The possibilities of using artificial neural networks (ANN) to approximate and extrapolate the orbits of GNSS satellites (global navigation satellite systems) are explored. Numerical experiments are performed using radial basis function networks (RBFN), as they are trained quickly enough and convenient for working with a small amount of data. The results show that RBFN successfully handle both interpolation and short-term satellite orbit prediction (extrapolation) and have notable advantages over traditionally used polynomial methods both in terms of accuracy achieved, and the speed of calculations. In particular, it is possible to use a single neural network to interpolate (extrapolate) all components of the location, while the standard approach requires a separate polynomial for each satellite coordinate