This paper presents an approach for the probabilistic analysis of stability margins and pointing errors for a satellite system subject to parametric uncertainties. To analyze the influence of the uncertainties on the system performance, probabilistic approaches provide more convincing insights than worst-case methods. The classical approach uses Monte Carlo simulations which come with high computational effort. As an alternative, we apply non-intrusive Polynomial Chaos Expansion, which approximates a function of stochastic arguments as a series of orthogonal basis polynomials. To deal with a high-dimensional uncertainty space, sparse grid quadrature is employed to calculate the coefficients of the polynomial system. We show that Polynomial Chaos Expansion can replicate the results of Monte Carlo simulations with almost perfect accuracy, while requiring 20-30 times lower computation times. The non-intrusive approach also allows flexible evaluation of various quantities of interest, proving the applicability of this method in the industrial Verification and Validation process.