It presents a mathematical model of the behaviour of polytropic gaseous stellar objects under the influence of their own gravity, known as the Lane-Emden equation.
He became associate professor of physics and meteorology at the Technical University of Munich (1907–1920)[2] and in 1907 published the classical work Gaskugeln: Anwendungen der mechanischen Wärmetheorie auf kosmologische und meteorologische probleme.
[4] Most of Emden's work related to thermodynamics applied to natural phenomena, while his published papers focused on geophysics and astrophysics.
[1] Emden's book Gaskugeln: Anwendungen der mechanischen Wärmetheorie auf kosmologische und meteorologische probleme presented a mathematical model to explain the expansion and compression of gas spheres.
[2] The Lane-Emden equations were later studied by Ralph H. Fowler who developed a new set of solutions for different values of n and for all types of boundary conditions.
They had six children of whom the names of five are known: Charlotte Schein; Emma Müller; Antonia Flach; Karl Emden, and Johanna Luise Berchtold-Emden.