Let N = {O, n1, n2, n3} be the Earth-centered inertial (ECI) reference frame, with its origin at the center of the Earth. The Earth-centered Earth-fixed (ECEF) reference frame E = {O, e1, e2, e3} has the same origin, but the unit direction vectors are fixed in the Earth. The angle g is the angle between the two frames. In the diagram, refers to the latitude angle and refers to the longitude angle for a location O on the Earth's surface. For (a) and (b) below, derive the expression for the inertial velocity for an object at a general location O (which is stationary with respect to the Earth's surface) in terms of general r, , , g and possibly time derivatives of these. (a) Express your answer in terms of {n1, n2, n3} components. (b) Express your answer in terms of {e1, e2, e3} components. (c) Assume O is the SpaceX South Texas Launch Site ( = 25.9875, = 97.1864, r = R = 6378 km). Express the inertial velocity in terms of {e1, e2, e3} components and in units of km/s.E q u a t o r North Pole 1