Alfie and Betty, two hedgehogs, are star-crossed lovers, standing on opposite sides of the Sun. In an effort to reach each other, they have drilled a hole through the diameter of the Sun. At the same time, Alfie and Betty step into the holes they have dug. Part A) Explicitly define a coordinate system for this problem and give the initial conditions (assuming they step into the hole at t = 0. Assume the sun has uniform density, a total mass Mo, and radius R, and that Alfie and Betty are pointlike and each have mass m and mB respectively. You may neflect collisions and the rotation of the sun. Write the gravitational potential energy felt by both hedgehogs as a function of their position.