Non-integrability of the planar elliptic restricted three-body problem

We present the non-integrability proof for the planar elliptic restricted three-body problem. Two versions of this problem are considered: the classical one when only gravitational interactions are taken into account, and the photo-gravitational version where radiation pressure from the primaries is also included. Our result is valid for nonzero eccentricity and arbitrary mass ratio of the primaries. In the proof, we apply the differential Galois approach to study the integrability.