The conjugate momenta (Pr, P. and px) are defined as follows: Pr = r Px = 12x cos?(4) where r is radial distance, 4 and A are angles, and t is time. These terms can be used to describe the motion of a satellite under Earth's gravitational potential, according to the following system of equations: dr dt = Pr dpr = + 72 73 + dt 73 cos2 (4) dip = Pp dt 72 dpp p sin(4) = dt 12 cos3 (4) dx Px = dt 12 cos? (4) where u is a constant and dim = 137-2. Note, you do not need to solve these equations or know how to obtain them to analyze their dimensions. (i) Obtain the dimensions of the three conjugate momenta. (ii) Show that the system of equations that describes the motion of a satellite is dimensionally homogeneous