1. A simple model for a gas giant planet assumes a "polytropic" equation of state, P = Kp, m5 s 2. This model yields the density profile sin(Tr/R) (r/R) where K is a parameter with units of kg p(r) = Pc (1) (2) where pe is the mass density at the center (r = 0) and R = TK/(2G) is the planet's outer radius. = 4rp(r)dr. Integrate dM (a) The mass in a shell of radius r and thickness dr is dM rom r = 0 to r = R to find the model's total mass M. (Hint: fx sin(kx) dx = sin(kx)/k x cos(kx)/k.) = 7.1 107 m and mass M = 1.90 107 kg, what are the (b) Given Jupiter's radius R corresponding values for K and pe? (Note: these values fit" the model to Jupiter.) (c) Using the values of K and pe you obtained, what central pressure Pc does this model predict