On October 7, 2019, 20 new moons were discovered orbiting Saturn. This important discovery made Saturn the new “moon king" of our solar system, with the planet having 82 identified moons. Saturn has a mass of 5.683 x 10^26 kg. One of the new moons is currently named S5605a2. That moon has an orbital radius of approximately 1.6 x 10 7 km (be sure to convert). How many Earth days does it take for this new moon to orbit Saturn?​

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)