My question is simple:

Given an algebraic group $G$ acting on a variety $X$ algebraically. If the orbits are of finite number then they form what is called an algebraic stratification of $X$.

Now my question is: **Is this (the stratification by $G$-orbits) also a Whitney Stratification?**

I think showing this by hand is quite painfull since the definition of a Whitney stratification is very unhandy.

I would appreciate any reference.