Given: G=6.67259 x 10^-11 N m^2/kg^2 Mimas, a moon of Saturn, has an orbital radius of 1.88 x 10^8 m and an orbital period of about 23.48 h.Use...

The Newton Kepler's Law of gravitation gives the relation of gravitational force and centrepetal force between planet and its satellite:

GMm/R^2 = mv^2/R^2 , where , M and m are the masses of planet and its satellite respectively. R is the distance between the centre of the planet and centre of its satellite and v is the velocity of the satellite.Replacing v by 2pR/T,( where T is the period of the satellite), we get M, the mass of the plannet:

M = (2P)^2* R^3/(G*T^2). ..........................(1)

By data, R = 1.88 x 10^8 m, distance between centres of Saturn and Mima .

G=6.67259 x 10^-11 N m^2 and

T = 23.48 hours = 23.48*60*60 seconds = 84528 seconds, is given to be the period of Mima, the moon of the Saturn.

Substituting the values in (1), we get:

M = 5.50221628*10^26 Kg is the estimated mass of the Saturn from this problem.