Approximate analytic solutions to the isothermal Lane-Emden equation

R. Iacono, M. De Felice

Research output: Contribution to journalArticle

5 Citations (Scopus)


We derive accurate analytic approximations to the solution of the isothermal Lane-Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of self-gravitating, isothermal fluid spheres. The solutions we obtain, using analytic arguments and rational approximations, have simple forms, and are accurate over a radial extent that is much larger than that covered by conventional series expansions around the origin. Our best approximation has a maximum error on density of 0.04 % at 10 core radii, and is still within 1 % from an accurate numerical solution at a radius three times larger. © 2014 Springer Science+Business Media Dordrecht.
Original languageEnglish
Pages (from-to)291 - 298
Number of pages8
JournalCelestial Mechanics and Dynamical Astronomy
Issue number3
Publication statusPublished - Mar 2014
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

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