In this talk, I will present some results on fermion ground states of the relativistic Vlasov-Poisson system arising in the semiclassical limit from relativistic quantum theory of white dwarfs. I'd like to discuss the existence and orbital stability of fermion ground states of the three dimensional relativistic Vlasov-Poisson system for subcritical mass. We will also see that the mass density of such fermion ground states satisfies the Chandrasekhar equation for white dwarfs. This is a joint work with Prof. Juhi Jang at USC.