To find Saturn's mass we need the time period and radius of an object orbiting it.

To find the radius of orbit we need to know how far away it is.

The Sun, Saturn and the Earth are in a straight line, so the distance from Earth to Saturn is the distance from the sun to Saturn take away the distance from Earth to the Sun:

Titan's orbit has an angular radius of 194 arcseconds, so now we know its distance we can calculate its real radius of orbit:

Now we know Titan's orbital radius and time period, we can calculate the mass of Saturn: