Question

3. Jupiter’s moon Callisto orbits the planet at a distance of 1.88x10⁹ m. Callisto’s orbital period about Jupiter is 16.7 days (in order to do that Callisto must have a velocity of 8,190 m/s). Use this to calculate the mass of Jupiter.

Answer 1

Kepler's Third law as modified by Newton's Laws will be useful here:
        P2 = a3/M
                Where P(years), a(AU), M(Solar Masses)
        By using the P and a of Callisto we can determine the mass 
        of Jupiter in Solar Masses.
        
        P = 16.7 days/(365.25 days/year) = 0.0457 years
                Gm = gigameter = million km.
        a = 1.88 Gm/150 Gm/AU = 0.0125 AU
        M = a3/P2 = (0.0125)3/(0.0457)2
        M(Jupiter) = 0.000935 = 1/1070 mass of Sun
                        = 2x1030 kg/1079 = 1.87x1027 kg