Let $G$ be a real algebraic group defined over $\mathbb{Q}$, let $\Gamma$ be an arithmetic subgroup, and let $T$ be a maximal $\mathbb{R}$-split torus. We classify the closed orbits for the action of $T$ on $G/\Gamma,$ and show that they all admit a simple algebraic description. In particular we show that if $G$ is reductive, an orbit $Tx\Gamma$ is closed if and only if $x^{-1}Tx$ is defined over $\mathbb{Q}$, and is (totally) divergent if and only if $x^{-1}Tx$ is defined over $\mathbb{Q}$ and $\mathbb{Q}$-split. Our analysis also yields the following: there is a compact $K \subset G/\Gamma$ which intersects every $T$-orbit. If $\mathbb{Q} {\rm -rank}(G)<\mathbb{R}{\rm -rank}(G)$, there are no divergent orbits for $T$.