The Christoffel numbers \(a_{\nu,n}^{(\lambda)G}\) for ultra-spherical weight functions \(w_{\lambda}(x)=(1-x^ 2)^{\lambda -1/2}\) are investigated. Using only elementary functions, the authors state new inequalities, monotonicity properties and asymptotic approximations, which improve several results. In particular, denoting by \(\theta^{(\lambda)}_{\nu,n}\) the trigonometric representation of the Gaussian nodes, the authors obtain for \(\lambda\in [0,1]\) the inequalities \[ \frac{\pi}{n+\lambda}\sin^{2\lambda}\theta^{(\lambda)}_{\nu,n}\{1- \frac{\lambda (1-\lambda)}{2(n+\lambda)^ 2\sin^ 2\theta^{(\lambda)}_{\nu,n}}\}\quad \leq \quad a_{\nu,n}^{(\lambda)G}\leq \frac{\pi}{n+\lambda}\sin^{2\lambda}\theta^{(\lambda)}_{\nu,n}, \] and similar results for \(\lambda\) \({\bar \in}(0,1)\). Furthermore, assuming that \(\theta^{(\lambda)}_{\nu,n}\) remains in a fixed interval, lying in the interior of (0,\(\pi\)), as \(n\to +\infty\) the authors for every fixed \(\lambda >-1/2\) obtain an asymptotic expansion for \(a_{\nu,n}^{(\lambda)G}\), which is too complicated to be cited here.