Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polytropic gas spheres: An approximate analytic solution of the
  Lane-Emden equation   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.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio