alt Hacker NewsIf you're talking about intuitions, you have no firsthand intuitions about lifting effort decreasing with distance to the Earth. We can intuit about constant gravity, and the math of constant gravity works fine for this description.
And while the real situation at scale is more complicated, the math is going to come out to the same answer, albeit with extra terms muddying everything up.
If someone says that something true can be illustrated intuitively with a thought experiment, "sure, but what if we take that to a scale where our intuitions fail" is a sort of odd place to take the discussion unless you're genuinely curious how the math is going to shake out.
I’m not talking about intuitions; I’m talking against them. The intuition about carrying something 1st to 2nd then to 3rd floor is clearly wrong as evidenced by the example I gave; it is less wrong in smaller scales, but it still is wrong.
If the floors were as high as the radius of the Earth, the first one would be three times as hard as the second one. The math doesn’t come out the same. It’s not at all linear, it’s the inverse square; that’s much more than just _extra terms muddying things_.
Calling this relation linear by just looking at the intuitions of tiny humans is akin to hyper-zooming an exponential graph and calling it linear. It is “approximately true” locally, but hey, the same is also true for velocity vs kinetic energy!