The Loner droplet theory proposed that the Moon was part of a liquid and very hot primordial Earth. At some moment, the Moon was a droplet on the smface, rotating along with the Earth. LL? a) Assume that at that moment, the duration of a day was the same as nowadays, that is 24 hours (you'll see that most probably it wasn't). Calculate the angular speed. b) Calculate the moment of inertia of the whole system with respect to Earth's symmetry axis. Assume that both objects are perfect solid spheres {I = 2f5MR2) and use M E = 6.0 x 102'1 kg, MM = 7.4 x 1022, R5 = 6.4 x 105 m, RM = 1.7 x 105. {I-ljnt: The parallel axes theorem mayr be of help). c) Calculate the total angular momentum of the System. d) Eventually the Moon leaves the surface of the Earth and moves away. If the angular momentum is conserved, what will happen to the angular speed of the System? How will this affect the duration of a day? Explain