We present the concept of a gravitational transport as an illustration to an introductory course of gravitation. Two points on the upper crust of the Earth, despite the technological difficulties involved, could be connected by a straight tunnel. A vehicle would go in free fall through this tunnel, using for that only the gravitational potential energy. This available energy is stored in the gravitational field due to the mass distribution of the Earth. The current calculations for this problem assume a uniform mass distribution. We present new calculations assuming more realistic non uniform mass distributions, obtained from experimental data. These improvements lead to relevant corrections, e.g., to the time elapsed in a travel between these two places on the Earth surface.