As far as I know in the old days astronomers and now scientists/NASA know more or less what the earth's rotational speed is. I think they calculate this by observing the position of the sun in the sky during eclipses like a solar eclipse. They have been doing that for well over 2000 years. But the rotational rate isn't a pure constant. Our normal day/night is about 10 to 25 millionths of a second "slower" every year give or take. I know from some Googeling and a TV show that it will take 100 to 140 million years before we will get a 25 hour day. Now I will be long dead before that

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