In this paper we present a tool to study the non-linear propagation of uncertainties for orbits around the Earth. The tool we introduce is known as Jet Transport and allows to propagate full neighborhoods of initial states instead of a single initial state by means of usual numerical integrators. The description of the transported neighborhood is ob- tained in a semi-analytical way by means of polynomials in 6 variables. These variables correspond to displacements in the phase space from the reference point selected in an orbit as initial condition. The basis of the procedure is a standard numerical integrator of ordinary differential equations (such as a Runge-Kutta or a Taylor method) where the usual arithmetic is replaced by a polynomial arithmetic. In this way, the solution of the variational equations is also obtained up to high order. This methodology is applied to the propagation of satellite trajectories and to the computation of images of uncertainty ellipsoids including high order nonlinear descriptions. The procedure can be specially adapted to the determination of collision probabilities with catalogued space debris or for the end of life analysis of spacecraft in Medium Earth Orbits