup$ Arguably, according to some, you can't see the curvature of this earth from any point either. It depends on your viewing equipment and pre-existing opinions. A more failsafe way is math. $\endgroup$
    – Plutian
    Feb 29 '20 at 23:22
  • $\begingroup$ How high is the 'lower atmosphere' on this big planet? $\endgroup$
    – user535733
    Feb 29 '20 at 23:36
  • $\begingroup$ My guess is that any planet that big would no longer be Earth-like. Do you just care about the pure geometry and the world can be handwaved, or does such a world need to form naturally? $\endgroup$
    – Zxyrra
    Mar 1 '20 at 0:35
  • $\begingroup$ @Zxyrra I care about the pure geometry of the problem. The world forming naturally I am not really concerned about, since it would eventually have to be so big as to end up becoming a gas giant or a star. So, hypothetically, if there weren't limits to a planet's maximum density and mass, I intuitively think it could reach a point in which curvature is no longer perceived at lower parts of said planet's atmosphere. I wanted to confirm if my intuition in said hypothetical was right. $\endgroup$
    – D3lf
    Mar 1 '20 at 3:26
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Impossible to not measure curvature, but possible to make it harder to see

The biggest planet detected so far is HAT-P67-b - being twice the diameter of Jupiter with a diameter of around 147000 km. It is this large only because its density is so low.

It is unfortunately a gas giant. Currently our planetary formation theories only support planets that large to be formed as gas giants. Any larger diameter, depending on density, would create a star instead as its inner core would be dense enough to enable fusion. A brown dwarf star can be formed in gas giants that are only slightly bigger than Jupiter.

You could argue Gas Giants do not have a 'horizon' in the same way rocky planets do, they are 'diffuse' and it would be difficult to perceive any radius as you are simply surrounded in gas.

However if restricting to rocky planets our radii are much smaller.

Kepler 10c is the largest rocky planet we have found, with a diameter 2.3 times Earth, about 29000km. This could be the very upper limit of a rocky planet. It's radius, being only twice as big as Earths, is much smaller than a gas giant, and you would still perceive the radius of this planet at a high enough altitude (or really mathematically at any altitude).

However - many things contribute to perceiving curvature. We can see curvature on an ocean at a height of only a few meters, by using a telescope to see a ship come over the horizon, but this is difficult to perceive on land because the irregularities in hills, mountains and surface features dilute the curvature such that we cannot perceive it readily. Perhaps this is a more realistic way to conceal curvature by making hard to perceive, rather than by size trying to make it large.

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  • $\begingroup$ Hey, thanks for the informative and elaborated response! I have a question regarding the last part. Would it be possible for a rocky planet to be large enough so that curvature cannot be perceived with the ship example, measuring from the surface of the ocean? Assume medieval technology (very rudimentary optics, spyglass level at best), so that telescopes aren't a problem. Thanks again! $\endgroup$
    – D3lf
    Mar 1 '20 at 3:14
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    $\begingroup$ @D3lf Actually, the radius of the planet would make a minimal impact on the ability to perceive the ship differently - in actual fact the disappearing of a ship over the horizon to prove the Earth was round was evident in Ptolemy's time (2000 years ago) before telescopes were invented 1500 years later. A tall ship with a square sail would be sufficient for the naked eye to perceive this curvature, as the hull disappears before (or emerges after) the sail. Another giveaway is the simple knowledge a mountain is not perceptible given sailing a certain distance away. Not possible unfortunately. $\endgroup$
    – flox
    Mar 1 '20 at 4:25
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Just make the planet foggy enough to never be able to see the horizon.
May work on planets with plenty of water, a strong magnetic field so that it maintains a thick atmosphere, and orbiting an energetic star (maybe a class A); the surface illumination is given by the fluorescence of the upper layers of atmosphere rather than direct star light.
Such a planet will likely be warm/tropical, with a small difference in temperature between day and night, so that is likely that the moisture in the atmosphere is always in the highest range.

Revisit Dagobah to get an idea.

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