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    Estimating distance on a Fractal World
    From: Frank Reed
    Date: 2019 Jan 13, 14:48 -0800

    A couple of days ago, the Chinese space agency released a video taken by Chang'e 4 as it landed on the far side of the Moon. At first the spacecraft is flying horizontally, in orbit but rapidly reducing its forward velocity. By about 0:40, you can see by looking at the distant craters that it is falling... By about 0:58, it is falling quickly, and the spacecraft then rotates to a vertical orientation to fire its rocket downward and land.

    From about 1:10 onward, there's an interesting navigational problem. And it's a problem that will surely lead to a CFIT accident in the future if anyone is flying visually (CFIT="controlled flight into terrain" and implies that a pilot has flown into the ground without realizing that anything was wrong until impact or moments before). As you watch the ground coming up to you, notice that it looks nearly the same at every altitude, and you can't really guess when the spacecraft is about to set down! In mathematical terms, the surface is "fractal". It is self-similar at all scales. Or in simpler terms, there are small craters on the big craters, and little craters on the small craters, and even on the little craters there are tiny craters. It looks more or less the same at every scale. Ten miles above the ground looks about the same as a mile above the ground. A mile above the ground looks nearly the same as 500 feet above the ground.

    Also, without an atmosphere, there is no extinction, no "blueing" of distant features. At every altitude, the surface appears crisp and sharp, as if it is right outside the window.

    If you ever visit the Moon, be sure to bring radar (or sat nav), or you'll probably fly right into the lunar surface...

    Frank Reed

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