A mad scientist fires a rocket with mass m from the moon, vaguely in the direction of the Earth, which has mass M. Astronomers on Earth measure its distance r from the center of the Earth, its angular position in the plane passing through Earth's equator, and its angular position relative to Earth's pole. Part A) Neglecting the moon and all bodies other than the rocket and the Earth, write the Lagrangian for the rocket in spherical coordinates, accounting for Earth's gravitational pull. Part B) Using the Lagrange equations, write out differential equations of motion for r, 0, and o. You do not need to solve them. Part C) Describe the resulting differential equations. How does the acceleration in each direction related to the force on the system? How does this relate to concepts you've learned in previous classical mechanics courses?