does the horizon on other, bigger planets (or suns) look the same as earth’s? How much higher do you have to go to see it curve?

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What happens with bigger planets or suns if you stand on them and look as far as you can? Does it look the same? A straight line, but much further away? So will you still be able to see objects hundreds of kilometres away because they’re before the curve? Thank you!!

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ELI5: If that planet has air and dust and fog like Earth does, it will look a lot like what you see here! But if the planet had NO air, and no trees or mountains were in the way, you could see really far!

The distance to the horizon scales with the size of the planet – the larger the planet, the further away the horizon is. Specifically, assuming a perfect sphere and a height much smaller than the radius of the planet, the distance to the horizon is sqrt(2 R h), where R is the radius of the planet and h is the height of the observer.

So for example, here on Earth (R = ~6000 km) a person (h = 1.5 m) can see about sqrt(2 * 6000 km * 1.5 m) = [a little over 4.2 km](https://www.wolframalpha.com/input?i=sqrt%282+*+6000+km+*+1.5+m%29) if the ground is perfectly flat.

On a world twice as large, doubling R would multiply this by about sqrt(2), for a distance of ~6 km.

Conveniently this formula works out so that multiplying the size of the planet has the same effect as multiplying your height. So the view on a planet twice as big would be the same as the view here on Earth if you were twice as tall, all else equal, over perfectly flat terrain, and ignoring atmospheric effects (and allowing for some tiny error since this formula is not quite exact).