Navigation, world mapping and astrometry with Galileo's moons

Galileo realized that the four moons he discovered, besides supporting the heliocentric system, could also serve as a clock in the sky for longitude determination. Navigation at sea by this method did not prove practical but G. Cassini used it to improve land mapping. O. Romer discovered that the interval between eclipses of the moons by Jupiter increased or decreased according to whether the Earth moved away from or toward Jupiter. He attributed this to the finite speed of light which he in 1676 determined with an error of about 25%. Timings of the eclipses by Jupiter have served to compute accurate orbits of the moons, notably by means of R. A. Sampson's theory of 1921. Beginning in 1973, light curves of mutual eclipses and occultations between pairs of moons have been made regularly at six years intervals. From these observations very accurate radii and positions of the moons have been obtained.