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:

1,443 times 10 to the 9 take 149.6 times 10 to the 9 equals 1,293.9 times 10 to the 9 equals 1,293,600,000,000m

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

r over d equals tan θ; r equals d tan θ; r equals 1,293.9 times 10 to the 9 times tan of (194 over 3,600) equals 1.2169 times 10 to the 9 equals 1,216,900,000m

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

M equals 4 Pi squared r cubed over G T squared; M equals 4 Pi squared times 1.2169 times 10 to the 9 cubed over (1,377,638 squared times 6.67 times 10 to the minus 11 which equals 5.6 times 10 to the 26)