Many astrophysical systems can be approximated as isothermal spheres. In an isothermal sphere, the “foreground” objects can act as lenses on “background” objects in the same distribution. We study gravitational lensing by a singular isothermal sphere analytically. Our results may have interesting applications. PACS numbers: 98.62.Sb, 95.30.Sf Typeset using REVTEX 1

this article investigates the nonlinear, steady boundary layer flow and heat transfer of an incompressible eyring-powell non-newtonian fluid from an isothermal sphere with biot number effects. the transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference keller box technique. the influ...

We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5 core-radii and to 0.1% within 10 core-radii.

It is shown that the comment by Costa and Meneses [1] did not point any technical or conceptual flaw in our paper titled " Conservative Force Fields in the application of the nonextensive distribution to the historical problem of the unbounded isothermal atmosphere under constant gravity is theoretically correct. It should be stressed that our solution is somewhat connected with a similar solut...