The integrable cases of the three-body problem at third-order resonance under the oblateness of the central planet

In the present paper the general spatial and restricted elliptic spatial three-body problem at third-order resonance $j:(j+3)$ are analytically integrated by quadratures with the help of the Weierstrass functions, using an expansion of the disturbing function up to and including the third-degree terms in the eccentricities and in the inclinations.