Only the positions along an axis through the equator of Jupiter are calculated. These 'X' coordinates are expressed in multiples of the radius of Jupiter. The results for two sets of hourly figures were compared with those produced by Manfred Dings Ephtool 2.0, and found to have a maximum error of 0.2 radii, typically better than 0.1 radii. Galileo saw the four moons in his newly constructed telescope, and described nightly observations of his 'Medicea sidera' for some days in his book Sidereus Nuncius . You can see the four 'Galilean' moons of Jupiter using almost any binoculars or small telescope.
Some people can see Callisto with the naked eye.
The recipe used here is adapted from Jan Meeus' book, Astronomical Alorithms . His 'lower precision' method is described in Chapters 42 and 43. The positions of the four Galilean moons are usually listed in ephemerides as a series of X and Y coordinates. The X coordinates tell you the positions of each moon along an axis through the equator of Jupiter. The Y coordinates tell you the displacement from this X axis, and are usually much smaller than the X coordinates.