You are correct that a spherical approximation is not correct, and indeed generally won't be very good, especially in the disk of the Galaxy. In a rigorous cal

You are correct that a spherical approximation is not correct, and indeed generally won't be very good, especially in the disk of the Galaxy. In a rigorous calculation of the Galaxy's potential, astronomers usually use five components: 1. The bulge, which is represented by a spheroidal potential 2. The stellar disk, which is represented by two exponential potentials (one radial, the other vertical) 3. The interstellar medium, represented by a single exponential potential 4. A bar, which generally doesn't have a simple analytic representation, but can be represented by a series of ellipsoidal potentials 5. A dark matter halo, represented by a two-component power law. The orbits of stars require the existence of this component of the potential. Interestingly, the dark matter halo is quite spherically symmetric and comprises nearly all of the Galaxy's mass, so a spherical potential is more correct the further away you get from the center!