13.16 A planar model for a satellite orbiting around the earth can be modeled as r=r2r2GM+w=r2r where r is the distance of the satellite from the center of the earth, is the angular position of the satellite in its orbit, G=6.67421011m3/kg/s2 is the universal gravitational constant, M=5.981024kg is the mass of the earth, and w (0,106) is random noise due to space debris, atmospheric drag, outgassing, and so on. a) Write a state-space model for this system with x1=r,x2=r,x3=, and x4=. b) What must be equal to in order for the orbit to have a constant radius when w=0 ? c) Linearize the model around the point r=r0,r=0,=0T,=0. What are the eigenvalues of the system matrix for the linearized system when r0=6.57106m ? What would you estimate to be the largest