  Polytropic models play a very important role in galactic dynamics and in the
theory of stellar structure and evolution. However, in general, the solution of
the Lane-Emden equation can not be given analytically but only numerically. In
the Lane-Emden equation can not be given analytically but only numerically. In
this paper we give a very good and simple analytic approximate solution of the
Lane-Emden equation. This approximation is very good for any finite polytropic
index $n$ and for the isothermal case (n equals infinity) at a level $<1\%$. We
also give analytic expressions of the mass, pressure, temperature, and
potential energy as a function of radius.
