   ===Earth Precession===  From the vector diagram, using bold to denote vectors it follows that  :R = r1 + r , :r = R - r1 , and  : r = |R - r1| .  Squaring and then taking the square root,  : r =   Factoring out R. : r =   Since we are interested in the case in which r > 0, we can invert both sides to get