Celestial Mechanics and Dynamical Astronomy

, Volume 118, Issue 3, pp 291–298 | Cite as

Approximate analytic solutions to the isothermal Lane–Emden equation

  • R. IaconoEmail author
  • M. De Felice
Original Article


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.


Isothermal Lane–Emden equation Bonnor–Ebert gas spheres  Padé approximants 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.ENEA, CR CasacciaRomeItaly

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