Consider a polytropic model for a star, in which so a star with Yp is an "n = = Yp P(r) = Kp(r) = Kp(r)1+1/n = = 4/3 5/3 is an "n 3/2 polytrope", and one with Yp 3 polytrope. (Here n is an index, not the number density.) The polytropic index p may or may not equal the adiabatic index (the ratio of specific heats), but Yp = in some cases, like fully degenerate or convective objects. 1. Use dimensional estimates for the star's pressure and density to show that K~ GM1-1/np/n1 Note: The equation is actually exact, if we write K = jnGM1-1/n R/n1 where jn is a function of n. Values of jn can be found in references on polytropic models for stars. You'll find the two values j3/2 = = 0.424 and j3 = 0.364 useful below.