Up to now we assumed spherical symmetry of the gravitational field of the earth. However, earth is not a perfect sphere, and therefore its gravitational field does not have perfect spherical symmetry. With the lack of that symmetry, the trajectories of objects in the field are no longer ellipses, but at any given point very close to an elliptic trajectory. We will see that these trajectories can be very well approximated by by slowly moving ellipses.