How large would a world have to be for a sailing ship to never make it past the horizon?

I have a sailing ship. It leaves port. As it goes away, it grows smaller and smaller. In our world, it eventually is hidden by the curvature of the Earth, such that the top mast stays visible longer. I want it to simply grow smaller and smaller and smaller, but (from the perspective of a human with a human lifespan of 100 years or so) "never" makes it past the horizon.

How big does my world have to be for that to happen?

Ignore the real-world problems such as normal planets that size turning into hydrogen-filled Jupiters, stars or black holes aspect of it. I'm going for a hollow Dyson world built (out of unobtanium of course, with tens of miles of rock, water and stuff piled on top) around a sufficiently massive object (say a star or a black hole) to give 1g gravitational acceleration at the (external facing) surface.

Edit: To preempt the question, yes, advanced optics are available, so the visual acuity of the human observer is not the issue here: as long it it can be reasonably detected and distinguished from the sea background using light, you can assume that it will. So no magic detectors, but imagine a high-performing scope, well built, but subject to the problems real optic instruments have -- air attenuation was pointed out in comments below. I'll assume the sails to be white, if that helps.

Later Edit: Since air attenuation might be a factor as pointed out in the comments, let's assume our ship is much like Santísima Trinidad: Galleon; Length: 51 m; 2,000 tons; Comp.: 400-800; Armament: 54 guns;

posted over 8 years ago

Serban Tanasa‭

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