I have a thought whilst in the shower this morning, it is usually said that shock waves only take part in star formation when other stars have formed and have exploded as supernova sending out a shock wave. Now I have been thinking, the usual equation for self gravitation is given by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{d^{2}r}{dt^{2}}=-\frac{Gm}{r^{2}}-\frac{1}{\rho}\frac{\partial p}{\partial r}

[/tex]

Upon writing [itex]v=dr/dt[/itex], it is possible to write the acceleration as:

[tex]

\frac{d^{2}r}{dt^{2}}=\frac{dv}{dt}=\frac{\partial v}{\partial t}+v\frac{\partial v}{\partial r}

[/tex]

So the equation becomes:

[tex]

\frac{\partial v}{\partial t}+v\frac{\partial v}{\partial r}=-\frac{Gm}{r^{2}}-\frac{1}{\rho}\frac{\partial p}{\partial r}

[/tex]

The above equation is a first order hyperbolic equation which allows the formation of shocks, in this case allows the possibility of converging shock waves from the mathematical standpoint at least.

Thoughts?

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# Formation of protostars

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