Astronomical distances and timescales are dumb hueg. But one thing that always impressed me is how precise measurements can get in astronomy even without advanced tools.
E.g.: Mercury's orbit is elliptical, but the ellipse rotates around the Sun slowly (called perihelion precession). It does so by about 43 milliarcsec per century. That's less than a thousandth of a degree rotation of the ellipse, discovered centuries ago. Done by eye, without computers, and had no real explanation until early last century (general relativity).
