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The periodic times (see Prob. 12.83) of the planet

The periodic times (see Prob. 12.83) of the planet Uranus’s moons Juliet and Titania have been observed to be 0.4931 days and 8.706 days, respectively. Knowing that the radius of Juliet’s orbit is 64 ×60 km, determine (a) the mass of Uranus, (b) the radius of Titania’s orbit.Prob. 12.83 A satellite is placed into a circular orbit about the planet Saturn at an altitude of 2100 mi. The satellite describes its orbit with a velocity of 54.7 × 103 mi/h. Knowing that the radius of the orbit about Saturn and the periodic time of Atlas, one of Saturn’s moons, are 85.54× 103 mi and 0.6017 days, respectively, determine (a) the radius of Saturn, (b) the mass of Saturn. (The periodic time of a satellite is the time it requires to complete one full revolution about the planet.)

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