Considering that Saturn is roughly ten times farther from Sun than Earth is, how does the luminosity of Sun on Earth compare to the luminosity of Sun on Saturn?
Stated otherwise: what is the ratio of the luminosity of Sun from Earth vs Saturn?
What you really mean is the ratio of brightness of sun from Earth vs Saturn. Luminosity is the total energy output of a star per second. The energy emitted spreads in a spherical pattern, assuming the star to be a sphere. The area over which it spreads is directly proportional to the square of radius of the spread area. In other words, the energy spread is directly proportional to the square of the distance from the star and hence the brightness will also fall proportional to square of distance (since the same energy is now spread over larger area, brightness, as seen from a location, falls). Using this analogy, if Earth is at a distance D from Sun, Saturn is at 10D from Sun. Hence the brightness of Sun, as seen from Earth, would be 10^2 = 100 times more than when observed from Saturn. That is, the ratio of Sun's Brightness from Earth vs. Saturn is 100:1.
Hope this helps.